This is my public collection. As much as possible, I will try to keep these backwards-compatible, so that all of your parameters will always render correctly in the future.
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}
;-------------------------------------------
; Quaternion/Hypercomplex math
;-------------------------------------------
Class QH {
import "common.ulb"
; Functions for Quaternion and Hypercomplex operations.
;
; For quaternions, multiplication is not commutative and division is always ; defined. ;
; For hypercomplex, multiplication is commutative and division is not always ; defined. The inverses which are not defined lieon two orthogonal ; 4D hyperplanes. ;
; The hypercomplex code is based upon the complex number methods of Clyde ; Davenport using his complex/complex model. ;
; H1 = [a1,a2]
;
; where a1 and a2 are both complex numbers. This is the method used in Fractint. ; a1 and a2 are converted to two new complex numbers: ;
; fa1 = a1 - conj(flip(a2))
; fa2 = a1 + conj(flip(a2))
;
; These new complex numbers (and correspondingly fb1 and fb2) can be used for ; ordinary complex math, including multiplication, division, trancendental ; functions, powers, etc. For example, sqrt: ;
; fa1 = sqrt(fa1)
; fa2 = sqrt(fa2)
;
; A second conversion is done at the end of the operation(s): ;
; c1 = 0.5*(fa1+fa2)
; c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
;
; H2 = [c1, c2]
; Operations for Spherical coordinates and 4D numbers added November 2009
; public:
; Quaternian multiplication
static func Qmul(Vector a, Vector b, Vector c)
; Q1*Q2 = [r1*r2 - V1.V2, r2*V1 + r1*V2 + V1xV2]
; calc V . V
float dot = a.m_y*b.m_y + a.m_z*b.m_z + a.m_w*b.m_w
; calc V x V
c.m_y = a.m_z*b.m_w - b.m_z*a.m_w
c.m_z = -(a.m_y*b.m_w - b.m_y*a.m_w)
c.m_w = a.m_y*b.m_z - b.m_y*a.m_z
c.m_x = a.m_x*b.m_x-dot
c.m_y = c.m_y + a.m_x*b.m_y + b.m_x*a.m_y
c.m_z = c.m_z + a.m_x*b.m_z + b.m_x*a.m_z
c.m_w = c.m_w + a.m_x*b.m_w + b.m_x*a.m_w
endfunc
; Quaternian division calculated as Q2*(1/Q1)
static func Qdiv(Vector a, Vector b, Vector c)
; 1/Q = [r, -V]/(r*r + V.V)
; then calculate Q2*(1/Q1) as for QMul
float denom = 1/(b.m_x*b.m_x + b.m_y*b.m_y + b.m_z*b.m_z + b.m_w*b.m_w)
; calc V . V
float dot = -(a.m_y*b.m_y + a.m_z*b.m_z + a.m_w*b.m_w)
; calc V x V
c.m_y = -a.m_z*b.m_w + b.m_z*a.m_w
c.m_z = a.m_y*b.m_w - b.m_y*a.m_w
c.m_w = -a.m_y*b.m_z + b.m_y*a.m_z
c.m_x = (a.m_x*b.m_x-dot)*denom
c.m_y = (c.m_y - a.m_x*b.m_y + b.m_x*a.m_y)*denom
c.m_z = (c.m_z - a.m_x*b.m_z + b.m_x*a.m_z)*denom
c.m_w = (c.m_w - a.m_x*b.m_w + b.m_x*a.m_w)*denom
endfunc
; Quaternian division calculated as 1/Q1)*Q2
static func Qdiv2(Vector a, Vector b, Vector c)
; 1/Q = [r, -V]/(r*r + V.V)
; then calculate (1/Q1)*Q2 as for QMul
float denom = 1/(b.m_x*b.m_x + b.m_y*b.m_y + b.m_z*b.m_z + b.m_w*b.m_w)
; calc V . V
float dot = -(a.m_y*b.m_y + a.m_z*b.m_z + a.m_w*b.m_w)
; calc V x V
c.m_y = -b.m_z*a.m_w + a.m_z*b.m_w
c.m_z = b.m_y*a.m_w - a.m_y*b.m_w
c.m_w = -b.m_y*a.m_z + a.m_y*b.m_z
c.m_x = (a.m_x*b.m_x-dot)*denom
c.m_y = (c.m_y + b.m_x*a.m_y - a.m_x*b.m_y)*denom
c.m_z = (c.m_z + b.m_x*a.m_z - a.m_x*b.m_z)*denom
c.m_w = (c.m_w + b.m_x*a.m_w - a.m_x*b.m_w)*denom
endfunc
; Quaternian square
static func Qsqr(Vector a, Vector b)
; Q*Q = [r*r-V.V, 2*r*V]
; calc V . V
float dot = a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w
if dot == 0
dot = 1e-100
endif
b.m_x = a.m_x*a.m_x-dot
b.m_y = 2*a.m_x*a.m_y
b.m_z = 2*a.m_x*a.m_z
b.m_w = 2*a.m_x*a.m_w
endfunc
; Quaternian square root
static func Qsqrt(Vector a, Vector b)
; derived from the inverse of the equations for Qsqr
; PLEASE NOTE!
; There are infinitely many square roots of any negative real number,
; which are all purely imaginary and equidistant from the origin; and,
; also, that negative real numbers are the only quaternions that have
; this property.
; As a simplification for this case, the quaternion of a real negative
; number will be treated as a complex number.
if a.m_x < 0 && a.m_y == 0 && a.m_z == 0 && a.m_w == 0
complex ir = a.m_x + flip(a.m_y)
ir = sqrt(ir)
b.init(real(ir),imag(ir),0,0)
else
float sdot = a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w
if sdot == 0
sdot = 1e-100
endif
b.m_x = sqrt((a.m_x + sqrt(a.m_x^2 + sdot))/2)
float factor = 1/(2*b.m_x)
b.m_y = a.m_y*factor
b.m_z = a.m_z*factor
b.m_w = a.m_w*factor
endif
endfunc
; Quaternian reciprocal or inverse
static func Qrecip(Vector a, Vector b)
; 1/Q = [r, -V]/(r*r + V.V)
float denom = 1/(a.m_x*a.m_x + a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
b.m_x = a.m_x*denom
b.m_y = -a.m_y*denom
b.m_z = -a.m_z*denom
b.m_w = -a.m_w*denom
endfunc
; Quaternian natural log
static func Qlog(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = log(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian exponential
static func Qexp(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = exp(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian power calculated as exp(ln(Q1)*Q2)
static func Qpower(Vector a, Vector b, Vector c)
; Q1^Q2 = exp(ln(Q1)*Q2)
; Find the log of Q1
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = log(z)
float at = imag(z)/norm
float x1 = real(z)
float y1 = at*a.m_y
float z1 = at*a.m_z
float w1 = at*a.m_w
; Multiply log by Q2
float dot = y1*b.m_y + z1*b.m_z + w1*b.m_w
; calc V x V
float y2 = z1*b.m_w - b.m_z*w1
float z2 = -(y1*b.m_w - b.m_y*w1)
float w2 = y1*b.m_z - b.m_y*z1
float x2 = x1*b.m_x-dot
y2 = y2 + x1*b.m_y + b.m_x*y1
z2 = z2 + x1*b.m_z + b.m_x*z1
w2 = w2 + x1*b.m_w + b.m_x*w1
; Take the exponential
norm = sqrt(y2*y2 + z2*z2 + w2*w2)
if norm == 0
norm = 1e-100
endif
z = x2 + flip(norm)
z = exp(z)
at = imag(z)/norm
c.m_x = real(z)
c.m_y = at*y2
c.m_z = at*z2
c.m_w = at*w2
endfunc
; Quaternian power calculated as exp(Q2*ln(Q1))
static func Qpower2(Vector a, Vector b, Vector c)
; Q1^Q2 = exp(Q2*ln(Q1))
; Find the log of Q1
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = log(z)
float at = imag(z)/norm
float x1 = real(z)
float y1 = at*a.m_y
float z1 = at*a.m_z
float w1 = at*a.m_w
; Multiply log by Q2
float dot = y1*b.m_y + z1*b.m_z + w1*b.m_w
; calc V x V
float y2 = -z1*b.m_w + b.m_z*w1
float z2 = (y1*b.m_w - b.m_y*w1)
float w2 = -y1*b.m_z + b.m_y*z1
float x2 = x1*b.m_x-dot
y2 = y2 + x1*b.m_y + b.m_x*y1
z2 = z2 + x1*b.m_z + b.m_x*z1
w2 = w2 + x1*b.m_w + b.m_x*w1
; Take the exponential
norm = sqrt(y2*y2 + z2*z2 + w2*w2)
if norm == 0
norm = 1e-100
endif
z = x2 + flip(norm)
z = exp(z)
at = imag(z)/norm
c.m_x = real(z)
c.m_y = at*y2
c.m_z = at*z2
c.m_w = at*w2
endfunc
; Quaternian sine
static func Qsin(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = sin(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian arcsine
static func Qasin(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = asin(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian cosine
static func Qcos(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = cos(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian arccosine
static func Qacos(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = acos(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian tangent
static func Qtan(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = tan(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian hyperbolic tangent
static func Qtanh(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = tanh(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian hyperbolic arctangent
static func Qatanh(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = atanh(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian arctangent
static func Qatan(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = atan(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian conjugate
static func Qconj(Vector a, Vector b)
; conj(Q) = [r,-V]
b.m_x = a.m_x
b.m_y = -a.m_y
b.m_z = -a.m_z
b.m_w = -a.m_w
endfunc
; Quaternian hyperbolic sine
static func Qsinh(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = sinh(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian hyperbolic cosine
static func Qcosh(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = cosh(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian hyperbolic arcsine
static func Qasinh(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = asinh(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian hyperbolic arccosine
static func Qacosh(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = acosh(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian cotangent
static func Qcotan(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = cotan(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Quaternian hyperbolic cotangent
static func Qcotanh(Vector a, Vector b)
float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
if norm == 0
norm = 1e-100
endif
complex z = a.m_x + flip(norm)
z = cotanh(z)
float at = imag(z)/norm
b.m_x = real(z)
b.m_y = at*a.m_y
b.m_z = at*a.m_z
b.m_w = at*a.m_w
endfunc
; Hypercomplex multiplication
static func Hmul(Vector a, Vector b, Vector c)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex b1 = b.m_x + flip(b.m_y)
complex b2 = b.m_z + flip(b.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
complex fb1 = b1 - conj(flip(b2))
complex fb2 = b1 + conj(flip(b2))
fa1 = fa1*fb1
fa2 = fa2*fb2
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
c.m_x = real(c1)
c.m_y = imag(c1)
c.m_z = real(c2)
c.m_w = imag(c2)
endfunc
; Hypercomplex division
static func Hdiv(Vector a, Vector b, Vector c)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex b1 = b.m_x + flip(b.m_y)
complex b2 = b.m_z + flip(b.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
complex fb1 = b1 - conj(flip(b2))
complex fb2 = b1 + conj(flip(b2))
fa1 = fa1/fb1
fa2 = fa2/fb2
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
c.m_x = real(c1)
c.m_y = imag(c1)
c.m_z = real(c2)
c.m_w = imag(c2)
endfunc
; Hypercomplex square
static func Hsqr(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = fa1*fa1
fa2 = fa2*fa2
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex square root
static func Hsqrt(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = sqrt(fa1)
fa2 = sqrt(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex reciprocal or inverse
static func Hrecip(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = 1/fa1
fa2 = 1/fa2
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex natural log
static func Hlog(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = log(fa1)
fa2 = log(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex exponential
static func Hexp(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = exp(fa1)
fa2 = exp(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex power
static func Hpower(Vector a, Vector b, Vector c)
; Q1^Q2 = exp(ln(Q1)*Q2)
;
; Find the log of Q1
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex b1 = b.m_x + flip(b.m_y)
complex b2 = b.m_z + flip(b.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
complex fb1 = b1 - conj(flip(b2))
complex fb2 = b1 + conj(flip(b2))
fa1 = log(fa1)
fa2 = log(fa2)
;
; Multiply log by Q2
fa1 = fa1*fb1
fa2 = fa2*fb2
;
; Take exponential
fa1 = exp(fa1)
fa2 = exp(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
c.m_x = real(c1)
c.m_y = imag(c1)
c.m_z = real(c2)
c.m_w = imag(c2)
endfunc
static func Hsin(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = sin(fa1)
fa2 = sin(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex cosine
static func Hcos(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = cos(fa1)
fa2 = cos(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex hyperbolic sine
static func Hsinh(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = sinh(fa1)
fa2 = sinh(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex hyperbolic cosine
static func Hcosh(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = cosh(fa1)
fa2 = cosh(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex conjugate
static func Hconj(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = conj(fa1)
fa2 = conj(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex tangent
static func Htan(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = tan(fa1)
fa2 = tan(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex arcsine
static func Hasin(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = asin(fa1)
fa2 = asin(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex arccosine
static func Hacos(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = acos(fa1)
fa2 = acos(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex arctangent
static func Hatan(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = atan(fa1)
fa2 = atan(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex hyperbolic tangent
static func Htanh(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = tanh(fa1)
fa2 = tanh(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex hyperbolic arcsine
static func Hasinh(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = asinh(fa1)
fa2 = asinh(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex hyperbolic arccosine
static func Hacosh(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = acosh(fa1)
fa2 = acosh(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex hyperbolic arctangent
static func Hatanh(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = atanh(fa1)
fa2 = atanh(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex cotangent
static func Hcotan(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = cotan(fa1)
fa2 = cotan(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
; Hypercomplex hyperbolic cotangent
static func Hcotanh(Vector a, Vector b)
complex a1 = a.m_x + flip(a.m_y)
complex a2 = a.m_z + flip(a.m_w)
complex fa1 = a1 - conj(flip(a2))
complex fa2 = a1 + conj(flip(a2))
fa1 = cotanh(fa1)
fa2 = cotanh(fa2)
c1 = 0.5*(fa1+fa2)
c2 = 0.5*(conj(flip(fa1)) - conj(flip(fa2)))
b.m_x = real(c1)
b.m_y = imag(c1)
b.m_z = real(c2)
b.m_w = imag(c2)
endfunc
default:
title = "Quat Hyper Methods"
int param v_quathyper
caption = "Version (Quat Hyper Methods)"
default = 100
hint = "This version parameter is used to detect when a change has been \
made to the formula that is incompatible with the previous version. \
When that happens, this field will reflect the old version number to \
alert you to the fact that an alternate rendering is being used."
visible = @v_quathyper < 100
endparam
}
;-------------------------------------------
; Misc 3D 4D Methods including mandelbulb and Msltoe 3D
;-------------------------------------------
Class MD {
$define debug
import "common.ulb"
; Spherical power
; Spherical complex representation for s = x + iy + jz
;
; r = x^2 + y^2 +z^2
; phi = atan2(x + iy) azimuth
; theta = atan2(cabs(x+iy) + iz) elevation
;
; x = r*cos(theta)*cos(phi)
; y = r*cos(theta)*sin(phi)
; z = r*sin(theta)
;
static func Spower(bool quadcor, bool altel, float power, Vector a, Vector b, float pfactor, int flagtype)
; Power function for s = x + iy + jz expressed in spherical coordinates
float r = 0
float phi = 0
float theta = 0
if flagtype == 6
if a.m_z* a.m_z < a.m_y* a.m_y
r = a.m_x*a.m_x+a.m_y*a.m_y+a.m_z*a.m_z+4*a.m_y*a.m_y*a.m_z*a.m_z
float r1 = sqrt(r)+1e-10
phi = atan2(a.m_x + flip(a.m_y))
theta = asin(a.m_z/r1)
else
r = a.m_x*a.m_x+a.m_y*a.m_y+a.m_z*a.m_z+4*a.m_y*a.m_y*a.m_z*a.m_z
float r1 = sqrt(r)+1e-10
theta = atan2(a.m_x + flip(a.m_z))
phi = asin(a.m_y/r1)
endif
endif
r = sqrt(a.m_x^2 + a.m_y^2 + a.m_z^2)+1e-10
if flagtype != 6
phi = atan2(a.m_x + flip(a.m_y)) ; azimuth
theta = 0
endif
float asa = 0
if flagtype ==0 || flagtype == 1
if altel
theta = asin(a.m_z/r)
else
theta = asin(-a.m_z/r)
endif
elseif flagtype == 9 || flagtype == 10\
|| flagtype == 11|| flagtype == 12|| flagtype == 13|| flagtype == 14\
|| flagtype == 15|| flagtype == 16|| flagtype == 17|| flagtype == 18\
|| flagtype == 19|| flagtype == 20|| flagtype == 21|| flagtype == 22\
|| flagtype == 23|| flagtype == 24|| flagtype == 25|| flagtype == 26\
|| flagtype == 27|| flagtype == 28|| flagtype == 29|| flagtype == 30\
|| flagtype == 31|| flagtype == 32|| flagtype == 33|| flagtype == 34\
|| flagtype == 35|| flagtype == 36|| flagtype == 37|| flagtype == 38\
|| flagtype == 39|| flagtype == 40|| flagtype == 41
phi = atan2(a.m_x + flip(a.m_z))
theta = asin(a.m_y/r)
elseif flagtype == 2
if altel
theta = acos(-a.m_z/r)
else
theta = acos(a.m_z/r)
endif
elseif flagtype == 7 || flagtype == 8
if altel
theta = acos(-a.m_y/r)
else
theta = acos(a.m_y/r)
endif
elseif flagtype == 3
if altel
theta = atan2(-a.m_x + flip(a.m_z))
else
theta = atan2(a.m_x + flip(a.m_z))
endif
endif
if flagtype == 42 || flagtype == 43 || flagtype == 44 || flagtype == 45\
|| flagtype == 46 || flagtype == 47 || flagtype == 48 || flagtype == 49\
|| flagtype == 50 || flagtype == 51 || (flagtype > 51 && flagtype <95)
if altel
theta = atan2(-a.m_x + flip(a.m_y))
else
theta = atan2(a.m_x + flip(a.m_y))
endif
phi = asin(a.m_z/r)
endif
if flagtype == 4 || flagtype == 5
phi = atan2(a.m_x + flip(a.m_y))
theta = asin(a.m_z/r)
endif
if flagtype == 7 || flagtype == 8
phi = atan2(a.m_x + flip(a.m_z))
theta = acos(a.m_y/r)
endif
r = r^power
phi = power*phi
theta = power*theta*pfactor
if flagtype ==0 || flagtype == 1
if quadcor
if theta > #pi/2
asa = sin(theta)
theta = asin(asa)
endif
if theta < -#pi/2
asa = sin(theta)
theta = asin(asa)
endif
endif
elseif flagtype == 2
if quadcor
if theta > #pi/2
asa = cos(theta)
theta = acos(asa)
endif
if theta < -#pi/2
asa = cos(theta)
theta = acos(asa)
endif
endif
elseif flagtype == 7 || flagtype == 8
if quadcor
if theta > #pi/2
asa = cos(theta)
theta = acos(asa)
endif
if theta < -#pi/2
asa = cos(theta)
theta = acos(asa)
endif
endif
elseif flagtype == 3
if quadcor
if theta > #pi/2
asa = tan(theta)
theta = atan(asa)
endif
if theta < -#pi/2
asa = tan(theta)
theta = atan(asa)
endif
endif
endif
if flagtype ==0 || flagtype == 1
b.m_x = r*cos(theta)*cos(phi)
b.m_y = r*cos(theta)*sin(phi)
if flagtype == 0
b.m_z = r*sin(theta)
elseif flagtype == 1
b.m_z = -r*sin(theta)
endif
elseif flagtype == 2
b.m_x = r*sin(theta)*sin(phi)
b.m_y = r*sin(theta)*cos(phi)
b.m_z = r*cos(theta)
elseif flagtype == 3
b.m_x = r*cos(theta)*cos(phi)
b.m_y = r*cos(theta)*sin(phi)
b.m_z = r*sin(theta)
elseif flagtype == 4 || flagtype == 5
b.m_x = r*cos(phi)*cos(theta)
b.m_z = r*cos(phi)*sin(theta)
if flagtype == 4
b.m_y = -r*sin(phi)
elseif flagtype == 5
b.m_y = r*sin(phi)
endif
elseif flagtype == 6
if a.m_z* a.m_z < a.m_y* a.m_y
b.m_x = r*cos(theta)*cos(phi)
b.m_y = r*sin(phi)*cos(theta)
b.m_z = -r*sin(theta)
else
b.m_x = r*cos(theta)*cos(phi)
b.m_y = -r*sin(theta)
b.m_z = r*sin(phi)*cos(theta)
endif
elseif flagtype == 7
b.m_x = r*sin(theta)*sin(phi)
b.m_y = r*cos(theta)
b.m_z = r*sin(theta)*cos(phi)
elseif flagtype == 8
b.m_x = r*sin(theta)*sin(phi)
b.m_y = -r*cos(theta)
b.m_z = r*sin(theta)*cos(phi)
elseif flagtype == 9
b.m_x = r*sin(theta)
b.m_y = -r*sin(phi)*cos(theta)
b.m_z = r*cos(theta)*cos(phi)
elseif flagtype == 10
b.m_x = -r*sin(theta)
b.m_y = r*cos(phi)*cos(theta)
b.m_z = r*cos(theta)*sin(phi)
elseif flagtype == 11
b.m_x = r*cos(theta)
b.m_y = -r*sin(phi)*sin(theta)
b.m_z = r*cos(phi)*sin(theta )
elseif flagtype == 12
b.m_x = r*cos(theta)
b.m_y = -r*sin(phi)*sin(theta)
b.m_z = -r*cos(phi)*sin(theta )
elseif flagtype == 13
b.m_x = -r*sin(theta)
b.m_y = -r*sin(phi)*cos(theta)
b.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 14
b.m_x = r*sin(theta)
b.m_y = r*sin(phi)*cos(theta)
b.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 15
b.m_x = -r*sin(theta)
b.m_y = r*sin(phi)*cos(theta)
b.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 16
b.m_x = r*sin(phi)*cos(theta)
b.m_y = -r*sin(theta)
b.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 17
b.m_x = -r*sin(phi)*sin(theta)
b.m_y = r*cos(theta)
b.m_z = -r*cos(phi)*sin(theta)
elseif flagtype == 18
b.m_x = -r*sin(phi)*sin(theta)
b.m_y = r*cos(theta)
b.m_z = r*cos(phi)*sin(theta)
elseif flagtype == 19
b.m_x = r*sin(phi)*cos(theta)
b.m_y = r*sin(theta)
b.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 20
b.m_x = -r*sin(phi)*cos(theta)
b.m_y = -r*sin(theta)
b.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 21
b.m_x = -r*sin(phi)*cos(theta)
b.m_y = r*sin(theta)
b.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 22
b.m_x = r*sin(phi)*sin(theta)
b.m_y = -r*cos(phi)*sin(theta)
b.m_z = r*cos(theta)
elseif flagtype == 23
b.m_x = -r*sin(phi)*cos(theta)
b.m_y = r*cos(phi)*cos(theta)
b.m_z = -r*sin(theta)
elseif flagtype == 24
b.m_x = r*sin(phi)*cos(theta)
b.m_y = r*cos(phi)*cos(theta)
b.m_z = r*sin(theta)
elseif flagtype == 25
b.m_x = -r*sin(phi)*sin(theta)
b.m_y = r*cos(phi)*sin(theta)
b.m_z = r*cos(theta)
elseif flagtype == 26
b.m_x = -r*sin(phi)*sin(theta)
b.m_y = -r*cos(phi)*sin(theta)
b.m_z = r*cos(theta)
elseif flagtype == 27
b.m_x = -r*sin(phi)*sin(theta)
b.m_y = r*cos(phi)*sin(theta)
b.m_z = r*cos(theta)
elseif flagtype == 28
b.m_x = r*cos(theta)
b.m_y = -r*cos(phi)*sin(theta)
b.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 29
b.m_x = r*cos(theta)
b.m_y = r*cos(phi)*sin(theta)
b.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 30
b.m_x = r*sin(theta)
b.m_y = r*cos(phi)*cos(theta)
b.m_z = r*sin(phi)*cos(theta)
elseif flagtype == 31
b.m_x = -r*sin(theta)
b.m_y = r*cos(phi)*cos(theta)
b.m_z = -r*sin(phi)*cos(theta)
elseif flagtype == 32
b.m_x = r*sin(theta)
b.m_y = r*cos(phi)*cos(theta)
b.m_z = -r*sin(phi)*cos(theta)
elseif flagtype == 33
b.m_x = -r*cos(phi)*sin(theta)
b.m_y = r*cos(theta)
b.m_z = r*sin(phi)*sin(theta)
elseif flagtype == 34
b.m_x = r*cos(phi)*cos(theta)
b.m_y = -r*sin(theta)
b.m_z = -r*sin(phi)*cos(theta)
elseif flagtype == 35
b.m_x = r*cos(phi)*cos(theta)
b.m_y = r*sin(theta)
b.m_z = r*sin(phi)*cos(theta)
elseif flagtype == 36
b.m_x = r*cos(phi)*sin(theta)
b.m_y = r*cos(theta)
b.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 37
b.m_x = -r*cos(phi)*sin(theta)
b.m_y = r*cos(theta)
b.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 38
b.m_x = r*cos(phi)*sin(theta)
b.m_y = r*cos(theta)
b.m_z = r*sin(phi)*sin(theta)
elseif flagtype == 39
b.m_x = r*cos(phi)*cos(theta)
b.m_y = -r*sin(phi)*cos(theta)
b.m_z = -r*sin(theta)
elseif flagtype == 40
b.m_x = r*cos(phi)*cos(theta)
b.m_y = -r*sin(phi)*cos(theta)
b.m_z = r*sin(theta)
elseif flagtype == 41
b.m_x = r*cos(phi)*sin(theta)
b.m_y = -r*sin(phi)*sin(theta)
b.m_z = r*cos(theta)
elseif flagtype == 42
b.m_x = r*cos(theta)
b.m_y = r*cos(phi)
b.m_z = r*sin(theta)
elseif flagtype == 43
b.m_x = r*cos(theta)
b.m_y = -r*cos(phi)
b.m_z = r*sin(theta)
elseif flagtype == 44
b.m_x = r*cos(theta)
b.m_y = -r*cos(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 45
b.m_x = r*cos(theta)
b.m_y = r*sin(theta)
b.m_z = r*cos(phi)
elseif flagtype == 46
b.m_x = r*cos(theta)
b.m_y = r*sin(phi)
b.m_z = r*cos(phi)
elseif flagtype == 47
b.m_x = r*cos(theta)
b.m_y = -r*sin(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 48
b.m_x = -r*cos(theta)
b.m_y = r*cos(phi)
b.m_z = r*sin(theta)
elseif flagtype == 49
b.m_x = -r*cos(theta)
b.m_y = r*cos(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 50
b.m_x = -r*cos(theta)
b.m_y = r*cos(phi)
b.m_z = r*sin(phi)
elseif flagtype == 51
b.m_x = -r*cos(theta)
b.m_y = r*cos(phi)
b.m_z = -r*sin(phi)
elseif flagtype == 52
b.m_x = r*cos(theta)
b.m_y = r*sin(phi)
b.m_z = r*sin(theta)
elseif flagtype == 53
b.m_x = r*cos(theta)
b.m_y = r*sin(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 54
b.m_x = -r*cos(theta)
b.m_y = -r*cos(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 55
b.m_x = -r*cos(theta)
b.m_y = -r*cos(phi)
b.m_z = -r*sin(phi)
elseif flagtype == 56
b.m_x = -r*cos(theta)
b.m_y = r*sin(theta)
b.m_z = r*cos(phi)
elseif flagtype == 57
b.m_x = -r*cos(theta)
b.m_y = r*sin(phi)
b.m_z = r*cos(phi)
elseif flagtype == 58
b.m_x = -r*cos(theta)
b.m_y = r*sin(phi)
b.m_z = r*sin(theta)
elseif flagtype == 59
b.m_x = -r*cos(theta)
b.m_y = r*sin(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 60
b.m_x = -r*cos(theta)
b.m_y = -r*sin(phi)
b.m_z = r*cos(phi)
elseif flagtype == 61
b.m_x = -r*cos(theta)
b.m_y = -r*sin(phi)
b.m_z = -r*cos(phi)
elseif flagtype == 62
b.m_x = -r*cos(theta)
b.m_y = -r*sin(phi)
b.m_z = r*sin(theta)
elseif flagtype == 63
b.m_x = -r*cos(theta)
b.m_y = -r*sin(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 64
b.m_x = r*cos(phi)
b.m_y = r*sin(phi)
b.m_z = r*cos(theta)
elseif flagtype == 65
b.m_x = r*cos(phi)
b.m_y = r*sin(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 66
b.m_x = r*cos(phi)
b.m_y = r*sin(phi)
b.m_z = r*sin(theta)
elseif flagtype == 67
b.m_x = r*cos(phi)
b.m_y = -r*sin(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 68
b.m_x = -r*cos(phi)
b.m_y = r*sin(phi)
b.m_z = r*cos(theta)
elseif flagtype == 69
b.m_x = -r*cos(phi)
b.m_y = r*sin(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 70
b.m_x = -r*cos(phi)
b.m_y = r*sin(phi)
b.m_z = r*sin(theta)
elseif flagtype == 71
b.m_x = -r*cos(phi)
b.m_y = r*sin(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 72
b.m_x = -r*cos(phi)
b.m_y = -r*sin(phi)
b.m_z = r*cos(theta)
elseif flagtype == 73
b.m_x = -r*cos(phi)
b.m_y = -r*sin(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 74
b.m_x = -r*cos(phi)
b.m_y = -r*sin(phi)
b.m_z = r*sin(theta)
elseif flagtype == 75
b.m_x = -r*cos(phi)
b.m_y = -r*sin(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 76
b.m_x = r*sin(theta)
b.m_y = -r*cos(theta)
b.m_z = r*sin(phi)
elseif flagtype == 77
b.m_x = r*sin(theta)
b.m_y = r*cos(phi)
b.m_z = r*cos(theta)
elseif flagtype == 78
b.m_x = r*sin(theta)
b.m_y = r*sin(phi)
b.m_z = r*cos(theta)
elseif flagtype == 79
b.m_x = r*sin(theta)
b.m_y = r*sin(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 80
b.m_x = r*sin(theta)
b.m_y = r*sin(phi)
b.m_z = r*cos(phi)
elseif flagtype == 81
b.m_x = -r*sin(theta)
b.m_y = r*cos(theta)
b.m_z = r*cos(phi)
elseif flagtype == 82
b.m_x = -r*sin(theta)
b.m_y = r*cos(phi)
b.m_z = r*sin(phi)
elseif flagtype == 83
b.m_x = -r*sin(theta)
b.m_y = -r*cos(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 84
b.m_x = -r*sin(theta)
b.m_y = r*sin(phi)
b.m_z = r*cos(theta)
elseif flagtype == 85
b.m_x = -r*sin(theta)
b.m_y = r*sin(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 86
b.m_x = -r*sin(theta)
b.m_y = -r*sin(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 87
b.m_x = -r*sin(theta)
b.m_y = -r*sin(phi)
b.m_z = r*cos(phi)
elseif flagtype == 88
b.m_x = r*sin(phi)
b.m_y = -r*cos(phi)
b.m_z = r*sin(theta)
elseif flagtype == 89
b.m_x = r*sin(phi)
b.m_y = -r*cos(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 90
b.m_x = -r*sin(phi)
b.m_y = r*cos(phi)
b.m_z = r*cos(theta)
elseif flagtype == 91
b.m_x = -r*sin(phi)
b.m_y = r*cos(phi)
b.m_z = -r*cos(theta)
elseif flagtype == 92
b.m_x = r*sin(phi)
b.m_y = r*cos(phi)
b.m_z = r*sin(theta)
elseif flagtype == 93
b.m_x = -r*sin(phi)
b.m_y = r*cos(phi)
b.m_z = -r*sin(theta)
elseif flagtype == 94
b.m_x = -r*sin(phi)
b.m_y = -r*cos(phi)
b.m_z = -r*cos(theta)
endif
b.m_w = 0
endfunc
; r = x^2 + y^2 +z^2
; theta = acos(a.m_z/r) elevation
; phi = atan2(x + iy) azimuth
; theta = theta*power;
; b.m_x = r*sin(theta)*cos(phi)
; b.m_y = r*sin(theta)*sin(phi)
; b.m_z = r*cos(theta)
; b.m_w = 0
; theta = acos(b.m_z/r) elevation
; phi = atan2(b.m_x + ib.m_y) azimuth
; phi = phi*power;
; r = r^power
; b.m_x = r*sin(theta)*cos(phi)
; b.m_y = r*sin(theta)*sin(phi)
; b.m_z = r*cos(theta)
; b.m_w = 0
static func Spower2(float power, Vector a, Vector b)
; Alternate Power function for s = x + iy + jz expressed in spherical coordinates
float r = sqrt(a.m_x^2 + a.m_y^2 + a.m_z^2)+1e-10
float phi = atan2(a.m_x + flip(a.m_y)) ; azimuth
float theta = acos(a.m_z/r)
theta = power*theta
b.m_x = r*sin(theta)*cos(phi)
b.m_y = r*sin(theta)*sin(phi)
b.m_z = r*cos(theta)
b.m_w = 0
theta = acos(b.m_z/r); elevation
phi = atan2(b.m_x + flip(b.m_y)) ; azimuth
phi = phi*power;
r = r^power
b.m_x = r*sin(theta)*cos(phi)
b.m_y = r*sin(theta)*sin(phi)
b.m_z = r*cos(theta)
b.m_w = 0
endfunc
static func SMult(bool quadcor,bool altel, Vector a, Vector b, Vector c, float pfactor, int flagtype)
float ra = 0
float rb = 0
float r = 0
float phia = 0
float phib = 0
float thetaa = 0
float thetab = 0
if flagtype == 6
if a.m_z* a.m_z < a.m_y* a.m_y
r = a.m_x*a.m_x+a.m_y*a.m_y+a.m_z*a.m_z+4*a.m_y*a.m_y*a.m_z*a.m_z
float r1 = sqrt(r)+1e-10
phia = atan2(a.m_x + flip(a.m_y))
thetaa = asin(a.m_z/r1)
else
r = a.m_x*a.m_x+a.m_y*a.m_y+a.m_z*a.m_z+4*a.m_y*a.m_y*a.m_z*a.m_z
float r1 = sqrt(r)+1e-10
thetaa = atan2(a.m_x + flip(a.m_z))
phia = asin(a.m_y/r1)
endif
if b.m_z* b.m_z < b.m_y* b.m_y
r = b.m_x*b.m_x+b.m_y*b.m_y+b.m_z*b.m_z+4*b.m_y*b.m_y*b.m_z*b.m_z
float r1 = sqrt(r)+1e-10
phib = atan2(b.m_x + flip(b.m_y))
thetab = asin(b.m_z/r1)
else
r = b.m_x*b.m_x+b.m_y*b.m_y+b.m_z*b.m_z+4*b.m_y*b.m_y*b.m_z*b.m_z
float r1 = sqrt(r)+1e-10
thetab = atan2(b.m_x + flip(b.m_z))
phib = asin(b.m_y/r1)
endif
endif
ra = sqrt(a.m_x^2 + a.m_y^2 + a.m_z^2)+1e-10
rb = sqrt(b.m_x^2 + b.m_y^2 + b.m_z^2)+1e-10
if flagtype != 6
float phia = atan2(a.m_x + flip(a.m_y)) ; azimuth
float thetaa = 0
endif
if flagtype == 7 || flagtype == 8
phia = atan2(a.m_x + flip(a.m_z))
thetaa = acos(a.m_y/ra)
endif
float asa = 0
if flagtype ==0 || flagtype == 1
if altel
thetaa = asin(a.m_z/ra)
else
thetaa = asin(-a.m_z/ra)
endif
elseif flagtype == 9 || flagtype == 10\
|| flagtype == 11|| flagtype == 12|| flagtype == 13|| flagtype == 14\
|| flagtype == 15|| flagtype == 16|| flagtype == 17|| flagtype == 18\
|| flagtype == 19|| flagtype == 20|| flagtype == 21|| flagtype == 22\
|| flagtype == 23|| flagtype == 24|| flagtype == 25|| flagtype == 26\
|| flagtype == 27|| flagtype == 28|| flagtype == 29|| flagtype == 30\
|| flagtype == 31|| flagtype == 32|| flagtype == 33|| flagtype == 34\
|| flagtype == 35|| flagtype == 36|| flagtype == 37|| flagtype == 38\
|| flagtype == 39|| flagtype == 40|| flagtype == 41
phia = atan2(a.m_x + flip(a.m_z))
thetaa = asin(a.m_y/ra)
elseif flagtype == 2
if altel
thetaa = acos(-a.m_z/ra)
else
thetaa = acos(a.m_z/ra)
endif
elseif flagtype == 7 || flagtype == 8
if altel
thetaa = acos(-a.m_y/ra)
else
thetaa = acos(a.m_y/ra)
endif
elseif flagtype == 3
if altel
thetaa = atan2(-a.m_x + flip(a.m_z))
else
thetaa = atan2(a.m_x + flip(a.m_z))
endif
endif
if flagtype == 42 || flagtype == 43 || flagtype == 44 || flagtype == 45\
|| flagtype == 46 || flagtype == 47|| flagtype == 48 || flagtype == 49\
|| flagtype == 50 || flagtype == 51 ||(flagtype > 51 && flagtype <95)
if altel
thetaa = atan2(-a.m_x + flip(a.m_y))
else
thetaa = atan2(a.m_x + flip(a.m_y))
endif
phia = asin(a.m_z/ra)
endif
if flagtype != 6
float phib = atan2(b.m_x + flip(b.m_y)) ; azimuth
float thetab = 0
endif
if flagtype == 7 || flagtype == 8
phib = atan2(b.m_x + flip(b.m_z))
thetab = acos(b.m_y/rb)
endif
if flagtype ==0 || flagtype == 1
if altel
thetab = asin(b.m_z/rb)
else
thetab = asin(-b.m_z/rb)
endif
elseif flagtype == 9 || flagtype == 10\
|| flagtype == 11|| flagtype == 12|| flagtype == 13|| flagtype == 14\
|| flagtype == 15|| flagtype == 16|| flagtype == 17|| flagtype == 18\
|| flagtype == 19|| flagtype == 20|| flagtype == 21|| flagtype == 22\
|| flagtype == 23|| flagtype == 24|| flagtype == 25|| flagtype == 26\
|| flagtype == 27|| flagtype == 28|| flagtype == 29|| flagtype == 30\
|| flagtype == 31|| flagtype == 32|| flagtype == 33|| flagtype == 34\
|| flagtype == 35|| flagtype == 36|| flagtype == 37|| flagtype == 38\
|| flagtype == 39|| flagtype == 40|| flagtype == 41
phib = atan2(b.m_x + flip(b.m_z))
thetab = asin(b.m_y/rb)
elseif flagtype == 2
if altel
thetab = acos(-b.m_z/rb)
else
thetab = acos(b.m_z/rb)
endif
elseif flagtype == 7 || flagtype == 8
if altel
thetab = acos(-b.m_y/rb)
else
thetab = acos(b.m_y/rb)
endif
elseif flagtype == 3
if altel
thetab = atan2(-b.m_x + flip(b.m_z))
else
thetab = atan2(b.m_x + flip(b.m_z))
endif
endif
if flagtype == 42 || flagtype == 43 || flagtype == 44 || flagtype == 45\
|| flagtype == 46 || flagtype == 47|| flagtype == 48 || flagtype == 49\
|| flagtype == 50 || flagtype == 51 ||(flagtype > 51 && flagtype <95)
if altel
thetab = atan2(-b.m_x + flip(b.m_y))
else
thetab = atan2(b.m_x + flip(b.m_y))
endif
phib = asin(b.m_z/rb)
endif
if flagtype == 4 || flagtype == 5
phia = atan2(a.m_x + flip(a.m_y))
phib = atan2(b.m_x + flip(b.m_y))
thetaa = asin(a.m_z/ra)
thetab = asin(b.m_z/rb)
endif
float r = ra*rb
float phi = phia + phib
float theta = (thetaa + thetab)*pfactor
if flagtype ==0 || flagtype == 1
if quadcor
if theta > #pi/2
asa = sin(theta)
theta = asin(asa)
endif
if theta < -#pi/2
asa = sin(theta)
theta = asin(asa)
endif
endif
elseif flagtype == 2
if quadcor
if theta > #pi/2
asa = cos(theta)
theta = acos(asa)
endif
if theta < -#pi/2
asa = cos(theta)
theta = acos(asa)
endif
endif
elseif flagtype == 3
if quadcor
if theta > #pi/2
asa = tan(theta)
theta = atan(asa)
endif
if theta < -#pi/2
asa = tan(theta)
theta = atan(asa)
endif
endif
elseif flagtype == 7 || flagtype == 8
if quadcor
if theta > #pi/2
asa = tan(theta)
theta = atan(asa)
endif
if theta < -#pi/2
asa = tan(theta)
theta = atan(asa)
endif
endif
endif
if flagtype ==0 || flagtype == 1
c.m_x = r*cos(theta)*cos(phi)
c.m_y = r*cos(theta)*sin(phi)
if flagtype == 0
c.m_z = r*sin(theta)
elseif flagtype == 1
c.m_z = -r*sin(theta)
endif
elseif flagtype == 2
c.m_x = r*sin(theta)*sin(phi)
c.m_y = r*sin(theta)*cos(phi)
c.m_z = r*cos(theta)
elseif flagtype == 3
c.m_x = r*cos(theta)*cos(phi)
c.m_y = r*cos(theta)*sin(phi)
c.m_z = r*sin(theta)
elseif flagtype == 4 || flagtype == 5
c.m_x = r*cos(phi)*cos(theta)
c.m_z = r*cos(phi)*sin(theta)
if flagtype == 4
c.m_y = -r*sin(phi)
elseif flagtype == 5
c.m_y = r*sin(phi)
endif
elseif flagtype == 6
if a.m_z* a.m_z < a.m_y* a.m_y
c.m_x = r*cos(theta)*cos(phi)
c.m_y = r*sin(phi)*cos(theta)
c.m_z = -r*sin(theta)
else
c.m_x = r*cos(theta)*cos(phi)
c.m_y = -r*sin(theta)
c.m_z = r*sin(phi)*cos(theta)
endif
elseif flagtype == 7
c.m_x = r*sin(theta)*sin(phi)
c.m_y = r*cos(theta)
c.m_z = r*sin(theta)*cos(phi)
elseif flagtype == 8
c.m_x = r*sin(theta)*sin(phi)
c.m_y = r*cos(theta)
c.m_z = r*sin(theta)*cos(phi)
elseif flagtype == 9
c.m_x = r*sin(theta)
c.m_y = -r*sin(phi)*cos(theta)
c.m_z = r*cos(theta)*cos(phi)
elseif flagtype == 10
c.m_x = -r*sin(theta)
c.m_y = r*cos(phi)*cos(theta)
c.m_z = r*cos(theta)*sin(phi)
elseif flagtype == 11
c.m_x = r*cos(theta)
c.m_y = -r*sin(phi)*sin(theta)
c.m_z = r*cos(phi)*sin(theta )
elseif flagtype == 12
c.m_x = r*cos(theta)
c.m_y = -r*sin(phi)*sin(theta)
c.m_z = -r*cos(phi)*sin(theta )
elseif flagtype == 13
c.m_x = -r*sin(theta)
c.m_y = -r*sin(phi)*cos(theta)
c.m_z = -r*cos(phi)*cos(theta)
elseif flagtype == 14
c.m_x = r*sin(theta)
c.m_y = r*sin(phi)*cos(theta)
c.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 15
c.m_x = -r*sin(theta)
c.m_y = r*sin(phi)*cos(theta)
c.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 16
c.m_x = r*sin(phi)*cos(theta)
c.m_y = -r*sin(theta)
c.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 17
c.m_x = -r*sin(phi)*sin(theta)
c.m_y = r*cos(theta)
c.m_z = -r*cos(phi)*sin(theta)
elseif flagtype == 18
c.m_x = -r*sin(phi)*sin(theta)
c.m_y = r*cos(theta)
c.m_z = r*cos(phi)*sin(theta)
elseif flagtype == 19
c.m_x = r*sin(phi)*cos(theta)
c.m_y = r*sin(theta)
c.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 20
c.m_x = -r*sin(phi)*cos(theta)
c.m_y = -r*sin(theta)
c.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 21
c.m_x = -r*sin(phi)*cos(theta)
c.m_y = r*sin(theta)
c.m_z = r*cos(phi)*cos(theta)
elseif flagtype == 22
c.m_x = r*sin(phi)*sin(theta)
c.m_y = -r*cos(phi)*sin(theta)
c.m_z = r*cos(theta)
elseif flagtype == 23
c.m_x = -r*sin(phi)*cos(theta)
c.m_y = r*cos(phi)*cos(theta)
c.m_z = -r*sin(theta)
elseif flagtype == 24
c.m_x = r*sin(phi)*cos(theta)
c.m_y = r*cos(phi)*cos(theta)
c.m_z = r*sin(theta)
elseif flagtype == 25
c.m_x = -r*sin(phi)*sin(theta)
c.m_y = r*cos(phi)*sin(theta)
c.m_z = r*cos(theta)
elseif flagtype == 26
c.m_x = -r*sin(phi)*sin(theta)
c.m_y = -r*cos(phi)*sin(theta)
c.m_z = r*cos(theta)
elseif flagtype == 27
c.m_x = -r*sin(phi)*sin(theta)
c.m_y = r*cos(phi)*sin(theta)
c.m_z = r*cos(theta)
elseif flagtype == 28
c.m_x = r*cos(theta)
c.m_y = -r*cos(phi)*sin(theta)
c.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 29
c.m_x = r*cos(theta)
c.m_y = r*cos(phi)*sin(theta)
c.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 30
c.m_x = r*sin(theta)
c.m_y = r*cos(phi)*cos(theta)
c.m_z = r*sin(phi)*cos(theta)
elseif flagtype == 31
c.m_x = -r*sin(theta)
c.m_y = r*cos(phi)*cos(theta)
c.m_z = -r*sin(phi)*cos(theta)
elseif flagtype == 32
c.m_x = r*sin(theta)
c.m_y = r*cos(phi)*cos(theta)
c.m_z = -r*sin(phi)*cos(theta)
elseif flagtype == 33
c.m_x = -r*cos(phi)*sin(theta)
c.m_y = r*cos(theta)
c.m_z = r*sin(phi)*sin(theta)
elseif flagtype == 34
c.m_x = r*cos(phi)*cos(theta)
c.m_y = -r*sin(theta)
c.m_z = -r*sin(phi)*cos(theta)
elseif flagtype == 35
c.m_x = r*cos(phi)*cos(theta)
c.m_y = r*sin(theta)
c.m_z = r*sin(phi)*cos(theta)
elseif flagtype == 36
c.m_x = r*cos(phi)*sin(theta)
c.m_y = r*cos(theta)
c.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 37
c.m_x = -r*cos(phi)*sin(theta)
c.m_y = r*cos(theta)
c.m_z = -r*sin(phi)*sin(theta)
elseif flagtype == 38
c.m_x = r*cos(phi)*sin(theta)
c.m_y = r*cos(theta)
c.m_z = r*sin(phi)*sin(theta)
elseif flagtype == 39
c.m_x = r*cos(phi)*cos(theta)
c.m_y = -r*sin(phi)*cos(theta)
c.m_z = -r*sin(theta)
elseif flagtype == 40
c.m_x = r*cos(phi)*cos(theta)
c.m_y = -r*sin(phi)*cos(theta)
c.m_z = r*sin(theta)
elseif flagtype == 41
c.m_x = r*cos(phi)*sin(theta)
c.m_y = -r*sin(phi)*sin(theta)
c.m_z = r*cos(theta)
elseif flagtype == 42
c.m_x = r*cos(theta)
c.m_y = r*cos(phi)
c.m_z = r*sin(theta)
elseif flagtype == 43
c.m_x = r*cos(theta)
c.m_y = -r*cos(phi)
c.m_z = r*sin(theta)
elseif flagtype == 44
c.m_x = r*cos(theta)
c.m_y = -r*cos(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 45
c.m_x = r*cos(theta)
c.m_y = r*sin(theta)
c.m_z = r*cos(phi)
elseif flagtype == 46
c.m_x = r*cos(theta)
c.m_y = r*sin(phi)
c.m_z = r*cos(phi)
elseif flagtype == 47
c.m_x = r*cos(theta)
c.m_y = -r*sin(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 48
c.m_x = -r*cos(theta)
c.m_y = r*cos(phi)
c.m_z = r*sin(theta)
elseif flagtype == 49
c.m_x = -r*cos(theta)
c.m_y = r*cos(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 50
c.m_x = -r*cos(theta)
c.m_y = r*cos(phi)
c.m_z = r*sin(phi)
elseif flagtype == 51
c.m_x = -r*cos(theta)
c.m_y = r*cos(phi)
c.m_z = -r*sin(phi)
elseif flagtype == 52
c.m_x = r*cos(theta)
c.m_y = r*sin(phi)
c.m_z = r*sin(theta)
elseif flagtype == 53
c.m_x = r*cos(theta)
c.m_y = r*sin(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 54
c.m_x = -r*cos(theta)
c.m_y = -r*cos(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 55
c.m_x = -r*cos(theta)
c.m_y = -r*cos(phi)
c.m_z = -r*sin(phi)
elseif flagtype == 56
c.m_x = -r*cos(theta)
c.m_y = r*sin(theta)
c.m_z = r*cos(phi)
elseif flagtype == 57
c.m_x = -r*cos(theta)
c.m_y = r*sin(phi)
c.m_z = r*cos(phi)
elseif flagtype == 58
c.m_x = -r*cos(theta)
c.m_y = r*sin(phi)
c.m_z = r*sin(theta)
elseif flagtype == 59
c.m_x = -r*cos(theta)
c.m_y = r*sin(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 60
c.m_x = -r*cos(theta)
c.m_y = -r*sin(phi)
c.m_z = r*cos(phi)
elseif flagtype == 61
c.m_x = -r*cos(theta)
c.m_y = -r*sin(phi)
c.m_z = -r*cos(phi)
elseif flagtype == 62
c.m_x = -r*cos(theta)
c.m_y = -r*sin(phi)
c.m_z = r*sin(theta)
elseif flagtype == 63
c.m_x = -r*cos(theta)
c.m_y = -r*sin(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 64
c.m_x = r*cos(phi)
c.m_y = r*sin(phi)
c.m_z = r*cos(theta)
elseif flagtype == 65
c.m_x = r*cos(phi)
c.m_y = r*sin(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 66
c.m_x = r*cos(phi)
c.m_y = r*sin(phi)
c.m_z = r*sin(theta)
elseif flagtype == 67
c.m_x = r*cos(phi)
c.m_y = -r*sin(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 68
c.m_x = -r*cos(phi)
c.m_y = r*sin(phi)
c.m_z = r*cos(theta)
elseif flagtype == 69
c.m_x = -r*cos(phi)
c.m_y = r*sin(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 70
c.m_x = -r*cos(phi)
c.m_y = r*sin(phi)
c.m_z = r*sin(theta)
elseif flagtype == 71
c.m_x = -r*cos(phi)
c.m_y = r*sin(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 72
c.m_x = -r*cos(phi)
c.m_y = -r*sin(phi)
c.m_z = r*cos(theta)
elseif flagtype == 73
c.m_x = -r*cos(phi)
c.m_y = -r*sin(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 74
c.m_x = -r*cos(phi)
c.m_y = -r*sin(phi)
c.m_z = r*sin(theta)
elseif flagtype == 75
c.m_x = -r*cos(phi)
c.m_y = -r*sin(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 76
c.m_x = r*sin(theta)
c.m_y = -r*cos(theta)
c.m_z = r*sin(phi)
elseif flagtype == 77
c.m_x = r*sin(theta)
c.m_y = r*cos(phi)
c.m_z = r*cos(theta)
elseif flagtype == 78
c.m_x = r*sin(theta)
c.m_y = r*sin(phi)
c.m_z = r*cos(theta)
elseif flagtype == 79
c.m_x = r*sin(theta)
c.m_y = r*sin(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 80
c.m_x = r*sin(theta)
c.m_y = r*sin(phi)
c.m_z = r*cos(phi)
elseif flagtype == 81
c.m_x = -r*sin(theta)
c.m_y = r*cos(theta)
c.m_z = r*cos(phi)
elseif flagtype == 82
c.m_x = -r*sin(theta)
c.m_y = r*cos(phi)
c.m_z = r*sin(phi)
elseif flagtype == 83
c.m_x = -r*sin(theta)
c.m_y = -r*cos(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 84
c.m_x = -r*sin(theta)
c.m_y = r*sin(phi)
c.m_z = r*cos(theta)
elseif flagtype == 85
c.m_x = -r*sin(theta)
c.m_y = r*sin(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 86
c.m_x = -r*sin(theta)
c.m_y = -r*sin(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 87
c.m_x = -r*sin(theta)
c.m_y = -r*sin(phi)
c.m_z = r*cos(phi)
elseif flagtype == 88
c.m_x = r*sin(phi)
c.m_y = -r*cos(phi)
c.m_z = r*sin(theta)
elseif flagtype == 89
c.m_x = r*sin(phi)
c.m_y = -r*cos(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 90
c.m_x = -r*sin(phi)
c.m_y = r*cos(phi)
c.m_z = r*cos(theta)
elseif flagtype == 91
c.m_x = -r*sin(phi)
c.m_y = r*cos(phi)
c.m_z = -r*cos(theta)
elseif flagtype == 92
c.m_x = r*sin(phi)
c.m_y = r*cos(phi)
c.m_z = r*sin(theta)
elseif flagtype == 93
c.m_x = -r*sin(phi)
c.m_y = r*cos(phi)
c.m_z = -r*sin(theta)
elseif flagtype == 94
c.m_x = -r*sin(phi)
c.m_y = -r*cos(phi)
c.m_z = -r*cos(theta)
endif
c.m_w = 0
endfunc
static func SDiv(bool quadcor,bool altel, Vector a, Vector b, Vector c,float pfactor)
; Vector b is the divisor
float ra = sqrt(a.m_x^2 + a.m_y^2 + a.m_z^2)+1e-10
float phia = atan2(a.m_x + flip(a.m_y)) ; azimuth
float thetaa = 0
float asa = 0
if altel
thetaa = asin(-a.m_z/ra)
else
thetaa = asin(a.m_z/ra)
endif
float rb = sqrt(b.m_x^2 + b.m_y^2 + b.m_z^2)+1e-10
float phib = atan2(b.m_x + flip(b.m_y)) ; azimuth
float thetab = 0
if altel
thetab = asin(-b.m_z/rb)
else
thetab = asin(b.m_z/rb)
endif
float r = ra/rb
float phi = phia - phib
float theta = (thetaa - thetab)*pfactor
if quadcor
if theta > #pi/2
asa = sin(theta)
theta = asin(asa)
endif
if theta < -#pi/2
asa = sin(theta)
theta = asin(asa)
endif
endif
c.m_x = r*cos(theta)*cos(phi)
c.m_y = r*cos(theta)*sin(phi)
c.m_z = r^pfactor*sin(theta)
c.m_w = 0
endfunc
static func SExp(Vector a, Vector b)
float t = a.m_z/sqrt(a.m_x^2+a.m_y^2)
float p = t*a.m_x + a.m_y
float m = t*a.m_x - a.m_y
float m2 = a.m_x - t*a.m_y
b.m_x = 0.5*exp(m2)*(cos(p) + exp(2*t*a.m_y)*cos(m))
b.m_y = 0.5*exp(m2)*(sin(p) - exp(2*t*a.m_y)*sin(m))
b.m_z = exp(sqrt(a.m_x^2+a.m_y^2))*sin(a.m_z)
b.m_w = 0
endfunc
static func SLn(Vector a, Vector b)
float t = (a.m_x-1)^2 + a.m_y^2
b.m_x = 0.25*log((2*a.m_z^2*((a.m_x-1)*a.m_x+(a.m_y-1)*a.m_y)*((a.m_x-1)*a.m_x+a.m_y^2+a.m_y))/t \
+ (a.m_x^2+a.m_y^2)^2 + a.m_z^4)
b.m_y = 0.25*(-atan2(flip((a.m_x-1)*a.m_z-sqrt(t)*a.m_y)+sqrt(t)*a.m_x+a.m_y*a.m_z) \
+atan2(flip(sqrt(t)*a.m_y+(a.m_x-1)*a.m_z)+sqrt(t)*a.m_x-a.m_y*a.m_z) \
-atan2(flip(-sqrt(t)*a.m_y-a.m_x*a.m_z+a.m_z)+sqrt(t)*a.m_x-a.m_y*a.m_z) \
+atan2(flip(sqrt(t)*a.m_y-a.m_x*a.m_z+a.m_z)+sqrt(t)*a.m_x+a.m_y*a.m_z))
b.m_z = atan(a.m_z/(sqrt(t)+1))
b.m_w = 0
endfunc
static func Tpower(Vector a, Vector b, Vector c, float pfactor, int flagtype)
; T1^T2 = exp(ln(T1)*T2)
Vector d = new Vector(0,0,0,0)
Vector f = new Vector(0,0,0,0)
Sln(a,d)
Smult(false,false,b,d,f,pfactor,flagtype)
Sexp(f,c)
c.m_w = 0
endfunc
default:
title = "Misc 3D 4D Methods"
int param v_3D4D
caption = "Version (Misc 3D 4D Methods)"
default = 100
hint = "This version parameter is used to detect when a change has been \
made to the formula that is incompatible with the previous version. When \
that happens, this field will reflect the old version number to alert you \
to the fact that an alternate rendering is being used."
visible = @v_3D4D < 100
endparam
}
Class LKM {
import "common.ulb"
; 3D Mandelbrot
; 3D representation for s = x + ij + jz
;
; Multiplication table for unit vectors:
;
; | r i j
; ------------------
; r | r i j
; i | i -j -r
; j | j -r -i
;
static func LKMsqr(Vector a, Vector b)
b.m_x = a.m_x^2 - 2*a.m_y*a.m_z
b.m_y = 2*a.m_x*a.m_y - a.m_z^2
b.m_z = 2*a.m_x*a.m_z - a.m_y^2
b.m_w = 0
endfunc
static func LKMmult(Vector a, Vector b, Vector c)
c.m_x = a.m_x*b.m_x - a.m_y*b.m_z - a.m_z*b.m_y
c.m_y = a.m_x*b.m_y + a.m_y*b.m_x - a.m_z*b.m_z
c.m_z = a.m_x*b.m_z - a.m_y*b.m_y + a.m_z*b.m_x
c.m_w = 0
endfunc
; 3D Mandelbrot2
; 3D representation for s = x + ij + jz
;
; Multiplication table for unit vectors:
;
; | r i j
; ------------------
; r | r i j
; i | i -r -j
; j | j -i -r
;
static func REBsqr(Vector a, Vector b)
b.m_x = a.m_x^2 - a.m_y^2 - a.m_z^2
b.m_y = 2*a.m_x*a.m_y - a.m_y*a.m_z
b.m_z = 2*a.m_x*a.m_z - a.m_y*a.m_z
b.m_w = 0
endfunc
static func REBmult(Vector a, Vector b, Vector c)
c.m_x = a.m_x*b.m_x - a.m_y*b.m_z - a.m_z*b.m_y
c.m_y = a.m_x*b.m_y + a.m_y*b.m_x - a.m_z*b.m_z
c.m_z = a.m_x*b.m_z - a.m_y*b.m_y + a.m_z*b.m_x
c.m_w = 0
endfunc
default:
title = "3D Vector Methods"
int param v_3D
caption = "Version (3D Vector Methods)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_3D < 100
endparam
}
;-------------------------------------------
; Mobius Transforms
;-------------------------------------------
class Mobius {
$define debug
; Creates Mobius transformations in a matrix format.
;
; T(z) = (az+b)/(cz+d)
;
; T is a Mobius Transformation were z, a, b, c and d are complex ; numbers. T is typically represented in normalized matrix form: ;
; T = | a b |
; | c d |
;
; T is normalized if the determinant of ad-bc = 1
;
; A Mobius Transformation can be viewed as a composition of translation, ; scaling and inversion. ;
; The Trace of T is TrT = a+ d
public:
; Mobius constructor for T(a, b, c, d)
; @param a = a value
; @param b = b value
; @param c = c value
; @param d = d value
func Mobius(complex a, complex b, complex c, complex d)
m_a = a
m_b = b
m_c = c
m_d = d
m_TrT = m_a + m_d
endfunc
; Circle to Mobius
func CircToMob(Sphere s)
; Lines and Circles can be represented as Mobius Transforms. Lines and
; Circles are equivalent in Riemann space. For convenience circles are
; represented as sphere objects
; method from Curtis McMullen
complex unit = 0
complex im = (0,1)
if s.frad <= 0
; matrix of line
unit = cos(-#pi*s.frad) + flip(sin(-#pi*s.frad))
m_a = im*unit
m_b = im*(conj(unit)*s.fcen-unit*conj(s.fcen))
m_c = 0
m_d = im*conj(unit)
else
; matrix of circle
m_a = s.fcen/s.frad
m_b = s.frad-|s.fcen|/s.frad
m_c = 1/s.frad
m_d = -conj(s.fcen)/s.frad
endif
endfunc
; Mobius to Circle
func MobToCirc(int level, int rgen, Sphere s)
; A Mobius Transform can be represented as a Line or Circle. In
; Reimann space a line is a circle with a negative radius. The
; 'level' and 'rgen' arguments are for the Kleinian inversion algorithms
; method from Curtis McMullen
float LINEFUZZ = 1e-5
if real(m_c) < LINEFUZZ && real(m_c) > - LINEFUZZ
; matrix to line
s.frad = -atan2(m_a)/#pi-1.5
s.fcen = -m_b*m_a/2
else
; matrix to circle
s.fcen = m_a/m_c
s.frad = cabs(1/real(m_c))
endif
s.flevel = level
s.fgen = rgen
endfunc
; Hermitian to Circle
func HermitToCirc(Circle C)
; A Hermitian matrix can be converted to a circle format.
; The method is from David Wright. In Riemann space both circles and
; lines are equivalent. The code handles both.
im = (0,1)
if m_a != 0
;Hermitian is for a circle
C.fcen = -m_b/m_a
C.frad = sqrt(|m_b|-real(m_a)*real(m_d)) \
/cabs(m_a)
else
;Hermitian is for a line
C.fcen = -m_d/(2*m_c)
C.frad = -atan2(im*m_b)/#pi
while C.frad > 0
C.frad = C.frad-1
endwhile
endif
endfunc
; Circle to Hermitian
func CircToHermit(Mobius H, Circle C)
; A circle can be converted to a Hermitian matrix.
; The method is from David Wright. In Riemann space both circles and
; lines are equivalent. The code handles both.
float vector = tan(-#pi*C.frad)
complex im = (0,1)
if C.frad > 0
;calculation for circle
H.m_a = 1
H.m_b = -C.fcen
H.m_c = conj(H.m_b)
H.m_d = |C.fcen|-C.frad^2
else
;calculation for line
H.m_a = 0
H.m_b = vector+im
H.m_c = conj(H.m_b)
H.m_d = -2*imag(C.fcen)*(1+vector^2)
endif
endfunc
; Mobius on Circle
func MobOnCirc(Circle C)
; Applies a Mobius transform to a circle
; The method is from David Wright. In Riemann space both circles and
; lines are equivalent. The code handles both.
Mobius I = new Mobius(m_d, -m_b, -m_c, m_a)
Mobius CT = new Mobius(conj(I.m_a),conj(I.m_c),conj(I.m_b),conj(I.m_d))
Mobius H = new Mobius(0,0,0,0)
this.CircToHermit(H,C)
complex temp1 = H.m_a, complex temp2 = H.m_b
complex temp3 = H.m_c, complex temp4 = H.m_d
H.m_a = temp1*I.m_a+temp2*I.m_c, H.m_b = temp1*I.m_b+temp2*I.m_d
H.m_c = temp3*I.m_a+temp4*I.m_c, H.m_d = temp3*I.m_b+temp4*I.m_d
temp1 = H.m_a, temp2 = H.m_b
temp3 = H.m_c, temp4 = H.m_d
H.m_a = CT.m_a*temp1+CT.m_b*temp3, H.m_b = CT.m_a*temp2+CT.m_b*temp4
H.m_c = CT.m_c*temp1+CT.m_d*temp3, H.m_d = CT.m_c*temp2+CT.m_d*temp4
H.HermitToCirc(C)
endfunc
; Normalize Mobius
func Normalize(Mobius T)
complex det = T.m_a*T.m_d-T.m_b*T.m_c
det = 1/sqrt(det)
T.m_a = m_a*det
T.m_b = m_b*det
T.m_c = m_c*det
T.m_d = m_d*det
endfunc
; Invert Mobius
func Invert(Mobius T)
complex det = m_a*m_d-m_b*m_c
T.m_a = m_d
T.m_b = -m_b
T.m_c = -m_c
T.m_d = m_a
if real(det) <= 0
T.m_a = -conj(T.m_a)
T.m_b = -conj(T.m_b)
T.m_c = -conj(T.m_c)
T.m_d = -conj(T.m_d)
endif
endfunc
; Multiplication
func Mult(Mobius T1, Mobius T2)
; T2 = T * T1 This does not commute.
;
complex det = m_a*m_d-m_b*m_c
if real(det) <= 0
T2.m_a = m_a*conj(T1.m_a)+m_b*conj(T1.m_c)
T2.m_b = m_a*conj(T1.m_b)+m_b*conj(T1.m_d)
T2.m_c = m_c*conj(T1.m_a)+m_d*conj(T1.m_c)
T2.m_d = m_c*conj(T1.m_b)+m_d*conj(T1.m_d)
else
T2.m_a = m_a*T1.m_a+m_b*T1.m_c
T2.m_b = m_a*T1.m_b+m_b*T1.m_d
T2.m_c = m_c*T1.m_a+m_d*T1.m_c
T2.m_d = m_c*T1.m_b+m_d*T1.m_d
endif
endfunc
; Conjugate
func MConj(Mobius T1,Mobius T2)
; T2 = T * T1 * inverse(T)
Mobius igen = new Mobius(0,0,0,0)
; Inverse of T
this.Invert(igen)
Mobius prod1 = new Mobius(0,0,0,0)
this.Mult(T1,prod1)
prod1.Mult(igen,T2)
endfunc
; Mobius Trace
complex func Trace()
return m_a + m_d
endfunc
complex m_a
complex m_b
complex m_c
complex m_d
complex m_TrT
default:
title = "Mobius Methods"
int param v_mobius
caption = "Version (Mobius Methods)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_mobius < 101
endparam
}
class MobiusArray(Array) {
; class for Mobius Transformation arrays
public:
import "common.ulb"
; Constructor for Mobius arrays
; @param plength = sets the size of the array
func MobiusArray(int plength)
setLength(m_T, plength)
endfunc
; Get array length
int func GetArrayLength()
return length(m_T)
endfunc
; Set array length
func SetArrayLength(int plength)
setLength(m_T, plength)
endfunc
; Copy array
func Copy(MobiusArray &dest)
int l = this.GetArrayLength()
if (dest == 0)
dest = new MobiusArray(l)
else
dest.SetArrayLength(l)
endif
int j = 0
while (j < l)
dest.m_T[j] = m_T[j]
j = j + 1
endwhile
endfunc
Mobius m_T[]
default:
title = "Mobius Array"
int param v_mobiusarray
caption = "Version (Mobius Array)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_mobiusarray < 100
endparam
}
;-------------------------------------------
; 3D Rotations
;-------------------------------------------
Class Rot {
import "common.ulb"
static func Rotate(float &x, float &y, float &z, float angle, Vector a)
float rmatrix[3,3]
float cangle = cos(angle*#pi/180)
float sangle = sin(angle*#pi/180)
rmatrix[0,0] = cangle+a.m_x^2*(1-cangle)
rmatrix[1,0] = a.m_x*a.m_y*(1-cangle)-a.m_z*sangle
rmatrix[2,0] = a.m_x*a.m_z*(1-cangle)+a.m_y*sangle
rmatrix[0,1] = a.m_x*a.m_y*(1-cangle)+a.m_z*sangle
rmatrix[1,1] = cangle+a.m_y^2*(1-cangle)
rmatrix[2,1] = a.m_y*a.m_z*(1-cangle)-a.m_x*sangle
rmatrix[0,2] = a.m_x*a.m_z*(1-cangle)-a.m_y*sangle
rmatrix[1,2] = a.m_y*a.m_z*(1-cangle)+a.m_x*sangle
rmatrix[2,2] = cangle+a.m_z^2*(1-cangle)
float tempx = x
float tempy = y
x = rmatrix[0,0]*x + rmatrix[1,0]*y + rmatrix[2,0]*z
y = rmatrix[0,1]*tempx + rmatrix[1,1]*y + rmatrix[2,1]*z
z = rmatrix[0,2]*tempx + rmatrix[1,2]*tempy + rmatrix[2,2]*z
endfunc
static func RotateX(float &x, float &y, float &z, float angle)
float rmatrix[3,3]
float cangle = cos(angle*#pi/180)
float sangle = sin(angle*#pi/180)
rmatrix[0,0] = 1
rmatrix[1,0] = 0
rmatrix[2,0] = 0
rmatrix[0,1] = 0
rmatrix[1,1] = cangle
rmatrix[2,1] = -sangle
rmatrix[0,2] = 0
rmatrix[1,2] = sangle
rmatrix[2,2] = cangle
float tempx = x
float tempy = y
x = rmatrix[0,0]*x + rmatrix[1,0]*y + rmatrix[2,0]*z
y = rmatrix[0,1]*tempx + rmatrix[1,1]*y + rmatrix[2,1]*z
z = rmatrix[0,2]*tempx + rmatrix[1,2]*tempy + rmatrix[2,2]*z
endfunc
static func RotateY(float &x, float &y, float &z, float angle)
float rmatrix[3,3]
float cangle = cos(angle*#pi/180)
float sangle = sin(angle*#pi/180)
rmatrix[0,0] = cangle
rmatrix[1,0] = 0
rmatrix[2,0] = sangle
rmatrix[0,1] = 0
rmatrix[1,1] = 1
rmatrix[2,1] = 0
rmatrix[0,2] = -sangle
rmatrix[1,2] = 0
rmatrix[2,2] = cangle
float tempx = x
float tempy = y
x = rmatrix[0,0]*x + rmatrix[1,0]*y + rmatrix[2,0]*z
y = rmatrix[0,1]*tempx + rmatrix[1,1]*y + rmatrix[2,1]*z
z = rmatrix[0,2]*tempx + rmatrix[1,2]*tempy + rmatrix[2,2]*z
endfunc
static func RotateZ(float &x, float &y, float &z, float angle)
float rmatrix[3,3]
float cangle = cos(angle*#pi/180)
float sangle = sin(angle*#pi/180)
rmatrix[0,0] = cangle
rmatrix[1,0] = -sangle
rmatrix[2,0] = 0
rmatrix[0,1] = sangle
rmatrix[1,1] = cangle
rmatrix[2,1] = 0
rmatrix[0,2] = 0
rmatrix[1,2] = 0
rmatrix[2,2] = 1
float tempx = x
float tempy = y
x = rmatrix[0,0]*x + rmatrix[1,0]*y + rmatrix[2,0]*z
y = rmatrix[0,1]*tempx + rmatrix[1,1]*y + rmatrix[2,1]*z
z = rmatrix[0,2]*tempx + rmatrix[1,2]*tempy + rmatrix[2,2]*z
endfunc
; rotations for Turtle orientation using the the Abelson diSessa paradigm.
; The turtle is oriented using three vectors H (heading), L (left) and U (up).
; H x L = U
static func RotateH(float &x, float &y, float &z, float angle)
float rmatrix[3,3]
float cangle = cos(angle*#pi/180)
float sangle = sin(angle*#pi/180)
rmatrix[0,0] = 1
rmatrix[1,0] = 0
rmatrix[2,0] = 0
rmatrix[0,1] = 0
rmatrix[1,1] = cangle
rmatrix[2,1] = -sangle
rmatrix[0,2] = 0
rmatrix[1,2] = sangle
rmatrix[2,2] = cangle
float tempx = x
float tempy = y
x = rmatrix[0,0]*x + rmatrix[1,0]*y + rmatrix[2,0]*z
y = rmatrix[0,1]*tempx + rmatrix[1,1]*y + rmatrix[2,1]*z
z = rmatrix[0,2]*tempx + rmatrix[1,2]*tempy + rmatrix[2,2]*z
endfunc
static func RotateL(float &x, float &y, float &z, float angle)
float rmatrix[3,3]
float cangle = cos(angle*#pi/180)
float sangle = sin(angle*#pi/180)
rmatrix[0,0] = cangle
rmatrix[1,0] = 0
rmatrix[2,0] = -sangle
rmatrix[0,1] = 0
rmatrix[1,1] = 1
rmatrix[2,1] = 0
rmatrix[0,2] = sangle
rmatrix[1,2] = 0
rmatrix[2,2] = cangle
float tempx = x
float tempy = y
x = rmatrix[0,0]*x + rmatrix[1,0]*y + rmatrix[2,0]*z
y = rmatrix[0,1]*tempx + rmatrix[1,1]*y + rmatrix[2,1]*z
z = rmatrix[0,2]*tempx + rmatrix[1,2]*tempy + rmatrix[2,2]*z
endfunc
static func RotateU(float &x, float &y, float &z, float angle)
float rmatrix[3,3]
float cangle = cos(angle*#pi/180)
float sangle = sin(angle*#pi/180)
rmatrix[0,0] = cangle
rmatrix[1,0] = sangle
rmatrix[2,0] = 0
rmatrix[0,1] = -sangle
rmatrix[1,1] = cangle
rmatrix[2,1] = 0
rmatrix[0,2] = 0
rmatrix[1,2] = 0
rmatrix[2,2] = 1
float tempx = x
float tempy = y
x = rmatrix[0,0]*x + rmatrix[1,0]*y + rmatrix[2,0]*z
y = rmatrix[0,1]*tempx + rmatrix[1,1]*y + rmatrix[2,1]*z
z = rmatrix[0,2]*tempx + rmatrix[1,2]*tempy + rmatrix[2,2]*z
endfunc
}
;-------------------------------------------
; 5. 3D Object classes
;-------------------------------------------
class Point {
; class for creating 3D point objects
public:
; Point constructor for (x, y, z)
; @param x = x value
; @param y = y value
; @param z = z value
func Point(float x, float y, float z)
fx = x
fy = y
fz = z
endfunc
float fx
float fy
float fz
default:
title = "Point"
int param v_point
caption = "Version (Point)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_point < 100
endparam
}
class PointArray(Array) {
; class for creating 3D point object arrays
public:
import "common.ulb"
; Constructor for plane arrays
; @param plength = sets the size of the array
func PointArray(int plength)
setLength(pt, plength)
endfunc
; Get array length
int func GetArrayLength()
return length(pt)
endfunc
; Set array length
func SetArrayLength(int plength)
setLength(pt, plength)
endfunc
; Copy array
func Copy(PointArray &dest)
int l = this.GetArrayLength()
if (dest == 0)
dest = new PointArray(l)
else
dest.SetArrayLength(l)
endif
int j = 0
while (j < l)
dest.pt[j] = pt[j]
j = j + 1
endwhile
endfunc
Point pt[]
default:
title = "Point Array"
int param v_pointarray
caption = "Version (Point Array)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_pointarray < 100
endparam
}
class Line {
; class for creating line objects
public:
import "common.ulb"
; Line constructor for a line defined by 2 points (x1, y1, z1, x2, y2, z2)
; @param x1 = x1 value
; @param y1 = y1 value
; @param z1 = z1 value
; @param x2 = x2 value
; @param y2 = y2 value
; @param z2 = z2 value
; @param vis = line visibility
; @param lcol = line color gradient
; @param dcol = line color direct color
; @param depth = recursion depth
; @param poly = is polygon
; @param lwidth = line width
; @param brratio = branching thickness ratio
func Line(float x1, float y1, float z1, float x2, float y2, float z2)
fx1 = x1
fy1 = y1
fz1 = z1
fx2 = x2
fy2 = y2
fz2 = z2
llength = sqrt((fx2-fx1)^2 + (fy2-fy1)^2 + (fz2-fz1)^2)
vis = true
lcol = 0.5
depth = 0
lwidth = 1
dcol = rgba(1,1,1,1)
poly = false
brratio = 1
sign = 1
jump = false
endfunc
func SetLength()
llength = sqrt((fx2-fx1)^2 + (fy2-fy1)^2 + (fz2-fz1)^2)
endfunc
func SetVis(bool svis)
vis = svis
endfunc
func SetJump(bool sjump)
jump = sjump
endfunc
func SetGradCol(float gradcol)
lcol = gradcol
endfunc
func SetWidth(float width)
lwidth = width
endfunc
func SetDirectColor(color dcolor)
dcol = dcolor
endfunc
func SetDepth(int j)
depth = j
endfunc
func SetPoly(bool ispoly)
poly = ispoly
endfunc
func SetBranchRatio(float branchratio)
brratio = branchratio
endfunc
func SetSign(float sign)
sign = sign/abs(sign)
endfunc
func GetVector(Vector &vec)
float x2 = fx2-fx1
float y2 = fy2-fy1
float z2 = fz2-fz1
vec = new Vector(x2,y2,z2,0)
vec.Normalize(vec)
endfunc
func Resize(float setsize)
fx1 = setsize*fx1
fy1 = setsize*fy1
fz1 = setsize*fz1
fx2 = setsize*fx2
fy2 = setsize*fy2
fz2 = setsize*fz2
llength = sqrt((fx2-fx1)^2 + (fy2-fy1)^2 + (fz2-fz1)^2)
endfunc
; rotate around the point x1, y1, z1
func Rotate(float theta)
float x1 = fx1-x1
float y1 = fy1-y1
float z1 = fz1-z1
float x2 = fx2-x1
float y2 = fy2-y1
float z2 = fz2-z1
vector vec = new Vector(x2,y2,z2,0)
rot.rotate(x2,y2,z2,theta,vec)
fx2 = x2+x1
fy2 = y2+y1
fz2 = z2+z1
endfunc
float llength
float lwidth
float fx1
float fy1
float fz1
float fx2
float fy2
float fz2
bool vis
float lcol
color dcol
int depth
bool poly
float brratio
float sign
bool jump
default:
title = "Line"
int param v_line
caption = "Version (Line)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_line < 100
endparam
}
class LineArray(Array) {
; class for creating 3D point object arrays
public:
import "common.ulb"
; Constructor for line arrays
; @param plength = sets the size of the array
func LineArray(int plength)
setLength(line, plength)
endfunc
; Get array length
int func GetArrayLength()
return length(line)
endfunc
; Set array length
func SetArrayLength(int plength)
setLength(line, plength)
endfunc
; Copy array
func Copy(LineArray &dest)
int l = this.GetArrayLength()
if (dest == 0)
dest = new LineArray(l)
else
dest.SetArrayLength(l)
endif
int j = 0
while (j < l)
dest.line[j] = line[j]
j = j + 1
endwhile
endfunc
Line line[]
default:
title = "LineArray"
int param v_linearray
caption = "Version (Line Array)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_linearray < 100
endparam
}
class Plane {
; class for creating plane objects
public:
; Plane constructor for Ax + By + C = 0
; @param A = A value
; @param B = B value
; @param C = C value
; @param D = D value
func Plane(float A, float B, float C, float D)
float norm = sqrt(A^2+B^2+C^2)
pnx = A/norm
pny = B/norm
pnz = C/norm
pspot = D/norm
pa = A
pb = B
pc = C
pd = D
endfunc
; Is a point on the plane
bool func OnPlane(float x, float y, float z, float tol)
bool opl = false
if (pa*x+pb*y+pc*z+pd < tol) && (pa*x+pb*y+pc*z+pd > -tol)
opl = true
endif
return opl
endfunc
float pnx
float pny
float pnz
float pspot
float pa
float pb
float pc
float pd
default:
title = "Plane"
int param v_plane
caption = "Version (Plane)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_plane < 100
endparam
}
class PlaneArray(Array) {
; class for creating plane object arrays
public:
import "common.ulb"
; Constructor for plane arrays.
func PlaneArray(int plength)
setLength(pl, plength)
endfunc
; Get array length
int func GetArrayLength()
return length(pl)
endfunc
; Set array length
func SetArrayLength(int plength)
setLength(pl, plength)
endfunc
; Copy array
func Copy(PlaneArray &dest)
int l = this.GetArrayLength()
if (dest == 0)
dest = new PlaneArray(l)
else
dest.SetArrayLength(l)
endif
int j = 0
while (j < l)
dest.pl[j] = pl[j]
j = j + 1
endwhile
endfunc
Plane pl[]
default:
title = "Plane Array"
int param v_planearray
caption = "Version (Plane Array)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_planearray < 100
endparam
}
class Triangle {
; class for creating triangle objects
public:
import "Common.ulb"
; Triangle constructor for (x1, y1, z1, x2, y2, z2, x3, y3, z3)
; @param x1 = x1 value
; @param y1 = y1 value
; @param z1 = z1 value
; @param x2 = x2 value
; @param y2 = y2 value
; @param z2 = z2 value
; @param x2 = x3 value
; @param y2 = y3 value
; @param z2 = z3 value
func Triangle(float x1, float y1, float z1, float x2, float y2, float z2, \
float x3, float y3, float z3)
fx1 = x1
fy1 = y1
fz1 = z1
fx2 = x2
fy2 = y2
fz2 = z2
fx3 = x3
fy3 = y3
fz3 = z3
r_fz1 = z1
r_fz2 = z2
r_fz3 = z3
t_norm = new Vector(0,0,0,0)
Norm()
t_norm.Normalize(t_norm)
; P*N + pspot = 0 this is the equation for the plane of the triangle
pspot = -(t_norm.m_x*fx1+t_norm.m_y*fy1+t_norm.m_z*fz1)
endfunc
; used to re-initialize the triangle parameters
func Init(float x1, float y1, float z1, float x2, float y2, float z2, \
float x3, float y3, float z3)
fx1 = x1
fy1 = y1
fz1 = z1
fx2 = x2
fy2 = y2
fz2 = z2
fx3 = x3
fy3 = y3
fz3 = z3
Norm()
t_norm.Normalize(t_norm)
; P*N + pspot = 0 this is the equation for the plane of the triangle
pspot = -(t_norm.m_x*fx1+t_norm.m_y*fy1+t_norm.m_z*fz1)
xy_ave = (fx1+fx2+fx3)/3 + flip((fy1+fy2+fy3)/3)
z_ave = (fz1+fz2+fz3)/3
endfunc
; 1 -> 2 ->3 must be counterclockwise
func Norm()
Vector V1 = new Vector(fx1-fx2, fy1-fy2, fz1-fz2, 0)
Vector V2 = new Vector(fx3-fx2, fy3-fy2, fz3-fz2, 0)
V1.Cross(V2, t_norm)
t_norm.m_w = 0
endfunc
; determine vector from camera to center of triangle
float fx1
float fy1
float fz1
float fx2
float fy2
float fz2
float fx3
float fy3
float fz3
float r_fz1
float r_fz2
float r_fz3
Vector t_norm
float pspot
complex xy_ave
float z_ave
default:
title = "Triangle"
int param v_triangle
caption = "Version (Triangle)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_triangle < 100
endparam
}
class TriangleArray(Array) {
; class for creating 3D Triangle object arrays
public:
import "common.ulb"
; Constructor for triangle arrays
; @param plength = sets the size of the array
func TriangleArray(int plength)
setLength(tr, plength)
endfunc
; Get array length
int func GetArrayLength()
return length(tr)
endfunc
; Set array length
func SetArrayLength(int plength)
setLength(tr, plength)
endfunc
; Copy array
func Copy(TriangleArray &dest)
int l = this.GetArrayLength()
if (dest == 0)
dest = new TriangleArray(l)
else
dest.SetArrayLength(l)
endif
int j = 0
while (j < l)
dest.tr[j] = tr[j]
j = j + 1
endwhile
endfunc
Triangle tr[]
default:
title = "Triangle Array"
int param v_Trianglearray
caption = "Version (Triangle Array)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Trianglearray < 100
endparam
}
class Sphere {
; class for creating sphere objects
;
; The sphere object contains arguments for recursion level and
; generator sphere identifier for facilitate use with Sphere
; Inversions
public:
; Sphere constructor
; @param center = (x,y) coordinates of the sphere center
; @param height = z coordinate of sphere center
; @param radius = sphere radius
; @param level = recursion level of the sphere
; @param generator = index of generator sphere
func Sphere(complex center, float height, float radius, int level, int generator)
fCen = center
fRad = radius
fZ = height
fLevel = level
fGen = generator
endfunc
int fLevel
complex fCen
float fRad
float fZ
int fGen
default:
title = "Sphere"
int param v_sphere
caption = "Version (Sphere)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_sphere < 100
endparam
}
class SphereArray(Array) {
; class for sphere arrays
public:
import "common.ulb"
; Sphere array constructor
; @param plength = size of the sphere array
func SphereArray(int plength)
setLength(sph, plength)
endfunc
; Get array length
int func GetArrayLength()
return length(sph)
endfunc
; Set array length
func SetArrayLength(int plength)
setLength(sph, plength)
endfunc
; Copy Array
; @param dest = SphereArray object to copy all values into
; previous contents of dest will be discarded.
func Copy(SphereArray &dest)
int l = this.GetArrayLength()
if (dest == 0)
dest = new SphereArray(l)
else
dest.SetArrayLength(l)
endif
int j = 0
while (j < l)
dest.sph[j] = sph[j]
j = j + 1
endwhile
endfunc
Sphere sph[]
default:
title = "Sphere Array"
int param v_spherearray
caption = "Version (Sphere Array)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_spherearray < 100
endparam
}
class Circle {
; class for creating circle objects
;
public:
; Circle constructor
; @param center = (x,y) coordinates of the sphere center
; @param radius = sphere radius
func Circle(complex center, float radius)
fCen = center
fRad = radius
endfunc
complex fCen
float fRad
default:
title = "Circle"
int param v_circle
caption = "Version (Circle)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_circle < 100
endparam
}
class CircleArray(Array) {
; class for circle arrays
public:
import "common.ulb"
; Circle array constructor
; @param plength = size of the circle array
func CircleArray(int plength)
setLength(cir, plength)
endfunc
; Get array length
int func GetArrayLength()
return length(cir)
endfunc
; Set array length
func SetArrayLength(int plength)
setLength(cir, plength)
endfunc
; Copy Array
; @param dest = CircleArray object to copy all values into
; previous contents of dest will be discarded.
func Copy(CircleArray &dest)
int l = this.GetArrayLength()
if (dest == 0)
dest = new CircleArray(l)
else
dest.SetArrayLength(l)
endif
int j = 0
while (j < l)
dest.cir[j] = cir[j]
j = j + 1
endwhile
endfunc
Circle cir[]
default:
title = "Circle Array"
int param v_circlearray
caption = "Version (Circle Array)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_circlearray < 100
endparam
}
;--------------------------------------------
; 3D Inversion Classes
;--------------------------------------------
Class InvertSphere(common.ulb:Generic) {
; sphere inversions starting with a tetrahedral geometery for the base set
; this is the base class
; it contains methods for
; 1. sphere initialization for base and generator sets
; 2. sphere inversion
; 3. recursion
; 4. heapsort and duplicate removal
;
$define debug
public:
import "common.ulb"
; constructor for sphere inversions with a tetrahedral geometry
func InvertSphere(Generic pparent)
;
; dynamically allocate the maximum number of spheres
;
s = new SphereArray(50000000)
flength = 50000000, fscle = 3 + sqrt(6), fks = 4, fk = fks, fii = 5, fjj = 5
rlevel = 5, fminsphere = @minsphere, mlevel = @MaxLevel, fbaserad = sqrt(2)
thresh = fminsphere/1000, scale = 0.3, reflect = @reflect, xrot = (0,1)^(@xang/90),
yrot = (0,1)^(@yang/90), zrot = (0,1)^(#angle*2/#pi), sflag = true
crad = 0, circles = false, showc = true, lace = false, cir3 = false
zsort = @zsort
initSpheres()
endfunc
; Initializes base and generator spheres
func InitSpheres()
complex Fc[10]
float Fz[10]
float Fr[10]
complex temp = 0
int i = 0
while i < 4
Fc[i] = (1,1)*exp(flip(i)*#pi/2)*fscle
Fr[i] = (fscle-1)*2
if i%2 == 0
Fz[i] = -fscle
else
Fz[i] = fscle
endif
i = i + 1
endwhile
Fc[i] = (0,0)
Fr[i] = 1
Fz[i] = 0
i = i + 1
while i < 9
Fc[i] = (1,1)*exp(flip(i-5)*#pi/2)
Fr[i] = fbaserad
if i%2 == 0
Fz[i] = -1
else
Fz[i] = 1
endif
i = i + 1
endwhile
Fc[i] = (0,0)
Fr[i] = sqrt(2)+sqrt(3)
Fz[i] = 0
; scale and translate the spheres to screen dimensions
i = 0
repeat
if reflect
Fc[i] = -conj(Fc[i])
else
Fc[i] = Fc[i]
endif
; Z axis rotation
Fc[i] = Fc[i]*zrot
; Y axis rotation
temp = real(Fc[i]) + flip(Fz[i])
temp = temp*yrot
Fc[i] = real(temp) + flip(imag(Fc[i]))
Fz[i] = imag(temp)
; X axis rotation
temp = imag(Fc[i]) + flip(Fz[i])
temp = temp*xrot
Fc[i] = real(Fc[i]) + flip(real(temp))
Fz[i] = imag(temp)
; scaling
Fc[i] = Fc[i]*#magn*scale
Fz[i] = Fz[i]*#magn*scale
if i > 4
Fr[i] = Fr[i]*#magn*scale*@bradadj
else
Fr[i] = Fr[i]*#magn*scale*@radadj
endif
i = i+1
until i == 10
; declare the generator spheres
; tetrahedron
i = 0
while i <= 4
fg[i] = new Sphere(Fc[i],Fz[i],Fr[i],0,i)
i = i + 1
endwhile
;
; declare the base Spheres
; tetrahedron
while i <= 9
fb[i-5] = new Sphere(Fc[i],Fz[i],Fr[i],0,i-5)
i = i + 1
endwhile
bradius = fb[0].frad
i = 0
while i < 4
s.sph[i] = fb[i]
i = i + 1
endwhile
endfunc
; Inverts a sphere
; @param target = sphere to be inverted
; @param inverter = sphere used for the inversion
; @param level = recursion level
; @param gen = index of generator (inverter) sphere
Sphere func Inverse(Sphere target, Sphere inverter, int level, int gen)
rgen = gen
if target != 0 && inverter != 0
float ar = inverter.frad
float br = target.frad
complex a = inverter.fcen
complex b = target.fcen
float ha = inverter.fz
float hb = target.fz
float temp = ar^2/(|a-b|+(ha-hb)^2-br^2)
float rad = abs(temp*br)
if lace && circles && cir3
rad = temp*br
endif
complex cen = temp*(b-a) + a
float z = temp*(hb-ha) + ha
return new Sphere(cen,z,rad,level,rgen)
else
return new Sphere((0,0),0,0,0,0)
endif
endfunc
; Top level recursion function - calls the function recurse2
func Recurse()
if mlevel > 0
int level = 0
level = level + 1
int ii = 0
int jj = 0
fk = fks
while ii < fii
while jj < fjj && fk < flength
if (|fb[jj].fcen-fg[ii].fcen|+ (fb[jj].fz-fg[ii].fz)^2)> \
(fb[jj].frad+fg[ii].frad)^2
s.sph[fk] = Inverse(fb[jj],fg[ii],level,jj)
fk = fk + 1
endif
jj = jj + 1
endwhile
ii = ii + 1
jj = 0
endwhile
;
; The exeception to the rule of target and generator are external to each other
;
s.sph[fk] = Inverse(fb[fjj-1],fg[fii-1],level,fjj-1)
if circles
crad = s.sph[fk].frad
endif
fk = fk + 1
int j = fjj-1
if level < mlevel
while j < fjj-1 + rlevel
recurse2(level,j)
j = j + 1
endwhile
endif
if sflag
heapsort(s,fk)
vanquish(s,fk)
endif
endif
if @zsort
heapsortz(s,fk)
endif
endfunc
; Function for recursive sphere inversion
; @param level = recursion level
; @param tarvalue = index of new sphere
func recurse2(int level, int tarvalue)
level = level + 1
int k = 0
while k < fii && fk < flength
if lace && circles && cir3
if (|s.sph[tarvalue].fcen-fg[k].fcen| + \
(s.sph[tarvalue].fz-fg[k].fz)^2)> \
(s.sph[tarvalue].frad+fg[k].frad)^2 && s.sph[tarvalue].frad > \
fminSphere
s.sph[fk] = Inverse(s.sph[tarvalue],fg[k],level,s.sph[tarvalue].fgen)
fk = fk + 1
if level < mlevel
recurse2(level,fk-1)
endif
endif
else
if (|s.sph[tarvalue].fcen-fg[k].fcen| + \
(s.sph[tarvalue].fz-fg[k].fz)^2)> \
(s.sph[tarvalue].frad+fg[k].frad)^2 && abs(s.sph[tarvalue].frad) > \
fminSphere
s.sph[fk] = Inverse(s.sph[tarvalue],fg[k],level,s.sph[tarvalue].fgen)
fk = fk + 1
if level < mlevel
recurse2(level,fk-1)
endif
endif
endif
k = k + 1
endwhile
endfunc
; Find the overall bounding volume for a set of spheres
; @param sa = sphere array to be bounded
; @param count = index range to be bounded
; @param xmin = min x boundary
; @param ymin = min y boundary
; @param zmin = min z boundary
; @param xmax = max x boundary
; @param ymax = max y boundary
; @param zmax = max z boundary
func findbound(SphereArray sa, int count, float &xmin, float &ymin, \
float &zmin, float &xmax, float &ymax, float &zmax)
xmin = 1e10
ymin = 1e10
zmin = 1e10
xmax = -1e10
xmax = -1e10
xmax = -1e10
float temp = 0
int i = 0
while i < count
temp = real(sa.sph[i].fcen) - abs(sa.sph[i].frad)
if temp < xmin
xmin = temp
endif
temp = real(sa.sph[i].fcen) + abs(sa.sph[i].frad)
if temp > xmax
xmax = temp
endif
temp = imag(sa.sph[i].fcen) - abs(sa.sph[i].frad)
if temp < ymin
ymin = temp
endif
temp = imag(sa.sph[i].fcen) + abs(sa.sph[i].frad)
if temp > ymax
ymax = temp
endif
temp = sa.sph[i].fz - abs(sa.sph[i].frad)
if temp < zmin
zmin = temp
endif
temp = sa.sph[i].fz + abs(sa.sph[i].frad)
if temp > zmax
zmax = temp
endif
i = i + 1
endwhile
endfunc
; Sort spheres in preparation for duplicate removal
; @param sa = sphere array to be sorted
; @param count = index range to be sorted
func heapsort(SphereArray sa,int count)
heapify(sa, count)
int end = count-1
while end > 0
swap(sa,end,0)
end = end-1
siftDown(sa, 0, end)
endwhile
endfunc
; Sort spheres by z value.
func heapsortz(SphereArray sa,int count)
heapifyz(sa, count)
int end = count-1
while end > 0
swap(sa,end,0)
end = end-1
siftDownz(sa, 0, end)
endwhile
endfunc
; A helper function for heapsort
; @param sa = sphere array to be sorted
; @param count = index range to be sorted
func heapify(SphereArray sa,int count)
int start = round((count-1)/2)
while start >= 0
siftDown(sa, start, count-1)
start = start-1
endwhile
endfunc
; A helper function for heapsortz
func heapifyz(SphereArray sa,int count)
int start = round((count-1)/2)
while start >= 0
siftDownz(sa, start, count-1)
start = start-1
endwhile
endfunc
; A helper function for heapsort
; @param sa = sphere array to be sorted
; @param start = start of the index index range
; @param end = end of the index range
func siftdown(SphereArray sa, int start,int end)
int root = start, float dx = 0, float dy = 0, float dz = 0, float dr = 0
int c = 0
while (root*2+1) <= end
int child = root*2+1
if sa.sph[child] != 0 && sa.sph[child+1] != 0
dx = real(sa.sph[child].fcen) - real(sa.sph[child + 1].fcen)
dy = imag(sa.sph[child].fcen) - imag(sa.sph[child + 1].fcen)
dz = sa.sph[child].fz - sa.sph[child + 1].fz
dr = sa.sph[child].frad - sa.sph[child + 1].frad
else
dx = 0
dy = 0
dz = 0
dr = 0
endif
if child < end
if dr < -thresh
c = -1
elseif dr > thresh
c = 1
elseif dy < -thresh
c = -1
elseif dy > thresh
c = 1
elseif dz < -thresh
c = -1
elseif dz > thresh
c = 1
elseif dx < -thresh
c = -1
elseif dx > thresh
c = 1
else
c = 0
endif
if c < 0
child = child+1
endif
endif
if sa.sph[child] != 0 && sa.sph[root] != 0
dx = real(sa.sph[root].fcen) - real(sa.sph[child].fcen)
dy = imag(sa.sph[root].fcen) - imag(sa.sph[child].fcen)
dz = sa.sph[root].fz - sa.sph[child].fz
dr = sa.sph[root].frad - sa.sph[child].frad
else
dx = 0
dy = 0
dz = 0
dr = 0
endif
if dr < -thresh
c = -1
elseif dr > thresh
c = 1
elseif dy < -thresh
c = -1
elseif dy > thresh
c = 1
elseif dz < -thresh
c = -1
elseif dz > thresh
c = 1
elseif dx < -thresh
c = -1
elseif dx > thresh
c = 1
else
c = 0
endif
if c < 0
swap(s,root,child)
root = child
else
return
endif
endwhile
endfunc
; A helper function for heapsortz
func siftdownz(SphereArray sa, int start,int end)
int root = start, float dz = 0
int c = 0
while (root*2+1) < end
int child = root*2+1
dz = sa.sph[child].fz - sa.sph[child+1].fz
if child < end
if dz < -thresh
c = -1
elseif dz > thresh
c = 1
else
c = 0
endif
if c > 0
child = child+1
endif
endif
dz = sa.sph[root].fz - sa.sph[child].fz
if dz < -thresh
c = -1
elseif dz > thresh
c = 1
else
c = 0
endif
if c > 0
swap(s,root,child)
root = child
else
return
endif
endwhile
endfunc
; A helper function for heapsort
; @param i = index of the first sphere to be swapped
; @param j = index of the second sphere to be swapped
func swap(SphereArray sa, int i, int j)
Sphere temp = sa.sph[j]
sa.sph[j] = sa.sph[i]
sa.sph[i] = temp
endfunc
; Removes duplicates from a sorted array
; @param sa = sphere array for duplicate element removal
; @param count = index range for duplicate removal
;------------------------------------------------
func vanquish(SphereArray sa, int count)
float dx = 0, float dy = 0, float dz = 0, float dr = 0, int c = 0
int ir = 1, int l = 0
while ir < count
if sa.sph[ir] != 0 && sa.sph[ir-1] != 0
dx = real(sa.sph[ir].fcen) - real(sa.sph[ir-1].fcen)
dy = imag(sa.sph[ir].fcen) - imag(sa.sph[ir-1].fcen)
dz = sa.sph[ir].fz - sa.sph[ir-1].fz
dr = sa.sph[ir].frad - sa.sph[ir-1].frad
else
dx = 0
dy = 0
dz = 0
dr = 0
endif
if dr < -thresh
c = -1
elseif dr > thresh
c = 1
elseif dy < -thresh
c = -1
elseif dy > thresh
c = 1
elseif dz < -thresh
c = -1
elseif dz > thresh
c = 1
elseif dx < -thresh
c = -1
elseif dx > thresh
c = 1
else
c = 0
endif
if c == 0
ir = ir + 1
else
sa.sph[l] = sa.sph[ir]
ir = ir +1
l = l + 1
endif
endwhile
fk = l
endfunc
Sphere fg[14]
float fscle
int flength
float fminSphere
Sphere fb[22]
int fk
int rgen
int mlevel
int fks
int fii
int fjj
int rlevel
float fbaserad
float fp
float fip
spherearray s
float thresh
float scale
bool reflect
complex xrot
complex yrot
complex zrot
float bradius
bool sflag
float crad
bool circles
bool showc
bool lace
bool cir3
bool zsort
float rcen
default:
title = "Tetrahedron"
int param v_tetrahedron
caption = "Version (Tetrahedron)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_tetrahedron < 100
endparam
heading
text = "Do not use 'Sort by depth' with reflections, refractions or \
transformations."
endheading
bool param zsort
caption = "Sort by depth"
default = false
hint = "Allows intersection test for simple raytracing to terminate \
at first hit."
endparam
float param minsphere
caption = "Min sphere size"
default = 0.01
min = 0.00001
endparam
int param maxLevel
caption = "Recursion level"
default = 2
min = 0
max = 1000
endparam
float param radadj
caption = "Gen Rad adj"
default = 1.0
endparam
float param bradadj
caption = "Base Rad adj"
default = 1.0
endparam
bool param reflect
caption = "Reflect Object"
default = false
endparam
float param xang
caption = "X Axis Rotation"
default = 0.0
endparam
float param yang
caption = "Y Axis Rotation"
default = 0.0
endparam
}
Class InvertCube(InvertSphere) {
; sphere inversions starting with a cubic geometery
; this is a child of InvertSphere
public:
import "common.ulb"
; constructor for sphere inversions with a cubic geometry
func InvertCube(Generic pparent)
InvertSphere.InvertSphere(0)
fscle = 3 + sqrt(3), fbaserad = sqrt(6)+sqrt(2)
scale = 0.34, fii = 7, fjj = 9, fks = 8, fk = fks, rlevel = 25
initSpheres()
endfunc
; Initializes base and generator spheres
func InitSpheres()
complex Fc[16]
float Fz[16]
float Fr[16]
int i = 0
complex grot = exp(flip(1)*#pi/2)
while i < 4
Fc[i] = (1,0)*grot^i*fscle
Fz[i] = 0
Fr[i] = fbaserad
i = i + 1
endwhile
Fc[4] = Fc[5] = Fc[6] = (0,0)
Fz[4] = fscle
Fz[5] = -fscle
Fz[6] = 0
Fr[4] = Fr[5] = fbaserad
Fr[6] = sqrt(2)
i = 7
while i < 15
Fc[i] = (1,1)*grot^(i-7)
if i < 11
Fz[i] = 1
else
Fz[i] = -1
endif
Fr[i] = 1
i = i + 1
endwhile
Fc[i] = (0,0)
Fz[i] = 0
Fr[i] = 1+sqrt(3)
; scale and translate the spheres to screen dimensions
;
i = 0
repeat
if reflect
Fc[i] = -conj(Fc[i])
else
Fc[i] = Fc[i]
endif
; Z axis rotation
Fc[i] = Fc[i]*zrot
; Y axis rotation
temp = real(Fc[i]) + flip(Fz[i])
temp = temp*yrot
Fc[i] = real(temp) + flip(imag(Fc[i]))
Fz[i] = imag(temp)
; X axis rotation
temp = imag(Fc[i]) + flip(Fz[i])
temp = temp*xrot
Fc[i] = real(Fc[i]) + flip(real(temp))
Fz[i] = imag(temp)
; scaling
Fc[i] = Fc[i]*#magn*scale
Fz[i] = Fz[i]*#magn*scale
if i > 6
Fr[i] = Fr[i]*#magn*scale*@bradadj
else
Fr[i] = Fr[i]*#magn*scale*@radadj
endif
i = i+1
until i == 16
; declare the generator spheres
;
; cube
i = 0
while i < 7
fg[i] = new Sphere(Fc[i],Fz[i],Fr[i],0,i)
i = i + 1
endwhile
;
; declare the base Spheres
;
; cube
while i < 16
fb[i-7] = new Sphere(Fc[i],Fz[i],Fr[i],0,i-7)
i = i + 1
endwhile
bradius = fb[0].frad
i = 0
while i < 8
s.sph[i] = fb[i]
i = i + 1
endwhile
endfunc
default:
title = "Cube"
int param v_cube
caption = "Version (Cube)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_cube < 100
endparam
}
Class InvertOctahedron(InvertSphere) {
; sphere inversions starting with a octahedral geometery
; this is a child of InvertSphere
public:
import "common.ulb"
; constructor for sphere inversions with an octahedral geometry
func InvertOctahedron(Generic pparent)
InvertSphere.InvertSphere(0)
fscle = 1+sqrt(2)/2, fbaserad = 1+sqrt(2), scale = 0.5, fii = 9, fjj = 7
fks = 6, fk = fks, rlevel = 25
initSpheres()
endfunc
; Initializes base and generator spheres
func InitSpheres()
complex Fc[22]
float Fz[22]
float Fr[22]
Fc[0] = (1,1)*fscle, Fc[1] = (-1,1)*fscle, Fc[2] = (1,-1)*fscle, Fc[3] = (1,1)*fscle
Fc[4] = (-1,-1)*fscle, Fc[5] = (-1,1)*fscle, Fc[6] = (1,-1)*fscle, Fc[7] = (-1,-1)*fscle
Fc[8] = (0,0), Fc[9] = (1,0), Fc[10] = (0,-1), Fc[11] = (0,0), Fc[12] = (-1,0)
Fc[13] = (0,1), Fc[14] = (0,0), Fc[15] = (0,0), Fc[16] = (1,0), Fc[17] = (0,-1)
Fc[18] = (0,0), Fc[19] = (-1,0), Fc[20] = (0,1), Fc[21] = (0,0)
Fz[0] = fscle, Fz[1] = fscle, Fz[2] = fscle, Fz[3] = -fscle, Fz[4] = fscle
Fz[5] = -fscle, Fz[6] = -fscle, Fz[7] = -fscle, Fz[8] = 0, Fz[9] = 0, Fz[10] = 0
Fz[11] = 1, Fz[12] = 0, Fz[13] = 0, Fz[14] = -1, Fz[15] = 0, Fz[16] = 0
Fz[17] = 0, Fz[18] = 1, Fz[19] = 0, Fz[20] = 0, Fz[21] = -1
Fr[0] = fbaserad, Fr[1] = fbaserad, Fr[2] = fbaserad, Fr[3] = fbaserad, Fr[4] = fbaserad
Fr[5] = fbaserad, Fr[6] = fbaserad, Fr[7] = fbaserad, Fr[8] = sqrt(2)/2, Fr[9] = sqrt(2)/2
Fr[10] = sqrt(2)/2, Fr[11] = sqrt(2)/2, Fr[12] = sqrt(2)/2, Fr[13] = sqrt(2)/2
Fr[14] = sqrt(2)/2, Fr[15] = 1+sqrt(2)/2, Fr[16] = sqrt(2)/2, Fr[17] = sqrt(2)/2
Fr[18] = sqrt(2)/2, Fr[19] = sqrt(2)/2, Fr[20] = sqrt(2)/2, Fr[21] = sqrt(2)/2
int i = 0
; scale and translate the spheres to screen dimensions
;
repeat
if reflect
Fc[i] = -conj(Fc[i])
else
Fc[i] = Fc[i]
endif
; Z axis rotation
Fc[i] = Fc[i]*zrot
; Y axis rotation
temp = real(Fc[i]) + flip(Fz[i])
temp = temp*yrot
Fc[i] = real(temp) + flip(imag(Fc[i]))
Fz[i] = imag(temp)
; X axis rotation
temp = imag(Fc[i]) + flip(Fz[i])
temp = temp*xrot
Fc[i] = real(Fc[i]) + flip(real(temp))
Fz[i] = imag(temp)
; scaling
Fc[i] = Fc[i]*#magn*scale
Fz[i] = Fz[i]*#magn*scale
if i > 8
Fr[i] = Fr[i]*#magn*scale*@bradadj
else
Fr[i] = Fr[i]*#magn*scale*@radadj
endif
i = i+1
until i == 22
; declare the generator spheres
;
; octahedron
fg[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0), fg[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,1)
fg[2] = new Sphere(Fc[2],Fz[2],Fr[2],0,2), fg[3] = new Sphere(Fc[3],Fz[3],Fr[3],0,3)
fg[4] = new Sphere(Fc[4],Fz[4],Fr[4],0,4), fg[5] = new Sphere(Fc[5],Fz[5],Fr[5],0,5)
fg[6] = new Sphere(Fc[6],Fz[6],Fr[6],0,6), fg[7] = new Sphere(Fc[7],Fz[7],Fr[7],0,7)
fg[8] = new Sphere(Fc[8],Fz[8],Fr[8],0,8)
;
; declare the base Spheres
;
; octahedron
fb[0] = new Sphere(Fc[9],Fz[9],Fr[9],0,0), fb[1] = new Sphere(Fc[10],Fz[10],Fr[10],0,1)
fb[2] = new Sphere(Fc[11],Fz[11],Fr[11],0,2), fb[3] = new Sphere(Fc[12],Fz[12],Fr[12],0,3)
fb[4] = new Sphere(Fc[13],Fz[13],Fr[13],0,4), fb[5] = new Sphere(Fc[14],Fz[14],Fr[14],0,5)
fb[6] = new Sphere(Fc[15],Fz[15],Fr[15],0,6)
bradius = fb[0].frad
s.sph[0] = new Sphere(Fc[16],Fz[16],Fr[16],0,0), s.sph[1] = new Sphere(Fc[17],Fz[17],Fr[17],0,1)
s.sph[2] = new Sphere(Fc[18],Fz[18],Fr[18],0,2), s.sph[3] = new Sphere(Fc[19],Fz[19],Fr[19],0,3)
s.sph[4] = new Sphere(Fc[20],Fz[20],Fr[20],0,4), s.sph[5] = new Sphere(Fc[21],Fz[21],Fr[21],0,5)
endfunc
default:
title = "Octahedron"
int param v_octahedron
caption = "Version (Octahedron)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_octahedron < 100
endparam
}
Class InvertDodecahedron(InvertSphere) {
; sphere inversions starting with a dodecahedral geometery
; this is a child of InvertSphere
public:
import "common.ulb"
; constructor for sphere inversions with a dodecahedral geometry
func InvertDodecahedron(Generic pparent)
InvertSphere.InvertSphere(0)
p = (1+sqrt(5))/2, ip = 1/p, fscle = (3+sqrt(3)*(p-1))/(p+1), fbaserad = fscle*2*sqrt(3)/3
scale = 0.4, fii = 13, fjj = 21, fks = 20, fk = fks, rlevel = 181
initSpheres()
endfunc
; Initializes base and generator spheres
func InitSpheres()
complex Fc[54]
float Fz[54]
float Fr[54]
Fc[0] = (1,0)*fscle, Fc[1] = (1,0)*fscle, Fc[2] = (-1,0)*fscle, Fc[3] = (-1,0)*fscle
Fc[4] = flip(p)*fscle, Fc[5] = flip(p)*fscle, Fc[6] = -flip(p)*fscle, Fc[7] = -flip(p)*fscle
Fc[8] = (p+flip(1))*fscle, Fc[9] = (p-flip(1))*fscle, Fc[10] = (-p+flip(1))*fscle
Fc[11] = (-p-flip(1))*fscle, Fc[12] = (0,0), Fc[13] = (1,1), Fc[14] = (-1,1)
Fc[15] = (1,-1), Fc[16] = (1,1), Fc[17] = (-1,-1), Fc[18] = (-1,1), Fc[19] = (1,-1)
Fc[20] = (-1,-1), Fc[21] = flip(ip), Fc[22] = -flip(ip), Fc[23] = flip(ip)
Fc[24] = -flip(ip), Fc[25] = ip+flip(p), Fc[26] = -ip+flip(p), Fc[27] = ip-flip(p)
Fc[28] = -ip-flip(p), Fc[29] = p, Fc[30] = -p, Fc[31] = p, Fc[32] = -p, Fc[33] = (0,0)
Fc[34] = (1,1), Fc[35] = (-1,1), Fc[36] = (1,-1), Fc[37] = (1,1), Fc[38] = (-1,-1)
Fc[39] = (-1,1), Fc[40] = (1,-1), Fc[41] = (-1,-1), Fc[42] = flip(ip), Fc[43] = -flip(ip)
Fc[44] = flip(ip), Fc[45] = -flip(ip), Fc[46] = ip+flip(p), Fc[47] = -ip+flip(p)
Fc[48] = ip-flip(p), Fc[49] = -ip-flip(p), Fc[50] = p, Fc[51] = -p, Fc[52] = p, Fc[53] = -p
Fz[0] = p*fscle, Fz[1] = -p*fscle, Fz[2] = p*fscle, Fz[3] = -p*fscle, Fz[4] = fscle
Fz[5] = -fscle, Fz[6] = fscle, Fz[7] = -fscle, Fz[8] = 0, Fz[9] = 0, Fz[10] = 0
Fz[11] = 0, Fz[12] = 0, Fz[13] = 1, Fz[14] = 1, Fz[15] = 1, Fz[16] = -1, Fz[17] = 1
Fz[18] = -1, Fz[19] = -1, Fz[20] = -1, Fz[21] = p, Fz[22] = p, Fz[23] = -p,, Fz[24] = -p
Fz[25] = 0, Fz[26] = 0, Fz[27] = 0, Fz[28] = 0, Fz[29] = ip, Fz[30] = ip, Fz[31] = -ip
Fz[32] = -ip, Fz[33] = 0, Fz[34] = 1, Fz[35] = 1, Fz[36] = 1, Fz[37] = -1, Fz[38] = 1
Fz[39] = -1, Fz[40] = -1, Fz[41] = -1, Fz[42] = p, Fz[43] = p, Fz[44] = -p
Fz[45] = -p, Fz[46] = 0, Fz[47] = 0, Fz[48] = 0, Fz[49] = 0, Fz[50] = ip, Fz[51] = ip
Fz[52] = -ip, Fz[53] = -ip
Fr[0] = fbaserad, Fr[1] = fbaserad, Fr[2] = fbaserad, Fr[3] = fbaserad, Fr[4] = fbaserad
Fr[5] = fbaserad, Fr[6] = fbaserad, Fr[7] = fbaserad, Fr[8] = fbaserad, Fr[9] = fbaserad
Fr[10] = fbaserad, Fr[11] = fbaserad, Fr[12] = p, Fr[13] = p-1, Fr[14] = p-1
Fr[15] = p-1, Fr[16] = p-1, Fr[17] = p-1, Fr[18] = p-1, Fr[19] = p-1, Fr[20] = p-1
Fr[21] = p-1, Fr[22] = p-1, Fr[23] = p-1, Fr[24] = p-1, Fr[25] = p-1, Fr[26] = p-1
Fr[27] = p-1, Fr[28] = p-1, Fr[29] = p-1, Fr[30] = p-1, Fr[31] = p-1, Fr[32] = p-1
Fr[33] = sqrt(3)+p-1, Fr[34] = p-1, Fr[35] = p-1, Fr[36] = p-1, Fr[37] = p-1
Fr[38] = p-1, Fr[39] = p-1, Fr[40] = p-1, Fr[41] = p-1, Fr[42] = p-1, Fr[43] = p-1
Fr[44] = p-1, Fr[45] = p-1, Fr[46] = p-1, Fr[47] = p-1, Fr[48] = p-1, Fr[49] = p-1
Fr[50] = p-1, Fr[51] = p-1, Fr[52] = p-1, Fr[53] = p-1
int i = 0
; scale and translate the spheres to screen dimensions
;
repeat
if reflect
Fc[i] = -conj(Fc[i])
else
Fc[i] = Fc[i]
endif
; Z axis rotation
Fc[i] = Fc[i]*zrot
; Y axis rotation
temp = real(Fc[i]) + flip(Fz[i])
temp = temp*yrot
Fc[i] = real(temp) + flip(imag(Fc[i]))
Fz[i] = imag(temp)
; X axis rotation
temp = imag(Fc[i]) + flip(Fz[i])
temp = temp*xrot
Fc[i] = real(Fc[i]) + flip(real(temp))
Fz[i] = imag(temp)
; scaling
Fc[i] = Fc[i]*#magn*scale
Fz[i] = Fz[i]*#magn*scale
if i > 12
Fr[i] = Fr[i]*#magn*scale*@bradadj
else
Fr[i] = Fr[i]*#magn*scale*@radadj
endif
i = i+1
until i == 54
; declare the generator spheres
;
; dodecahedron
fg[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0), fg[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,1)
fg[2] = new Sphere(Fc[2],Fz[2],Fr[2],0,2), fg[3] = new Sphere(Fc[3],Fz[3],Fr[3],0,3)
fg[4] = new Sphere(Fc[4],Fz[4],Fr[4],0,4), fg[5] = new Sphere(Fc[5],Fz[5],Fr[5],0,5)
fg[6] = new Sphere(Fc[6],Fz[6],Fr[6],0,6), fg[7] = new Sphere(Fc[7],Fz[7],Fr[7],0,7)
fg[8] = new Sphere(Fc[8],Fz[8],Fr[8],0,8), fg[9] = new Sphere(Fc[9],Fz[9],Fr[9],0,9)
fg[10] = new Sphere(Fc[10],Fz[10],Fr[10],0,10), fg[11] = new Sphere(Fc[11],Fz[11],Fr[11],0,11)
fg[12] = new Sphere(Fc[12],Fz[12],Fr[12],0,12)
;
; declare the base Spheres
;
; dodecahedron
fb[0] = new Sphere(Fc[13],Fz[13],Fr[13],0,0), fb[1] = new Sphere(Fc[14],Fz[14],Fr[14],0,1)
fb[2] = new Sphere(Fc[15],Fz[15],Fr[15],0,2), fb[3] = new Sphere(Fc[16],Fz[16],Fr[16],0,3)
fb[4] = new Sphere(Fc[17],Fz[17],Fr[17],0,4), fb[5] = new Sphere(Fc[18],Fz[18],Fr[18],0,5)
fb[6] = new Sphere(Fc[19],Fz[19],Fr[19],0,6), fb[7] = new Sphere(Fc[20],Fz[20],Fr[20],0,7)
fb[8] = new Sphere(Fc[21],Fz[21],Fr[21],0,8), fb[9] = new Sphere(Fc[22],Fz[22],Fr[22],0,9)
fb[10] = new Sphere(Fc[23],Fz[23],Fr[23],0,10), fb[11] = new Sphere(Fc[24],Fz[24],Fr[24],0,11)
fb[12] = new Sphere(Fc[25],Fz[25],Fr[25],0,12), fb[13] = new Sphere(Fc[26],Fz[26],Fr[26],0,13)
fb[14] = new Sphere(Fc[27],Fz[27],Fr[27],0,14), fb[15] = new Sphere(Fc[28],Fz[28],Fr[28],0,15)
fb[16] = new Sphere(Fc[29],Fz[29],Fr[29],0,16), fb[17] = new Sphere(Fc[30],Fz[30],Fr[30],0,17)
fb[18] = new Sphere(Fc[31],Fz[31],Fr[31],0,18), fb[19] = new Sphere(Fc[32],Fz[32],Fr[32],0,19)
fb[20] = new Sphere(Fc[33],Fz[33],Fr[33],0,20)
bradius = fb[0].frad
s.sph[0] = new Sphere(Fc[34],Fz[34],Fr[34],0,0), s.sph[1] = new Sphere(Fc[35],Fz[35],Fr[35],0,1)
s.sph[2] = new Sphere(Fc[36],Fz[36],Fr[36],0,2), s.sph[3] = new Sphere(Fc[37],Fz[37],Fr[37],0,3)
s.sph[4] = new Sphere(Fc[38],Fz[38],Fr[38],0,4), s.sph[5] = new Sphere(Fc[39],Fz[39],Fr[39],0,5)
s.sph[6] = new Sphere(Fc[40],Fz[40],Fr[40],0,6), s.sph[7] = new Sphere(Fc[41],Fz[41],Fr[41],0,7)
s.sph[8] = new Sphere(Fc[42],Fz[42],Fr[42],0,8), s.sph[9] = new Sphere(Fc[43],Fz[43],Fr[43],0,9)
s.sph[10] = new Sphere(Fc[44],Fz[44],Fr[44],0,10), s.sph[11] = new Sphere(Fc[45],Fz[45],Fr[45],0,11)
s.sph[12] = new Sphere(Fc[46],Fz[46],Fr[46],0,12), s.sph[13] = new Sphere(Fc[47],Fz[47],Fr[47],0,13)
s.sph[14] = new Sphere(Fc[48],Fz[48],Fr[48],0,14), s.sph[15] = new Sphere(Fc[49],Fz[49],Fr[49],0,15)
s.sph[16] = new Sphere(Fc[50],Fz[50],Fr[50],0,16), s.sph[17] = new Sphere(Fc[51],Fz[51],Fr[51],0,17)
s.sph[18] = new Sphere(Fc[52],Fz[52],Fr[52],0,18), s.sph[19] = new Sphere(Fc[53],Fz[53],Fr[53],0,19)
endfunc
float p
float ip
default:
title = "Dodecahedron"
int param v_dodecahedron
caption = "Version (Dodecahedron)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_dodecahedron < 100
endparam
}
Class InvertCircles(InvertSphere) {
;
; circle inversions
;
; This is a child of InvertSphere. For the case of 3 base circles ; (Apollonian Gasket) methods for perturbation of the initiating circles ; are available. ;
$define debug public: import "common.ulb" ; constructor for circle inversions using spheres func InvertCircles(Generic pparent) InvertSphere.InvertSphere(0) ang = 2*#pi/@ncircle ipi = flip(#pi) cpi = flip(#pi/@ncircle) complex cr1 = exp((0,0)*ang+ipi) complex cr2 = exp((0,1)*ang+ipi) float rdd = cabs(cr1-cr2)/2 dd = cabs(cr1) float dtan = sqrt(dd*dd-rdd*rdd) fscle = (dd+rdd)/dtan pert = @pert pert = 11 - pert fscle2 = 1 fbaserad = fscle*2*sqrt(3)/3 fii = @ncircle+1 fjj = @ncircle+1 fks = @ncircle fk = fks g = 0 b = 0 circles = true showc = @showc lace = @lace if @ncircle == 3 rlevel = 4 scale = 0.5 if @ptype == "Inner Circle" && pert <= 2 cir3 = true endif if @ptype == "None" fscle = 2 + sqrt(3) fscle2 = 1 elseif @ptype == "Outer Circles" fscle = (2 + sqrt(3))*cos(#pi/(pert+6)) fscle2 = (fscle-sqrt(3)-1.5)/0.5 else if pert == 10 fscle2 = 1.0041268407 elseif pert == 9 fscle2 = 1.0049465720 elseif pert == 8 fscle2 = 1.0060422243 elseif pert == 7 fscle2 = 1.0075560883 elseif pert == 6 fscle2 = 1.0097381547 elseif pert == 5 fscle2 = 1.0130643119 elseif pert == 4 fscle2 = 1.0185254 elseif pert == 3 fscle2 = 1.0286754 elseif pert == 2 fscle2 = 1.0515254 elseif pert == 1 fscle2 = 1.1277437913 endif endif elseif @ncircle == 4 rlevel = 9 scale = 0.55 elseif @ncircle == 5 rlevel = 16 scale = 0.6 elseif @ncircle == 6 rlevel = 25 scale = 0.65 elseif @ncircle == 7 rlevel = 36 scale = 0.65 elseif @ncircle == 8 rlevel = 49 scale = 0.7 elseif @ncircle == 9 rlevel = 64 scale = 0.7 elseif @ncircle == 10 rlevel = 81 scale = 0.7 elseif @ncircle == 11 rlevel = 100 scale = 0.7 elseif @ncircle == 12 rlevel = 121 scale = 0.7 endif initSpheres() endfunc ; Initializes base and generator spheres func InitSpheres() complex Fc[26] float Fz[26] float Fr[26] ; generator set int i = 0 while i < @ncircle Fc[i] = exp(flip(i)*ang+ipi)*fscle Fz[i] = 0 i = i + 1 endwhile Fc[i] = 0 if @ncircle == 3 Fr[0] = sqrt(3)+1.5 else Fr[0] = cabs(Fc[0]-Fc[1])/2 endif i = 1 while i < @ncircle Fr[i] = Fr[0] i = i + 1 endwhile if @ncircle == 3 if @ptype == "None" Fr[3] = 0.5 elseif @ptype == "Outer Circles" Fr[3] = fscle-sqrt(3)-1.5 elseif @ptype == "Inner Circle" if pert == 10 Fr[3] = 0.5151714074 elseif pert == 9 Fr[3] = 0.5181320854 elseif pert == 8 Fr[3] = 0.5220631074 elseif pert == 7 Fr[3] = 0.5274464005 elseif pert == 6 Fr[3] = 0.5351105381 elseif pert == 5 Fr[3] = 0.5465863845 elseif pert == 4 Fr[3] = 0.564987 elseif pert == 3 Fr[3] = 0.597588 elseif pert == 2 Fr[3] = 0.665053 elseif pert == 1 Fr[3] = 0.8524941755 endif endif else Fr[i] = cabs(Fc[0])-Fr[0] endif g = i ; Base set i = i + 1 if @ncircle%2 == 0 while i < 2*@ncircle+1 Fc[i] = exp(flip(i-4)*ang+cpi)*fscle2 Fz[i] = 0 i = i + 1 endwhile else sflag = false while i < 2*@ncircle+1 Fc[i] = exp(flip(i-3)*ang)*fscle2 Fz[i] = 0 i = i + 1 endwhile endif Fc[i] = 0 if @ncircle == 3 if @ptype == "Outer Circles" || @ptype == "None" Fr[4] = sqrt(3)/2*fscle2 Fr[7] = Fr[4]+fscle2 elseif @ptype == "Inner Circle" if pert == 10 Fr[4] = 0.8618985631 elseif pert == 9 Fr[4] = 0.8610788318 elseif pert == 8 Fr[4] = 0.8599831795 elseif pert == 7 Fr[4] = 0.8584693155 elseif pert == 6 Fr[4] = 0.8562872491 elseif pert == 5 Fr[4] = 0.8529610919 elseif pert == 4 Fr[4] = 0.8475 elseif pert == 3 Fr[4] = 0.83735 elseif pert == 2 Fr[4] = 0.8145 elseif pert == 1 Fr[4] = 0.7382816125 endif Fr[7] = Fr[4] + 1 endif else Fr[@ncircle+1] = cabs(Fc[@ncircle+1]-Fc[@ncircle+2])/2 endif i = @ncircle+2 while i < 2*@ncircle+1 Fr[i] = Fr[@ncircle+1] i = i + 1 endwhile if @ncircle != 3 dd = cabs(Fc[0]) Fr[i] = sqrt(dd*dd-Fr[0]*Fr[0]) endif b = i i = 0 ; scale and translate the spheres to screen dimensions ; repeat if reflect Fc[i] = -conj(Fc[i]) else Fc[i] = Fc[i] endif ; Z axis rotation Fc[i] = Fc[i]*zrot ; Y axis rotation temp = real(Fc[i]) + flip(Fz[i]) temp = temp*yrot Fc[i] = real(temp) + flip(imag(Fc[i])) Fz[i] = imag(temp) ; X axis rotation temp = imag(Fc[i]) + flip(Fz[i]) temp = temp*xrot Fc[i] = real(Fc[i]) + flip(real(temp)) Fz[i] = imag(temp) ; scaling Fc[i] = Fc[i]*#magn*scale Fz[i] = Fz[i]*#magn*scale if i > 12 Fr[i] = Fr[i]*#magn*scale*@bradadj else Fr[i] = Fr[i]*#magn*scale*@radadj endif i = i+1 until i == 2*@ncircle+2 ; ; declare the generator spheres i = 0 while i <= g fg[i] = new Sphere(Fc[i],Fz[i],Fr[i],0,i) i = i + 1 endwhile ; declare the base Spheres i = 0 while i <= g fb[i] = new Sphere(Fc[i+g+1],Fz[i+g+1],Fr[i+g+1],0,i) i = i + 1 endwhile bradius = fb[0].frad i = 0 while i <= g s.sph[i] = fb[i] i = i + 1 endwhile endfunc int g int b float ang complex ipi complex cpi float dd int pert float fscle2 bool showc default: title = "Circle Inversions" int param v_invcircle caption = "Version (Circle Inversions)" default = 100 hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used." visible = @v_invcircle < 100 endparam int param ncircle caption = "# of Circles (3-12)" default = 3 min = 3 max = 12 endparam int param maxLevel caption = "Recursion level" default = 20 min = 0 max = 200 endparam bool param showc caption = "Show Center Circle" default = true endparam bool param lace caption = "Display as Lace" default = false visible = @ptype == "Inner Circle" && (@pert >=8) && @ncircle == 3 endparam heading text = "Perturbation of Inversion Circles \ by overlap." visible = @ncircle == 3 endheading param ptype caption = "Perturb Type" default = 0 enum = "None" "Outer Circles" "Inner Circle" visible = @ncircle == 3 endparam param pert caption = "Perturb Level (1-10)" default = 1 min = 1 max = 10 visible = @ptype != "None" && @ncircle == 3 endparam float param xang caption = "X Axis Rotation" default = 0.0 endparam float param yang caption = "Y Axis Rotation" default = 0.0 endparam } class InvertMobius(InvertSphere) { ;
; Derived from the public C code of Curtis McMullen and
; material from Indra's Pearls by Mumford, Series and Wright
; A new method for InitSpheres is needed, as both spheres
; and Kleinian Group matricies must be initalized.
;
public:
import "common.ulb"
$define debug
; constructor for Mobius (Kleinian) sphere inversions
func InvertMobius(Generic pparent)
invertSphere.Invertsphere(0)
PARAFUZZ = 1e-3, LINEFUZZ = 1e-5, im = (0,1),gi = 0
fii = 4, fks = 1, fk = fks, scale = 0.7, sscale = 1, iend = 4
ss = new SphereArray(50000000)
InitSpheresK()
endfunc
; Initialize spheres, inversion matricies and trace values
func InitSpheresK()
; This function initializes the base sphere(s), the Kleinian group
; inversion matrices and the trace values
complex Fc[4]
float Fz[4]
float Fr[4]
int i = 0
complex ta = @ta
complex tb = @tb
float cir = @cir
complex cira = @cira
Complex cirs = @cirs
float rada = @rada
float rads = @rads
float radam = @radam
complex m = @m
complex tab = 0
complex gz0 = 0
complex gz = 0
complex gQ = 0
complex gR = 0
complex tabAB = @tabAB
Fz[0] = 0
Fz[1] = 0
Fz[2] = 0
Fz[3] = 0
if @cusptype == "Nearby group"
ta = (1.91,-0.05)
tb = (2,0)
cir = 0.297
elseif @cusptype == "Accident"
ta = (1.9021130325903071442328786667588,0)
tb = (1.9021130325903071442328786667588,0)
elseif @cusptype == "Troel's Point"
ta = (1.6168866453,-0.7056734968)
tb = (2,0)
cir = 0.13091
elseif @cusptype == "Degenerate Spiral"
ta = (1.9264340533,-0.0273817919)
tb = (2,0)
cir = 0.2419
elseif @cusptype == "Double Cusp"
tb = (2,0)
if @cusp == "0/1"
ta = (2,0)
cir = 0.5
elseif @cusp == "1/100"
ta = (1.99599050389291,-0.000302826761310194)
cir = 0.3091
elseif @cusp == "2/99"
ta = (1.99599050389291,-0.000302826761310194)
cir = 0.2676
elseif @cusp == "3/100"
ta = (1.99118310579765,-0.000982081178197968)
cir = 0.2427
elseif @cusp == "4/99"
ta = (1.98427416931522,-0.00237401043014847)
cir = 0.2351
elseif @cusp == "1/15"
ta = (1.95859103011179,-0.0112785606117653)
cir = 0.32870768
elseif @cusp == "1/10"
ta = (1.91342329586682,-0.0362880775225429)
cir = 0.32365169
elseif @cusp == "2/19"
ta = (1.90377999779718,-0.0395799512688805)
cir = 0.2604321
elseif @cusp == "1/9"
ta = (1.89640725094921,-0.0487530128986506)
cir = 0.32176507
elseif @cusp == "7/43"
ta = (1.80785523999043,-0.136998687907137)
cir = 0.229796
elseif @cusp == "3/10"
ta = (1.65831239517773,-0.5)
cir = 0.2316625
elseif @cusp == "2/5"
ta = (1.64213876865348,-0.766588417465459)
cir = 0.2665884
elseif @cusp == "1/2"
ta = (1.73205080756888,-1)
cir = 0.36602539
elseif @cusp == "21/34"
ta = (1.6179907967521,-1.29170028664218)
cir = 0.166461
endif
endif
; Grandma's Special algorithm
if !(@cusptype == "Grandma's Special #2" || @cusptype == "Maskit")
if @showcusp == "Both"
Fc[0] = 1-cir
Fr[0] = cir
Fc[1] = -(1-cir)
Fr[1] = cir
Fc[2] = (0,0)
Fr[2] = 1
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
s.sph[2] = new Sphere(Fc[2],Fz[2],Fr[2],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
ss.sph[2] = s.sph[2]
elseif @showcusp == "Alternate"
Fc[0] = (1-cir)
Fr[0] = cir
Fc[1] = -(1-cir)
Fr[1] = cir
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
elseif @showcusp == "Standard"
Fc[0] = (0,0)
Fr[0] = 1
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
ss.sph[0] = s.sph[0]
endif
complex tab = (ta*tb+sqrt(ta*ta*tb*tb-4*(ta*ta+tb*tb)))/2
if @alttab
tab = (ta*tb-sqrt(ta*ta*tb*tb-4*(ta*ta+tb*tb)))/2
endif
complex gz0 = (tab-2)*tb/(tb*tab-2*ta+2*(0,1)*tab)
mob[0] = new Mobius((tb-(0,2))/2, tb/2, tb/2, conj((tb-(0,2))/2))
mob[1] = new Mobius(mob[0].m_d, -mob[0].m_b, -mob[0].m_c, mob[0].m_a)
mob[2] = new Mobius(ta/2, (ta*tab-2*tb-(0,4))*gz0/(2*tab-4), \
(ta*tab-2*tb+(0,4))/((2*tab+4)*gz0), ta/2)
if @trans
temp1 = mob[2].m_b
mob[2].m_b = mob[2].m_c
mob[2].m_c = temp1
endif
mob[3] = new Mobius(mob[2].m_d, -mob[2].m_b, -mob[2].m_c, mob[2].m_a)
endif
; Figure 11.1 from the Indra's Pearls book
if @cusptype == "Indra 11.1"
tabAB = (0,0)
tb = (2,0)
sscale = 2.4
ta = (1.924781, 0.047529)
rads = 0.41421381
cirs = (0, 0.272591599)
cira = (0.168208, 0)
rada = 0.2211131
endif
; Grandma's Special #2 algorithm
if !(@cusptype == "Grandma's Special" || @cusptype == "Maskit" ||\
@cusptype == "Double Cusp" || @cusptype == "Nearby Group" ||\
@cusptype == "Troel's Point"|| @cusptype == "Degenerate Spiral")
if @showcusp == "Both"
Fc[0] = cirs
Fr[0] = rads-cabs(cirs)
if @lines
Fr[0] = -Fr[0]
endif
Fc[1] = -cirs
Fr[1] = Fr[0]
Fc[2] = cira
Fr[2] = rada-cabs(cira)
if @linea
Fr[2] = -Fr[2]
endif
Fc[3] = -cira
Fr[3] = Fr[2]
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
s.sph[2] = new Sphere(Fc[2],Fz[2],Fr[2],0,0)
s.sph[3] = new Sphere(Fc[3],Fz[3],Fr[3],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
ss.sph[2] = s.sph[2]
ss.sph[3] = s.sph[3]
elseif @showcusp == "Alternate"
Fc[0] = cira
Fr[0] = rada-cabs(cira)
if @linea
Fr[0] = -Fr[0]
endif
Fc[1] = -cira
Fr[1] = Fr[0]
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
else
Fc[0] = cirs
Fr[0] = rads-cabs(cirs)
if @lines
Fr[0] = -Fr[0]
endif
Fc[1] = -cirs
Fr[1] = Fr[0]
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
endif
gz = 0.5*sqrt(ta^2*tb^2-4*ta^2-4*tb^2+4*tabAB+8)
tab = 0.5*ta*tb-gz
if @alttab
tab = 0.5*ta*tb+gz
endif
gQ = sqrt(2-tabAB)
gR = sqrt(2+tabAB)
if cabs(tabAB+im*gQ*gR)<2
gR = -gR
endif
gz0 = (tab-2)*(tb+gR)/(tb*tab-2*ta+im*gQ*tab)
mob[0] = new Mobius((tb-im*gQ)/2, (tb*tab-2*ta-im*gQ*tab)/((2*tab+4)*gz0),\
(tb*tab-2*ta+im*gQ*tab)*gz0/(2*tab-4), (tb+im*gQ)/2)
mob[1] = new Mobius(mob[0].m_d, -mob[0].m_b, -mob[0].m_c, mob[0].m_a)
mob[2] = new Mobius(ta/2, (ta*tab-2*tb+2*im*gQ)/((2*tab+4)*gz0), \
(ta*tab-2*tb-2*im*gQ)*gz0/(2*tab-4), ta/2)
if @trans
temp1 = mob[2].m_b
mob[2].m_b = mob[2].m_c
mob[2].m_c = temp1
endif
mob[3] = new Mobius(mob[2].m_d, -mob[2].m_b, -mob[2].m_c, mob[2].m_a)
endif
if @cusptype == "Maskit"
if @showcuspm == "Predefined"
if @cuspm == "0/1"
m = (0,2)
radam = 0.5
elseif @cuspm == "1/15"
m = (-0.0112785606117653, 1.95859103011179)
radam = 0.489661311
elseif @cuspm == "1/10"
m = (-0.0362880775225429,1.91342329586682)
radam = 0.47852888
elseif @cuspm == "2/19"
m = (-0.0395799512688805,1.90377999779718)
radam = 0.35214005
elseif @cuspm == "1/9"
m = (-0.0487530128986506,1.89640725094921)
radam = 0.4744165
elseif @cuspm == "7/43"
m = (-0.136998687907137,1.80785523999043)
radam = 0.2983515
elseif @cuspm == "3/10"
m = (-0.5,1.65831239517773)
radam = 0.3015111
elseif @cuspm == "2/5"
m = (-0.766588417465459,1.64213876865348)
radam = 0.363491
elseif @cuspm == "1/2"
m = (-1,1.73205080756888)
radam = 0.57735015
elseif @cuspm == "21/34"
m = (1.29170028664218,1.6179907967521)
radam = 0.1997052
endif
endif
if @showcuspm == "Both" || (@showcuspm == "Predefined" \
&& @showcuspm2 == "Both")
Fc[0] = 1 + flip(radam)
Fr[0] = radam
Fc[1] = (1,0)
Fr[1] = 0
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
s.sph[1] = new Sphere(Fc[1],Fz[1],Fr[1],0,0)
ss.sph[0] = s.sph[0]
ss.sph[1] = s.sph[1]
elseif @showcuspm == "Alternate" || (@showcuspm == "Predefined" \
&& @showcuspm2 == "Alternate")
Fc[0] = 1 + flip(radam)
Fr[0] = radam
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
ss.sph[0] = s.sph[0]
else
Fc[0] = (1,0)
Fr[0] = 0
s.sph[0] = new Sphere(Fc[0],Fz[0],Fr[0],0,0)
ss.sph[0] = s.sph[0]
endif
mob[0] = new Mobius(m, 1, 1, 0)
mob[1] = new Mobius(mob[0].m_d, -mob[0].m_b, -mob[0].m_c, mob[0].m_a)
mob[2] = new Mobius(1, 0, 2, 1)
mob[3] = new Mobius(mob[2].m_d, -mob[2].m_b, -mob[2].m_c, mob[2].m_a)
endif
; normalize the matrices
i = 0
while i < 4
mob[i].Normalize(mob[i])
i = i + 1
endwhile
endfunc
; Inverts a sphere - Mobius inversion The return value may be a sphere or a plane.
; The Euclidian flavor is closely equivalent to Voronoi texturing.
; Jim Blue's random number generator was essential to its development.
; Additional methods of fractal modulation have been added based upon the
; Worley model.
public:
import "common.ulb"
import "jlb.ulb"
; Constructor
func REB_TrapShapeWorleyLite(Generic pparent)
TrapShape.TrapShape(pparent)
rndi = new JLB_Random(0)
rndi.Init(@seed)
rndi.SetNMax(5000)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
complex fzc
complex fzz
float dst
float dst2
complex fzc1
complex fzc2
complex fzc3
complex fzc4
complex cells[12]
float distance = 0
float test = 0
complex diff = 0
int rnds[24]
float rp[12]
float ip[12]
int i = 1
rnds[0] = rndi.RandomIntInRange(@seed)
while i < 24
rnds[i] = rndi.RandomIntInRange(0)
i = i + 1
endwhile
dst = 1e10
dst2 = 1e10
complex near = 0
complex z = (pz+(10,10))/@psize
fzc = round(z)
fzz = z - fzc
; create the grid
fzc1 = fzc + (1,1)/2
fzc2 = fzc + (1,-1)/2
fzc3 = fzc + (-1,1)/2
fzc4 = fzc + (-1,-1)/2
; create the random points
; cell 1
rp[0] = ((real(fzc1)-rnds[0])^5%rnds[6] - (imag(fzc1)+rnds[12])^3%rnds[18])^2 %2 - 1
ip[0] = ((real(fzc1)-rnds[1])^5%rnds[7] - (imag(fzc1)+rnds[13])^3%rnds[19])^2 %2 - 1
rp[1] = ((real(fzc1)-rnds[2])^5%rnds[8] - (imag(fzc1)+rnds[14])^3%rnds[20])^2 %2 - 1
ip[1] = ((real(fzc1)-rnds[3])^5%rnds[8] - (imag(fzc1)+rnds[15])^3%rnds[21])^2 %2 - 1
rp[2] = ((real(fzc1)-rnds[4])^5%rnds[10] - (imag(fzc1)+rnds[16])^3%rnds[22])^2 %2 - 1
ip[2] = ((real(fzc1)-rnds[5])^5%rnds[11] - (imag(fzc1)+rnds[17])^3%rnds[23])^2 %2 - 1
; cell 2
rp[3] = ((real(fzc2)-rnds[0])^5%rnds[6] - (imag(fzc2)+rnds[12])^3%rnds[18])^2 %2 - 1
ip[3] = ((real(fzc2)-rnds[1])^5%rnds[7] - (imag(fzc2)+rnds[13])^3%rnds[19])^2 %2 - 1
rp[4] = ((real(fzc2)-rnds[2])^5%rnds[8] - (imag(fzc2)+rnds[14])^3%rnds[20])^2 %2 - 1
ip[4] = ((real(fzc2)-rnds[3])^5%rnds[8] - (imag(fzc2)+rnds[15])^3%rnds[21])^2 %2 - 1
rp[5] = ((real(fzc2)-rnds[4])^5%rnds[10] - (imag(fzc2)+rnds[16])^3%rnds[22])^2 %2 - 1
ip[5] = ((real(fzc2)-rnds[5])^5%rnds[11] - (imag(fzc2)+rnds[17])^3%rnds[23])^2 %2 - 1
; cell 3
rp[6] = ((real(fzc3)-rnds[0])^5%rnds[6] - (imag(fzc3)+rnds[12])^3%rnds[18])^2 %2 - 1
ip[6] = ((real(fzc3)-rnds[1])^5%rnds[7] - (imag(fzc3)+rnds[13])^3%rnds[19])^2 %2 - 1
rp[7] = ((real(fzc3)-rnds[2])^5%rnds[8] - (imag(fzc3)+rnds[14])^3%rnds[20])^2 %2 - 1
ip[7] = ((real(fzc3)-rnds[3])^5%rnds[8] - (imag(fzc3)+rnds[15])^3%rnds[21])^2 %2 - 1
rp[8] = ((real(fzc3)-rnds[4])^5%rnds[10] - (imag(fzc3)+rnds[16])^3%rnds[22])^2 %2 - 1
ip[8] = ((real(fzc3)-rnds[5])^5%rnds[11] - (imag(fzc3)+rnds[17])^3%rnds[23])^2 %2 - 1
; cell 4
rp[9] = ((real(fzc4)-rnds[0])^5%rnds[6] - (imag(fzc4)+rnds[12])^3%rnds[18])^2 %2 - 1
ip[9] = ((real(fzc4)-rnds[1])^5%rnds[7] - (imag(fzc4)+rnds[13])^3%rnds[19])^2 %2 - 1
rp[10] = ((real(fzc4)-rnds[2])^5%rnds[8] - (imag(fzc4)+rnds[14])^3%rnds[20])^2 %2 - 1
ip[10] = ((real(fzc4)-rnds[3])^5%rnds[8] - (imag(fzc4)+rnds[15])^3%rnds[21])^2 %2 - 1
rp[11] = ((real(fzc4)-rnds[4])^5%rnds[10] - (imag(fzc4)+rnds[16])^3%rnds[22])^2 %2 - 1
ip[11] = ((real(fzc4)-rnds[5])^5%rnds[11] - (imag(fzc4)+rnds[17])^3%rnds[23])^2 %2 - 1
; put into the grids
cells[0] = (rp[0] + flip(ip[0]) + (1,1))/2
cells[1] = (rp[1] + flip(ip[1]) + (1,1))/2
cells[2] = (rp[2] + flip(ip[2]) + (1,1))/2
cells[3] = (rp[3] + flip(ip[3]) + (1,-1))/2
cells[4] = (rp[4] + flip(ip[4]) + (1,-1))/2
cells[5] = (rp[5] + flip(ip[5]) + (1,-1))/2
cells[6] = (rp[6] + flip(ip[6]) + (-1,1))/2
cells[7] = (rp[7] + flip(ip[7]) + (-1,1))/2
cells[8] = (rp[8] + flip(ip[8]) + (-1,1))/2
cells[9] = (rp[9] + flip(ip[9]) + (-1,-1))/2
cells[10] = (rp[10] + flip(ip[10]) + (-1,-1))/2
cells[11] = (rp[11] + flip(ip[11]) + (-1,-1))/2
i = 0
while i < 12
diff = fzz - cells[i]
if @flavor == "Euclidian"
test = cabs(diff)
elseif @flavor == "Manhattan"
test = (abs(real(diff))^real(@mp) + abs(imag(diff))^imag(@mp))
elseif @flavor == "Chebychev"
if abs(real(diff)) > abs(imag(diff))
test = abs(real(diff))
else
test = abs(imag(diff))
endif
elseif @flavor == "Minkovsky"
test = (abs(real(diff))^@ex + abs(imag(diff))^@ex)^(1/@ex)
elseif @flavor == "Exp/Log Manhattan"
test = log(exp(abs(real(diff))) + exp(abs(imag(diff))))
endif
if test < dst
dst2 = dst
dst = test
near = fzc + cells[i]
elseif test < dst2
dst2 = test
endif
i = i + 1
endwhile
if @type == "Distance"
distance = dst^@thick
elseif @type == "2nd Distance"
distance = (@smod*dst2-dst)^@thick
elseif @type == "2nd Distance variant"
distance = dst2^@thick
elseif @type == "Mosaic"
distance = cabs(1000*near) + 1000*atan(cabs(near)+#pi)%1
endif
if @dmod != 0
distance = distance*@dmod
endif
if @type != "Mosaic"
if @invert
distance = abs(1-distance)
endif
else
distance = distance % 1
endif
m_LastZ = exp(flip(2 * #pi * sqrt(2) * distance))
return distance
endfunc
protected:
JLB_Random rndi
default:
title = "Worley Lite"
int param v_worleylite
caption = "Version (Worley Lite)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_worleylite < 100
endparam
param flavor
caption = "Flavor"
default = 4
enum = "Chebychev" "Euclidian" "Manhattan" "Exp/Log Manhattan" "Minkovsky"
endparam
float param ex
caption = "Minkovsky param"
default = 4
visible = @flavor == "Minkovsky"
endparam
complex param mp
caption = "Manhattan pwr"
default = (1,1)
visible = @flavor == "Manhattan"
endparam
param type
caption = "Worley type"
default = 2
enum = "Distance" "2nd Distance" "2nd Distance variant" "Mosaic"
endparam
float param smod
caption = "2nd dist mod"
default = 1.0
visible = @type == "2nd Distance"
endparam
param psize
caption = "Pattern Size"
default = .15
endparam
float param thick
caption = "Thickness"
default = 0.1
endparam
float param dmod
caption = "Dist modulator"
default = 0.0
min = 0.0
endparam
bool param invert
caption = "Invert"
default = false
visible = @type != "Mosaic"
endparam
int param seed
caption = "Worley seed"
default = 123
endparam
}
class REB_ConvolutionShapeWrapper(common.ulb:TrapShape) {
; This wrapper allows you to use any trap shape and any convolution
; filter to produce blurred or sharpened (or other) trap effects.
; This is largely based upon BlurTrapWrapper of Damien Jones
public:
import "common.ulb"
import "dmj5.ulb"
func REB_ConvolutionShapeWrapper(Generic pparent)
TrapShape.TrapShape(pparent)
m_Filter = new @f_filter(this)
m_Samples = length(m_Filter.m_Offsets)
if @f_filter != REB_MedianFilter && @f_filter != REB_ColorPencilFilter && \
@f_filter != REB_OilPaintFilter
setLength(m_TrapShapes, m_Samples)
int j = 0
while (j < m_Samples)
m_TrapShapes[j] = new @f_trapshape(this)
j = j + 1
endwhile
else
setLength(m_TrapShapes, 1)
setlength(med,m_samples)
m_TrapShapes[0] = new @f_trapshape(this)
endif
endfunc
func Init(complex pz)
TrapShape.Init(pz)
if @f_filter != REB_MedianFilter && @f_filter != REB_ColorPencilFilter && \
@f_filter != REB_OilPaintFilter
int j = 0
while (j < m_Samples)
m_TrapShapes[j].Init(pz)
j = j + 1
endwhile
else
m_TrapShapes[0].Init(pz)
endif
if (@p_filterreset == 0 && DMJ_VariableConvolutionFilter(m_Filter) != 0)
m_Filter.Init(pz)
endif
endfunc
float func Iterate(complex pz)
trapshape.Iterate(pz)
if (@p_filterreset == 1 && DMJ_VariableConvolutionFilter(m_Filter) != 0)
m_Filter.Init(pz)
endif
float dist = 0
float d = 0
float w = 0
float o = 0
int j = 0
if @f_filter != REB_MedianFilter && @f_filter != REB_ColorPencilFilter && \
@f_filter != REB_OilPaintFilter
while (j < m_Samples)
dist = m_TrapShapes[j].Iterate(pz+m_Filter.m_Offsets[j])
w = m_Filter.m_Weights[j]
d = d + dist * w
j = j + 1
endwhile
w = m_Filter.m_Multiplier
o = m_Filter.m_Bias
d = d * w + o
else
int k = 0
int l = 0
float tmp = 0
int si = 0
int sj = 0
bool continue = true
float dmin = 1e10
float dmax = 0
int bin[100]
while k < 100
bin[k] = 0
k = k + 1
endwhile
int val = 0
float maxval = 0
int maxvalidx = 0
k = 0
j = 0
while (j < m_Samples)
med[j] = m_TrapShapes[0].Iterate(pz+m_Filter.m_Offsets[j])
if @f_filter == REB_ColorPencilFilter
if med[j] < dmin
dmin = med[j]
endif
if med[j] > dmax
dmax = med[j]
endif
endif
if @f_filter == REB_OilPaintFilter
; create a 100 bin histogram to determine the most common value
val = round(med[j]*100) % 100
bin[val] = bin[val] + 1
if maxval < bin[val]
maxval = bin[val]
maxvalidx = j
endif
endif
j = j + 1
endwhile
if @f_filter == REB_MedianFilter
;heapsort without recursion
l = round(m_samples/2)+1
k = m_samples
tmp = 0
repeat
if l > 1
l = l-1
tmp = med[l-1]
else
tmp = med[k-1]
med[k-1] = med[0]
k = k-1
if k == 0
med[0] = tmp
continue = false
endif
endif
if continue == true
si = l
sj = 2*l
endif
while (sj <= k) && (continue == true)
if sj < k
if med[sj-1] < med[sj]
sj = sj + 1
endif
endif
if tmp < med[sj-1]
med[si-1] = med[sj-1]
si = sj
sj = sj + sj
else
sj = k + 1
endif
endwhile
if (continue == true)
med[si-1] = tmp
endif
until continue == false
; end heapsort
d = med[round(m_samples/2)]
endif
if @f_filter == REB_ColorPencilFilter
float r = med[round(m_samples/2)]
float md = 0
float maskr = 0
if r == dmax
md = 0
else
md = abs(r-dmin)
if md < abs(r-dmax)
md = abs(r-dmax)
endif
endif
md = md*255
r = r*255
maskr = 1/(md/(sqrt(r+1)/3)+1)
d = (r + @cpr*((255-r)*maskr-md*r/100))/255
endif
if @f_filter == REB_OilPaintFilter
d = med[maxvalidx]
endif
endif
return d
endfunc
protected:
DMJ_ConvolutionFilter m_Filter
int m_Samples
TrapShape m_TrapShapes[]
float med[]
default:
title = "Convolution Shape Wrapper"
int param v_REB_ConvolutionShapeWrapper
caption = "Version (REB_ConvolutionShapeWrapper)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_REB_ConvolutionShapeWrapper < 100
endparam
heading
text = "To use with image import (images as textures) replace the \
trap shape under Trap Position with Image Tile Texture."
endheading
TrapShape param f_trapshape
caption = "Trap Shape"
default = TrapShapeBlock
hint = "Sets the trap shape that the convolution filter will be applied to."
endparam
DMJ_ConvolutionFilter param f_filter
caption = "Convolution Filter"
default = REB_NullFilter
hint = "Sets the filter that will be applied."
endparam
float param cpr
caption = "Color Pencil Intensity"
default = 0.5
visible = @f_filter == REB_ColorPencilFilter
endparam
int param p_filterreset
caption = "Reset Filter"
default = 1
enum = "first iteration" "every iteration"
hint = "Some convolution filters are position-dependent: the filter's effect varies from one part of the complex plane to another. For this kind of filter, you may choose whether to recompute the filter's effect only at the first iteration or on every iteration."
visible = (@f_filter == DMJ_VariableConvolutionFilter)
endparam
}
class Monnier_SFBM_II_Texture(common.ulb:TrapShape) {
; Trap shape based upon Sam Monnier's S.F.B.M. II ucl
; Converts the colors of an imported image to greyscale and then converts
; the greyscale value to a complex number to use as a texture.
;
public:
import "common.ulb"
; Constructor
func REB_ImageTileTexture(Generic pparent)
TrapShape.TrapShape(pparent)
m_img = new @f_image(0)
m_empty = m_img.GetEmpty()
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
color pcolor = rgba(0,0,0,0)
if !m_empty
complex m_zi = (0,1)^(@iangle/90.0)
complex m_zs = (0,1)^(@sangle/90.0)
complex pzrs = pz
; offset
if !@itile
pzrs = pzrs+@ioffset
endif
; aspect ratio
pzrs = real(pzrs) + flip(imag(pzrs)*@iaspect)
; rotation
pzrs = pzrs*m_zi
; skew
pzrs = real(pzrs)*m_zs + flip(imag(pzrs))
float width = m_img.getWidth()
float height = m_img.getHeight()
if @itile
if @v_trapshapeimagetiletexture >= 103
pzrs = (pzrs+500+flip(500))*@scale*500
else
pzrs = (pzrs+#width/2+flip(#height/2))*@scale*#width
endif
complex c = @adjx-2*((real(pzrs) % (width-1))/width) + \
flip(@adjy-2*((imag(pzrs) % (height-1))/height))
pcolor = m_img.getColor(c)
else
pcolor = m_img.getColor(pzrs*@scale)
endif
endif
m_LastZ = exp(flip(2 * #pi * sqrt(2) * (1 - (0.3 * red(pcolor)+ 0.59 * green(pcolor) + 0.11 * blue(pcolor)))))
return 1 - (0.3 * red(pcolor)+ 0.59 * green(pcolor) + 0.11 * blue(pcolor))
endfunc
protected:
ImageImport m_img
int m_image_width
int m_image_height
float m_ratio
bool m_empty
default:
title = "Image Tile Texture"
int param v_trapshapeimagetiletexture
caption = "Version (Trap Shape Image Tile Texture)"
default = 103
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeimagetiletexture < 103
endparam
heading
caption = "Image Parameters"
endheading
ImageImport param f_image
caption = "Image"
default = ImageImport
endparam
float param scale
caption = "Image scale"
default = 1
min = 0
hint = "Changes the scale of the image."
endparam
float param adjx
caption = "Tile adj x"
default = 0.99
min = 0.9
max = 1.1
endparam
float param adjy
caption = "Tile adj y"
default = 0.999
min = 0.9
max = 1.1
endparam
complex param ioffset
caption = "Image offset"
default = (0,0)
visible = !@itile
endparam
float param iaspect
caption = "Image aspect"
default = 1.0
endparam
float param iangle
caption = "Image rotation"
default = 0
hint = "Rotates the image"
endparam
float param sangle
caption = "Image skew"
default = 0
hint = "Skews the image"
endparam
bool param itile
caption = "Tile the image"
default = false
endparam
}
class REB_TrapShapeChip(common.ulb:TrapShape) {
; Based upon the Chip strange attractor. Can also be used as a texture.
; This class can be used to explore in the two "hybridised" planes.
; Type SJ iterates in the "zc" plane, and type 3RDIM in the "cz" plane.
; The trap can create multiple fractal images of the chosen function.
public:
import "common.ulb"
; Constructor
func REB_TrapShape4DOrbit(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
p = (0,0)
px = pz*@scale
c = 0
if @function == "Julia Frame-Robert" || @function == "Julia Ikenaga" || \
@function == "Julia Lambda" || @function == "Julia"
px = @seed
p = pz*@scale
endif
if @variant == "SJ"
p = real(p) + flip(imag(p)*@r)
c = @t + @r*real(px) + flip(imag(px))
else
p = @r*real(p) + flip(imag(p))
c = @t + real(px) + flip(imag(px)*@r)
endif
p = @fn1(p)
rt_iter = 0
while rt_iter < @max_iterations && (|p| < @bailout)
if @function == "Mandelbrot" || @function == "Julia"
p = p*p + c
elseif @function == "Julia Lambda"
p = c*p*(1-p)
elseif @function == "Ikenaga" || @function == "Julia Ikenaga"
p = p*p*p + (c-1)*p-c
elseif @function == "Frame-Robert" || @function == "Julia Frame-Robert"
p = p*p*p/5 + p*p + c
endif
rt_iter = rt_iter + 1
endwhile
m_LastZ = @fn2(p)
float d = abs(cabs(pz)-cabs(m_LastZ))
return d
endfunc
protected:
complex p
complex px
complex c
int rt_iter
default:
title = "4D Orbit"
int param v_trapshape4dorbit
caption = "Version (Trap Shape 4D Orbit)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshape4dorbit < 101
endparam
param t
caption = "Translation"
default = -0.75
endparam
param r
caption = "Tilt"
default = 0.5
min = 0
max = 1
hint = "This parameter takes values between 0 and 1 inclusive."
endparam
param variant
caption = "4D variant"
default = 0
enum = "SJ" "3RDIM"
hint = "These variants are based upon Gordon Lamb's 4D formulas."
endparam
param max_iterations
caption = "4D iterations"
hint = "This is the number of iterations for the 4D formula."
default = 10
endparam
float param bailout
caption = "Bailout"
default = 10000.0
endparam
float param scale
caption = "Scale"
default = 1.0
endparam
param function
caption = "4D Fractal"
default = 1
enum = "Frame-Robert" "Ikenaga" "Mandelbrot" "Julia Frame-Robert" \
"Julia Ikenaga" "Julia Lambda" "Julia"
endparam
complex param seed
caption = "Julia seed"
default = (0,0)
visible = @function == "Julia Frame-Robert" || @function == "Julia Ikenaga" \
|| @function == "Julia Lambda" || @function == "Julia"
endparam
func fn1
caption = "Pre Function"
default = ident()
endfunc
func fn2
caption = "Post Function"
default = ident()
endfunc
}
class REB_TrapShapeCosMartin(common.ulb:TrapShape) {
; Uses the CosMartin strange attractor as the trap shape. Can also be used as a texture.
; The Sprott attractors were developed by Julien C. Sprott, and are
; based upon polynomials and linear differential equations of polynomials.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSprott3D(Generic pparent)
TrapShape.TrapShape(pparent)
s3[0,1]=0.3,s3[0,2]=-0.8,s3[0,3]=-0.8,s3[0,4]=1.2,s3[0,5]=0.6,s3[0,6]=0.3,s3[0,7]=-0.7,s3[0,8]=0.5,s3[0,9]=-0.7,s3[0,10]=0.1,s3[0,11]=0.1,s3[0,12]=-0.4,s3[0,13]=0.7,s3[0,14]=0.7
s3[0,15]=-0.3,s3[0,16]=-0.5,s3[0,17]=1.0,s3[0,18]=-0.7,s3[0,19]=0.9,s3[0,20]=-0.3,s3[0,21]=0.1,s3[0,22]=0.8,s3[0,23]=0.4,s3[0,24]=-1.0,s3[0,25]=0.3,s3[0,26]=-1.0,s3[0,27]=0.6,s3[0,28]=0.2,s3[0,29]=-0.5,s3[0,30]=0.7
s3[1,1]=0.2,s3[1,2]=-0.6,s3[1,3]=1.1,s3[1,4]=-0.9,s3[1,5]=1.0,s3[1,6]=-0.4,s3[1,7]=1.2,s3[1,8]=-0.2,s3[1,9]=-0.3,s3[1,10]=-0.3,s3[1,11]=0.2,s3[1,12]=-0.5,s3[1,13]=0.7,s3[1,14]=0.3
s3[1,15]=-0.5,s3[1,16]=-0.1,s3[1,17]=0.2,s3[1,18]=-1.1,s3[1,19]=-0.2,s3[1,20]=-0.9,s3[1,21]=-0.6,s3[1,22]=0.5,s3[1,23]=1.1,s3[1,24]=-0.7,s3[1,25]=-0.9,s3[1,26]=-0.5,s3[1,27]=0.8,s3[1,28]=0.6,s3[1,29]=0.9,s3[1,30]=0.9
s3[2,1]=-1.0,s3[2,2]=0.2,s3[2,3]=-0.2,s3[2,4]=-0.1,s3[2,5]=-0.5,s3[2,6]=1.0,s3[2,7]=-0.5,s3[2,8]=-0.6,s3[2,9]=0.8,s3[2,10]=0.6,s3[2,11]=0.2,s3[2,12]=-0.9,s3[2,13]=-1.0,s3[2,14]=0.8
s3[2,15]=0.4,s3[2,16]=-0.4,s3[2,17]=0.3,s3[2,18]=-0.5,s3[2,19]=1.2,s3[2,20]=-0.5,s3[2,21]=0.8,s3[2,22]=-0.7,s3[2,23]=-0.6,s3[2,24]=-1.1,s3[2,25]=0.1,s3[2,26]=-1.2,s3[2,27]=-0.1,s3[2,28]=1.1,s3[2,29]=0.3,s3[2,30]=-1.0
s3[3,1]=-0.2,s3[3,2]=0.5,s3[3,3]=-0.6,s3[3,4]=0.3,s3[3,5]=0.6,s3[3,6]=-1.1,s3[3,7]=0.7,s3[3,8]=-0.3,s3[3,9]=0.6,s3[3,10]=-0.7,s3[3,11]=-0.3,s3[3,12]=0.6,s3[3,13]=-0.6,s3[3,14]=0.4
s3[3,15]=-1.1,s3[3,16]=-0.6,s3[3,17]=0.7,s3[3,18]=-1.2,s3[3,19]=0.5,s3[3,20]=-1.1,s3[3,21]=0.7,s3[3,22]=0.0,s3[3,23]=-0.4,s3[3,24]=0.1,s3[3,25]=0.5,s3[3,26]=0.4,s3[3,27]=-0.5,s3[3,28]=0.4,s3[3,29]=0.5,s3[3,30]=-0.9
s3[4,1]=-0.4,s3[4,2]=0.6,s3[4,3]=1.2,s3[4,4]=-0.5,s3[4,5]=1.0,s3[4,6]=-0.6,s3[4,7]=-1.0,s3[4,8]=1.2,s3[4,9]=0.4,s3[4,10]=0.8,s3[4,11]=-0.6,s3[4,12]=0.9,s3[4,13]=0.6,s3[4,14]=0.0
s3[4,15]=0.1,s3[4,16]=-0.8,s3[4,17]=0.2,s3[4,18]=-0.1,s3[4,19]=-0.5,s3[4,20]=-0.3,s3[4,21]=-0.4,s3[4,22]=0.6,s3[4,23]=0.0,s3[4,24]=-0.8,s3[4,25]=-1.0,s3[4,26]=-0.6,s3[4,27]=-1.2,s3[4,28]=0.8,s3[4,29]=-0.6,s3[4,30]=0.9
s3[5,1]=-1.1,s3[5,2]=-0.9,s3[5,3]=-0.4,s3[5,4]=-0.9,s3[5,5]=0.3,s3[5,6]=-0.7,s3[5,7]=0.5,s3[5,8]=0.7,s3[5,9]=0.4,s3[5,10]=0.2,s3[5,11]=-0.1,s3[5,12]=-1.0,s3[5,13]=-0.6,s3[5,14]=-0.5
s3[5,15]=0.6,s3[5,16]=-1.0,s3[5,17]=1.2,s3[5,18]=-0.5,s3[5,19]=-1.0,s3[5,20]=1.2,s3[5,21]=0.5,s3[5,22]=-1.0,s3[5,23]=-0.2,s3[5,24]=-0.9,s3[5,25]=0.6,s3[5,26]=0.4,s3[5,27]=-1.0,s3[5,28]=0.5,s3[5,29]=-0.1,s3[5,30]=-0.1
s3[6,1]=-0.2,s3[6,2]=0.8,s3[6,3]=0.9,s3[6,4]=1.0,s3[6,5]=0.7,s3[6,6]=-0.7,s3[6,7]=0.4,s3[6,8]=1.1,s3[6,9]=-0.8,s3[6,10]=1.0,s3[6,11]=0.8,s3[6,12]=0.5,s3[6,13]=-0.1,s3[6,14]=-0.5
s3[6,15]=-0.2,s3[6,16]=-0.9,s3[6,17]=-0.5,s3[6,18]=-0.8,s3[6,19]=0.6,s3[6,20]=0.7,s3[6,21]=-0.1,s3[6,22]=-0.3,s3[6,23]=-0.8,s3[6,24]=0.5,s3[6,25]=-0.6,s3[6,26]=0.3,s3[6,27]=-0.1,s3[6,28]=-0.1,s3[6,29]=0.6,s3[6,30]=0.8
s3[7,1]=-0.2,s3[7,2]=0.3,s3[7,3]=-1.2,s3[7,4]=-0.8,s3[7,5]=-1.0,s3[7,6]=0.4,s3[7,7]=-0.3,s3[7,8]=1.0,s3[7,9]=1.0,s3[7,10]=-0.8,s3[7,11]=0.1,s3[7,12]=0.8,s3[7,13]=1.2,s3[7,14]=-0.6
s3[7,15]=0.3,s3[7,16]=-1.2,s3[7,17]=1.2,s3[7,18]=0.8,s3[7,19]=0.5,s3[7,20]=-0.6,s3[7,21]=0.4,s3[7,22]=0.1,s3[7,23]=-0.4,s3[7,24]=-0.8,s3[7,25]=-0.6,s3[7,26]=-0.6,s3[7,27]=-0.7,s3[7,28]=-0.3,s3[7,29]=-0.4,s3[7,30]=-0.1
s3[8,1]=1.0,s3[8,2]=-0.4,s3[8,3]=-1.1,s3[8,4]=0.6,s3[8,5]=-0.2,s3[8,6]=-0.7,s3[8,7]=-0.7,s3[8,8]=-0.1,s3[8,9]=1.0,s3[8,10]=1.2,s3[8,11]=-0.2,s3[8,12]=1.2,s3[8,13]=-0.9,s3[8,14]=-0.6
s3[8,15]=0.6,s3[8,16]=-0.1,s3[8,17]=-0.4,s3[8,18]=0.8,s3[8,19]=0.1,s3[8,20]=-0.3,s3[8,21]=-0.1,s3[8,22]=0.5,s3[8,23]=-0.7,s3[8,24]=0.2,s3[8,25]=-0.8,s3[8,26]=-0.6,s3[8,27]=-0.6,s3[8,28]=-1.0,s3[8,29]=0.4,s3[8,30]=1.0
s3[9,1]=0.6,s3[9,2]=-0.3,s3[9,3]=-0.8,s3[9,4]=-0.2,s3[9,5]=0.7,s3[9,6]=0.4,s3[9,7]=1.2,s3[9,8]=0.7,s3[9,9]=0.2,s3[9,10]=0.5,s3[9,11]=0.1,s3[9,12]=-0.8,s3[9,13]=0.2,s3[9,14]=-0.6
s3[9,15]=0.8,s3[9,16]=0.3,s3[9,17]=0.0,s3[9,18]=0.7,s3[9,19]=-1.1,s3[9,20]=0.2,s3[9,21]=-0.7,s3[9,22]=1.0,s3[9,23]=1.2,s3[9,24]=0.8,s3[9,25]=0.5,s3[9,26]=0.0,s3[9,27]=-0.7,s3[9,28]=-0.9,s3[9,29]=0.5,s3[9,30]=1.1
s3[10,1]=-0.2,s3[10,2]=0.4,s3[10,3]=0.7,s3[10,4]=1.2,s3[10,5]=0.5,s3[10,6]=1.0,s3[10,7]=-1.1,s3[10,8]=0.0,s3[10,9]=1.2,s3[10,10]=-0.6,s3[10,11]=0.1,s3[10,12]=-1.1,s3[10,13]=-0.5,s3[10,14]=0.1
s3[10,15]=-0.7,s3[10,16]=-0.6,s3[10,17]=0.0,s3[10,18]=0.2,s3[10,19]=0.6,s3[10,20]=0.6,s3[10,21]=0.3,s3[10,22]=-0.5,s3[10,23]=-0.2,s3[10,24]=0.6,s3[10,25]=1.1,s3[10,26]=-0.4,s3[10,27]=0.7,s3[10,28]=-0.1,s3[10,29]=-0.2,s3[10,30]=-0.8
s3[11,1]=0.1,s3[11,2]=0.6,s3[11,3]=-0.5,s3[11,4]=0.9,s3[11,5]=0.0,s3[11,6]=-0.4,s3[11,7]=1.0,s3[11,8]=-0.8,s3[11,9]=1.2,s3[11,10]=0.9,s3[11,11]=0.1,s3[11,12]=0.1,s3[11,13]=-0.3,s3[11,14]=0.6
s3[11,15]=0.8,s3[11,16]=0.1,s3[11,17]=0.2,s3[11,18]=-1.0,s3[11,19]=0.3,s3[11,20]=-0.9,s3[11,21]=0.7,s3[11,22]=0.3,s3[11,23]=-0.7,s3[11,24]=-1.0,s3[11,25]=1.0,s3[11,26]=0.9,s3[11,27]=-0.5,s3[11,28]=0.1,s3[11,29]=0.2,s3[11,30]=-1.1
s3[12,1]=1.0,s3[12,2]=-0.4,s3[12,3]=-0.3,s3[12,4]=-0.4,s3[12,5]=-0.2,s3[12,6]=0.6,s3[12,7]=-0.8,s3[12,8]=1.2,s3[12,9]=0.9,s3[12,10]=0.6,s3[12,11]=-0.1,s3[12,12]=0.3,s3[12,13]=-0.6,s3[12,14]=0.0
s3[12,15]=-0.3,s3[12,16]=-0.8,s3[12,17]=-0.1,s3[12,18]=0.0,s3[12,19]=0.7,s3[12,20]=1.0,s3[12,21]=-0.9,s3[12,22]=0.6,s3[12,23]=0.6,s3[12,24]=0.4,s3[12,25]=0.8,s3[12,26]=-0.6,s3[12,27]=0.7,s3[12,28]=-0.4,s3[12,29]=1.1,s3[12,30]=1.0
s3[13,1]=1.2,s3[13,2]=0.7,s3[13,3]=-0.9,s3[13,4]=-1.1,s3[13,5]=1.2,s3[13,6]=-0.4,s3[13,7]=-0.7,s3[13,8]=0.8,s3[13,9]=-0.9,s3[13,10]=0.4,s3[13,11]=0.0,s3[13,12]=0.3,s3[13,13]=-0.5,s3[13,14]=-0.6
s3[13,15]=-0.9,s3[13,16]=0.7,s3[13,17]=0.5,s3[13,18]=0.2,s3[13,19]=-0.2,s3[13,20]=-1.0,s3[13,21]=-0.1,s3[13,22]=-0.1,s3[13,23]=0.1,s3[13,24]=-0.5,s3[13,25]=-0.2,s3[13,26]=1.1,s3[13,27]=-0.4,s3[13,28]=0.8,s3[13,29]=-0.1,s3[13,30]=-1.0
s3[14,1]=-0.5,s3[14,2]=0.1,s3[14,3]=0.7,s3[14,4]=-0.6,s3[14,5]=0.9,s3[14,6]=-0.9,s3[14,7]=-0.5,s3[14,8]=-0.9,s3[14,9]=0.3,s3[14,10]=-0.3,s3[14,11]=-0.3,s3[14,12]=-0.3,s3[14,13]=-0.2,s3[14,14]=0.8
s3[14,15]=0.4,s3[14,16]=0.3,s3[14,17]=1.1,s3[14,18]=-0.6,s3[14,19]=-0.2,s3[14,20]=0.1,s3[14,21]=1.2,s3[14,22]=0.2,s3[14,23]=0.2,s3[14,24]=-1.1,s3[14,25]=0.9,s3[14,26]=0.3,s3[14,27]=0.9,s3[14,28]=-1.1,s3[14,29]=1.2,s3[14,30]=-0.7
s3[15,1]=-0.5,s3[15,2]=-0.5,s3[15,3]=0.9,s3[15,4]=0.3,s3[15,5]=-0.3,s3[15,6]=-0.7,s3[15,7]=0.9,s3[15,8]=-0.9,s3[15,9]=-0.2,s3[15,10]=0.1,s3[15,11]=0.0,s3[15,12]=0.7,s3[15,13]=0.5,s3[15,14]=0.9
s3[15,15]=0.4,s3[15,16]=0.2,s3[15,17]=0.9,s3[15,18]=0.1,s3[15,19]=-0.3,s3[15,20]=1.2,s3[15,21]=0.7,s3[15,22]=-0.3,s3[15,23]=-1.2,s3[15,24]=-0.2,s3[15,25]=0.7,s3[15,26]=-1.1,s3[15,27]=-0.5,s3[15,28]=1.2,s3[15,29]=0.4,s3[15,30]=-1.0
s3[16,1]=-1.0,s3[16,2]=-0.2,s3[16,3]=-0.2,s3[16,4]=-0.3,s3[16,5]=-0.5,s3[16,6]=-1.1,s3[16,7]=0.0,s3[16,8]=1.0,s3[16,9]=0.6,s3[16,10]=0.9,s3[16,11]=-0.3,s3[16,12]=0.9,s3[16,13]=1.1,s3[16,14]=-1.1
s3[16,15]=0.2,s3[16,16]=0.3,s3[16,17]=0.5,s3[16,18]=0.2,s3[16,19]=-0.2,s3[16,20]=0.3,s3[16,21]=0.5,s3[16,22]=-0.6,s3[16,23]=-1.2,s3[16,24]=1.1,s3[16,25]=0.4,s3[16,26]=0.3,s3[16,27]=-0.5,s3[16,28]=0.2,s3[16,29]=-0.3,s3[16,30]=-0.7
s3[17,1]=0.1,s3[17,2]=0.4,s3[17,3]=0.0,s3[17,4]=-0.6,s3[17,5]=1.0,s3[17,6]=0.8,s3[17,7]=1.0,s3[17,8]=-0.2,s3[17,9]=-0.9,s3[17,10]=-0.2,s3[17,11]=-0.6,s3[17,12]=-1.1,s3[17,13]=0.7,s3[17,14]=-0.7
s3[17,15]=0.0,s3[17,16]=-0.8,s3[17,17]=0.3,s3[17,18]=0.6,s3[17,19]=-0.1,s3[17,20]=1.2,s3[17,21]=0.2,s3[17,22]=-0.8,s3[17,23]=-1.2,s3[17,24]=0.4,s3[17,25]=0.9,s3[17,26]=0.0,s3[17,27]=-0.4,s3[17,28]=-0.7,s3[17,29]=-0.3,s3[17,30]=-0.2
s3[18,1]=-0.6,s3[18,2]=1.2,s3[18,3]=1.2,s3[18,4]=1.0,s3[18,5]=0.2,s3[18,6]=0.5,s3[18,7]=0.5,s3[18,8]=0.6,s3[18,9]=0.5,s3[18,10]=0.9,s3[18,11]=-0.7,s3[18,12]=1.1,s3[18,13]=1.2,s3[18,14]=0.3
s3[18,15]=0.2,s3[18,16]=-0.2,s3[18,17]=0.6,s3[18,18]=1.1,s3[18,19]=0.0,s3[18,20]=-0.4,s3[18,21]=0.5,s3[18,22]=0.7,s3[18,23]=-0.5,s3[18,24]=0.9,s3[18,25]=1.0,s3[18,26]=0.2,s3[18,27]=-0.6,s3[18,28]=0.2,s3[18,29]=0.0,s3[18,30]=0.2
s3[19,1]=0.6,s3[19,2]=0.7,s3[19,3]=-1.0,s3[19,4]=-1.1,s3[19,5]=1.0,s3[19,6]=0.7,s3[19,7]=0.1,s3[19,8]=-0.2,s3[19,9]=-0.8,s3[19,10]=-0.4,s3[19,11]=-0.1,s3[19,12]=-0.4,s3[19,13]=0.9,s3[19,14]=-0.8
s3[19,15]=-0.1,s3[19,16]=-0.6,s3[19,17]=-0.7,s3[19,18]=-0.1,s3[19,19]=-0.1,s3[19,20]=-0.1,s3[19,21]=-0.1,s3[19,22]=0.9,s3[19,23]=-0.3,s3[19,24]=0.3,s3[19,25]=-0.1,s3[19,26]=-0.9,s3[19,27]=0.3,s3[19,28]=0.3,s3[19,29]=-0.8,s3[19,30]=-0.5
s3[20,1]=0.4,s3[20,2]=0.7,s3[20,3]=-1.2,s3[20,4]=0.6,s3[20,5]=1.0,s3[20,6]=0.2,s3[20,7]=-0.3,s3[20,8]=0.1,s3[20,9]=0.7,s3[20,10]=-1.0,s3[20,11]=0.4,s3[20,12]=0.7,s3[20,13]=1.2,s3[20,14]=-1.1
s3[20,15]=0.8,s3[20,16]=0.8,s3[20,17]=-1.0,s3[20,18]=-1.2,s3[20,19]=1.0,s3[20,20]=-1.1,s3[20,21]=0.0,s3[20,22]=-0.9,s3[20,23]=-1.2,s3[20,24]=1.0,s3[20,25]=-0.1,s3[20,26]=0.0,s3[20,27]=-0.2,s3[20,28]=-1.1,s3[20,29]=-0.7,s3[20,30]=-0.3
s3[21,1]=0.3,s3[21,2]=1.1,s3[21,3]=-0.9,s3[21,4]=-1.2,s3[21,5]=0.2,s3[21,6]=-0.1,s3[21,7]=-1.2,s3[21,8]=1.1,s3[21,9]=0.3,s3[21,10]=0.2,s3[21,11]=-0.8,s3[21,12]=0.3,s3[21,13]=1.2,s3[21,14]=-1.2
s3[21,15]=1.1,s3[21,16]=-0.1,s3[21,17]=0.9,s3[21,18]=-0.7,s3[21,19]=0.2,s3[21,20]=0.8,s3[21,21]=-0.7,s3[21,22]=-0.3,s3[21,23]=0.5,s3[21,24]=-0.1,s3[21,25]=-0.1,s3[21,26]=0.3,s3[21,27]=0.0,s3[21,28]=-1.1,s3[21,29]=-0.4,s3[21,30]=0.4
s3[22,1]=0.5,s3[22,2]=-0.7,s3[22,3]=-1.1,s3[22,4]=0.1,s3[22,5]=-0.5,s3[22,6]=0.3,s3[22,7]=-0.2,s3[22,8]=-0.9,s3[22,9]=-0.7,s3[22,10]=-0.1,s3[22,11]=-0.6,s3[22,12]=-1.0,s3[22,13]=-0.9,s3[22,14]=0.1
s3[22,15]=-0.7,s3[22,16]=-0.7,s3[22,17]=-0.6,s3[22,18]=-1.1,s3[22,19]=-1.1,s3[22,20]=0.2,s3[22,21]=-0.6,s3[22,22]=-0.2,s3[22,23]=-0.9,s3[22,24]=-0.2,s3[22,25]=-0.6,s3[22,26]=-0.6,s3[22,27]=0.0,s3[22,28]=0.6,s3[22,29]=-0.9,s3[22,30]=-1.1
s3[23,1]=0.8,s3[23,2]=-0.7,s3[23,3]=-0.9,s3[23,4]=-1.0,s3[23,5]=-0.3,s3[23,6]=0.9,s3[23,7]=0.5,s3[23,8]=-0.1,s3[23,9]=0.7,s3[23,10]=-1.0,s3[23,11]=0.5,s3[23,12]=-1.0,s3[23,13]=0.3,s3[23,14]=1.1
s3[23,15]=-0.2,s3[23,16]=-0.4,s3[23,17]=-0.2,s3[23,18]=1.0,s3[23,19]=0.4,s3[23,20]=-0.7,s3[23,21]=0.5,s3[23,22]=-1.2,s3[23,23]=-0.5,s3[23,24]=0.8,s3[23,25]=0.2,s3[23,26]=-0.8,s3[23,27]=0.0,s3[23,28]=1.1,s3[23,29]=-0.2,s3[23,30]=0.5
s3[24,1]=-1.0,s3[24,2]=-0.2,s3[24,3]=1.1,s3[24,4]=0.3,s3[24,5]=-0.4,s3[24,6]=-0.2,s3[24,7]=0.6,s3[24,8]=-0.1,s3[24,9]=0.5,s3[24,10]=-0.7,s3[24,11]=0.7,s3[24,12]=-0.4,s3[24,13]=0.7,s3[24,14]=0.2
s3[24,15]=-0.2,s3[24,16]=0.2,s3[24,17]=-1.2,s3[24,18]=0.0,s3[24,19]=0.0,s3[24,20]=-1.2,s3[24,21]=-0.5,s3[24,22]=-0.4,s3[24,23]=0.5,s3[24,24]=0.2,s3[24,25]=-0.5,s3[24,26]=-0.1,s3[24,27]=0.6,s3[24,28]=-0.4,s3[24,29]=0.1,s3[24,30]=1.0
s3[25,1]=-0.1,s3[25,2]=1.2,s3[25,3]=0.8,s3[25,4]=0.9,s3[25,5]=0.4,s3[25,6]=0.0,s3[25,7]=0.2,s3[25,8]=0.1,s3[25,9]=0.9,s3[25,10]=-1.1,s3[25,11]=-0.4,s3[25,12]=-0.4,s3[25,13]=0.5,s3[25,14]=-0.2
s3[25,15]=-0.8,s3[25,16]=-0.1,s3[25,17]=0.0,s3[25,18]=-0.6,s3[25,19]=0.9,s3[25,20]=0.9,s3[25,21]=-0.3,s3[25,22]=0.2,s3[25,23]=-0.3,s3[25,24]=1.1,s3[25,25]=1.0,s3[25,26]=0.0,s3[25,27]=0.8,s3[25,28]=-0.4,s3[25,29]=-0.4,s3[25,30]=-0.5
s3[26,1]=0.6,s3[26,2]=-1.0,s3[26,3]=-0.7,s3[26,4]=-1.0,s3[26,5]=-0.1,s3[26,6]=0.2,s3[26,7]=0.7,s3[26,8]=-1.2,s3[26,9]=0.5,s3[26,10]=0.2,s3[26,11]=0.3,s3[26,12]=-0.7,s3[26,13]=0.1,s3[26,14]=0.0
s3[26,15]=-0.9,s3[26,16]=-0.1,s3[26,17]=0.4,s3[26,18]=0.2,s3[26,19]=1.2,s3[26,20]=0.9,s3[26,21]=-0.7,s3[26,22]=-0.9,s3[26,23]=1.1,s3[26,24]=-0.7,s3[26,25]=-0.5,s3[26,26]=0.9,s3[26,27]=0.9,s3[26,28]=0.8,s3[26,29]=1.0,s3[26,30]=0.7
s3[27,1]=-0.3,s3[27,2]=-0.4,s3[27,3]=0.9,s3[27,4]=-1.2,s3[27,5]=-1.1,s3[27,6]=0.2,s3[27,7]=0.9,s3[27,8]=0.7,s3[27,9]=-0.8,s3[27,10]=0.6,s3[27,11]=-0.3,s3[27,12]=-0.7,s3[27,13]=0.9,s3[27,14]=-0.3
s3[27,15]=0.1,s3[27,16]=-0.6,s3[27,17]=-1.1,s3[27,18]=0.0,s3[27,19]=-0.2,s3[27,20]=-0.1,s3[27,21]=1.0,s3[27,22]=-0.4,s3[27,23]=-0.7,s3[27,24]=-0.3,s3[27,25]=-0.2,s3[27,26]=1.2,s3[27,27]=1.1,s3[27,28]=0.5,s3[27,29]=-0.8,s3[27,30]=1.0
s3[28,1]=-0.5,s3[28,2]=0.4,s3[28,3]=-0.5,s3[28,4]=-1.0,s3[28,5]=-0.1,s3[28,6]=0.2,s3[28,7]=1.2,s3[28,8]=-1.1,s3[28,9]=0.4,s3[28,10]=1.0,s3[28,11]=-0.3,s3[28,12]=-0.6,s3[28,13]=0.2,s3[28,14]=0.7
s3[28,15]=-0.8,s3[28,16]=1.2,s3[28,17]=-0.6,s3[28,18]=-0.7,s3[28,19]=0.1,s3[28,20]=1.1,s3[28,21]=0.3,s3[28,22]=0.6,s3[28,23]=0.7,s3[28,24]=1.2,s3[28,25]=-0.4,s3[28,26]=0.3,s3[28,27]=-0.6,s3[28,28]=-0.1,s3[28,29]=-0.7,s3[28,30]=0.7
s3[29,1]=0.4,s3[29,2]=0.1,s3[29,3]=-0.4,s3[29,4]=0.4,s3[29,5]=1.1,s3[29,6]=-0.1,s3[29,7]=0.3,s3[29,8]=-1.1,s3[29,9]=0.1,s3[29,10]=-0.8,s3[29,11]=-0.5,s3[29,12]=-0.4,s3[29,13]=0.4,s3[29,14]=-0.6
s3[29,15]=-0.1,s3[29,16]=0.3,s3[29,17]=0.3,s3[29,18]=1.2,s3[29,19]=-0.4,s3[29,20]=-1.0,s3[29,21]=-0.8,s3[29,22]=-1.2,s3[29,23]=0.7,s3[29,24]=0.7,s3[29,25]=-1.1,s3[29,26]=-1.0,s3[29,27]=0.4,s3[29,28]=-1.0,s3[29,29]=0.8,s3[29,30]=0.0
s3[30,1]=-0.6,s3[30,2]=-0.5,s3[30,3]=-1.0,s3[30,4]=0.7,s3[30,5]=-0.9,s3[30,6]=-1.0,s3[30,7]=1.1,s3[30,8]=1.0,s3[30,9]=-0.9,s3[30,10]=0.8,s3[30,11]=0.4,s3[30,12]=0.0,s3[30,13]=-0.4,s3[30,14]=-0.7
s3[30,15]=-0.6,s3[30,16]=-1.2,s3[30,17]=0.8,s3[30,18]=-1.2,s3[30,19]=-0.3,s3[30,20]=-0.7,s3[30,21]=0.0,s3[30,22]=-0.9,s3[30,23]=-0.2,s3[30,24]=-0.2,s3[30,25]=-0.8,s3[30,26]=0.7,s3[30,27]=0.2,s3[30,28]=1.1,s3[30,29]=-0.2,s3[30,30]=-0.4
s3[31,1]=-0.1,s3[31,2]=-0.3,s3[31,3]=-0.2,s3[31,4]=-1.2,s3[31,5]=-0.2,s3[31,6]=-0.4,s3[31,7]=0.7,s3[31,8]=0.1,s3[31,9]=0.2,s3[31,10]=0.0,s3[31,11]=0.5,s3[31,12]=0.6,s3[31,13]=-0.1,s3[31,14]=1.0
s3[31,15]=1.1,s3[31,16]=-0.5,s3[31,17]=0.1,s3[31,18]=0.0,s3[31,19]=-0.1,s3[31,20]=0.1,s3[31,21]=1.0,s3[31,22]=0.4,s3[31,23]=-0.8,s3[31,24]=0.5,s3[31,25]=-0.1,s3[31,26]=0.0,s3[31,27]=-0.6,s3[31,28]=-0.6,s3[31,29]=-1.1,s3[31,30]=0.9
s3[32,1]=0.0,s3[32,2]=0.3,s3[32,3]=-0.2,s3[32,4]=-1.0,s3[32,5]=0.0,s3[32,6]=-0.7,s3[32,7]=1.1,s3[32,8]=0.4,s3[32,9]=0.2,s3[32,10]=0.1,s3[32,11]=0.1,s3[32,12]=0.7,s3[32,13]=-0.3,s3[32,14]=1.0
s3[32,15]=-1.0,s3[32,16]=-0.7,s3[32,17]=-0.6,s3[32,18]=-0.5,s3[32,19]=0.4,s3[32,20]=-0.4,s3[32,21]=0.2,s3[32,22]=-0.8,s3[32,23]=-0.3,s3[32,24]=-0.1,s3[32,25]=0.8,s3[32,26]=0.4,s3[32,27]=0.3,s3[32,28]=0.0,s3[32,29]=-1.2,s3[32,30]=0.4
s3[33,1]=0.9,s3[33,2]=-1.2,s3[33,3]=-0.2,s3[33,4]=-0.6,s3[33,5]=-0.7,s3[33,6]=0.5,s3[33,7]=0.9,s3[33,8]=-0.4,s3[33,9]=-0.4,s3[33,10]=-0.2,s3[33,11]=0.2,s3[33,12]=0.3,s3[33,13]=-0.5,s3[33,14]=0.7
s3[33,15]=0.3,s3[33,16]=-1.0,s3[33,17]=0.5,s3[33,18]=0.3,s3[33,19]=-0.3,s3[33,20]=0.2,s3[33,21]=-1.2,s3[33,22]=0.1,s3[33,23]=-1.0,s3[33,24]=1.0,s3[33,25]=-0.7,s3[33,26]=-1.2,s3[33,27]=1.1,s3[33,28]=-0.1,s3[33,29]=1.0,s3[33,30]=0.8
s3[34,1]=0.2,s3[34,2]=-0.8,s3[34,3]=-0.9,s3[34,4]=-0.5,s3[34,5]=-0.9,s3[34,6]=-0.7,s3[34,7]=-0.8,s3[34,8]=-0.6,s3[34,9]=0.9,s3[34,10]=-0.5,s3[34,11]=0.0,s3[34,12]=0.2,s3[34,13]=0.2,s3[34,14]=0.1
s3[34,15]=0.2,s3[34,16]=-0.6,s3[34,17]=0.9,s3[34,18]=-1.2,s3[34,19]=0.1,s3[34,20]=0.9,s3[34,21]=-0.2,s3[34,22]=0.4,s3[34,23]=0.1,s3[34,24]=-0.8,s3[34,25]=0.9,s3[34,26]=0.7,s3[34,27]=0.7,s3[34,28]=0.7,s3[34,29]=0.8,s3[34,30]=-0.3
s3[35,1]=-0.4,s3[35,2]=0.1,s3[35,3]=0.5,s3[35,4]=0.5,s3[35,5]=-0.3,s3[35,6]=1.1,s3[35,7]=1.1,s3[35,8]=1.0,s3[35,9]=-1.0,s3[35,10]=0.3,s3[35,11]=-0.2,s3[35,12]=0.3,s3[35,13]=-0.8,s3[35,14]=0.9
s3[35,15]=-0.6,s3[35,16]=-1.2,s3[35,17]=0.6,s3[35,18]=-0.6,s3[35,19]=0.1,s3[35,20]=0.3,s3[35,21]=-0.3,s3[35,22]=-0.1,s3[35,23]=0.1,s3[35,24]=0.3,s3[35,25]=-0.1,s3[35,26]=0.6,s3[35,27]=-0.5,s3[35,28]=1.0,s3[35,29]=-0.2,s3[35,30]=-0.6
s3[36,1]=0.3,s3[36,2]=-0.6,s3[36,3]=0.3,s3[36,4]=-1.0,s3[36,5]=0.4,s3[36,6]=-0.2,s3[36,7]=0.8,s3[36,8]=0.8,s3[36,9]=-0.9,s3[36,10]=0.1,s3[36,11]=0.8,s3[36,12]=-0.4,s3[36,13]=-1.0,s3[36,14]=0.6
s3[36,15]=0.8,s3[36,16]=0.6,s3[36,17]=-0.1,s3[36,18]=-0.3,s3[36,19]=0.3,s3[36,20]=-1.0,s3[36,21]=0.6,s3[36,22]=-1.2,s3[36,23]=0.8,s3[36,24]=0.6,s3[36,25]=0.3,s3[36,26]=-0.4,s3[36,27]=0.3,s3[36,28]=-0.3,s3[36,29]=-0.4,s3[36,30]=-0.5
s3[37,1]=0.5,s3[37,2]=-1.2,s3[37,3]=1.0,s3[37,4]=0.8,s3[37,5]=-0.5,s3[37,6]=0.1,s3[37,7]=-0.5,s3[37,8]=0.2,s3[37,9]=-1.1,s3[37,10]=-0.1,s3[37,11]=0.0,s3[37,12]=-0.5,s3[37,13]=-0.6,s3[37,14]=-0.2
s3[37,15]=-0.3,s3[37,16]=0.8,s3[37,17]=0.2,s3[37,18]=-0.4,s3[37,19]=-0.5,s3[37,20]=-0.1,s3[37,21]=0.5,s3[37,22]=0.2,s3[37,23]=-0.3,s3[37,24]=-0.8,s3[37,25]=0.3,s3[37,26]=-0.1,s3[37,27]=-0.4,s3[37,28]=0.2,s3[37,29]=0.7,s3[37,30]=-0.2
s3[38,1]=0.7,s3[38,2]=-1.0,s3[38,3]=0.1,s3[38,4]=-0.3,s3[38,5]=0.9,s3[38,6]=0.3,s3[38,7]=-1.1,s3[38,8]=0.7,s3[38,9]=-0.7,s3[38,10]=0.5,s3[38,11]=0.4,s3[38,12]=-0.7,s3[38,13]=-1.0,s3[38,14]=0.3
s3[38,15]=1.2,s3[38,16]=-0.4,s3[38,17]=1.2,s3[38,18]=0.4,s3[38,19]=-0.3,s3[38,20]=0.4,s3[38,21]=0.2,s3[38,22]=-0.8,s3[38,23]=1.1,s3[38,24]=0.7,s3[38,25]=-0.5,s3[38,26]=-0.2,s3[38,27]=0.6,s3[38,28]=0.6,s3[38,29]=-1.1,s3[38,30]=0.5
s3[39,1]=-0.2,s3[39,2]=-1.0,s3[39,3]=0.1,s3[39,4]=0.4,s3[39,5]=-0.5,s3[39,6]=-1.2,s3[39,7]=-0.9,s3[39,8]=-0.1,s3[39,9]=-1.1,s3[39,10]=-0.4,s3[39,11]=0.0,s3[39,12]=0.4,s3[39,13]=0.9,s3[39,14]=-0.1
s3[39,15]=0.7,s3[39,16]=-0.2,s3[39,17]=0.7,s3[39,18]=0.4,s3[39,19]=-0.3,s3[39,20]=-1.0,s3[39,21]=0.1,s3[39,22]=-0.2,s3[39,23]=-0.7,s3[39,24]=-0.3,s3[39,25]=-0.3,s3[39,26]=-0.7,s3[39,27]=0.4,s3[39,28]=0.5,s3[39,29]=-0.8,s3[39,30]=0.7
s3[40,1]=0.4,s3[40,2]=0.9,s3[40,3]=-0.3,s3[40,4]=-0.3,s3[40,5]=0.3,s3[40,6]=0.9,s3[40,7]=-0.6,s3[40,8]=0.6,s3[40,9]=0.3,s3[40,10]=-0.9,s3[40,11]=0.3,s3[40,12]=0.0,s3[40,13]=-0.5,s3[40,14]=0.9
s3[40,15]=0.0,s3[40,16]=1.2,s3[40,17]=-1.1,s3[40,18]=0.9,s3[40,19]=-0.4,s3[40,20]=-0.1,s3[40,21]=1.2,s3[40,22]=-0.8,s3[40,23]=-0.4,s3[40,24]=0.6,s3[40,25]=0.7,s3[40,26]=0.0,s3[40,27]=-1.0,s3[40,28]=0.3,s3[40,29]=-0.9,s3[40,30]=0.0
s3[41,1]=-0.7,s3[41,2]=0.3,s3[41,3]=0.4,s3[41,4]=-1.2,s3[41,5]=0.5,s3[41,6]=0.3,s3[41,7]=-0.6,s3[41,8]=0.4,s3[41,9]=0.3,s3[41,10]=0.6,s3[41,11]=1.2,s3[41,12]=0.5,s3[41,13]=-0.5,s3[41,14]=0.6
s3[41,15]=-0.1,s3[41,16]=0.6,s3[41,17]=-0.9,s3[41,18]=-0.6,s3[41,19]=0.3,s3[41,20]=-0.1,s3[41,21]=-0.9,s3[41,22]=-0.3,s3[41,23]=0.0,s3[41,24]=0.1,s3[41,25]=-0.1,s3[41,26]=0.6,s3[41,27]=-0.4,s3[41,28]=-0.5,s3[41,29]=-0.7,s3[41,30]=-0.7
s3[42,1]=-0.3,s3[42,2]=-0.6,s3[42,3]=-0.5,s3[42,4]=-0.1,s3[42,5]=1.0,s3[42,6]=-0.6,s3[42,7]=-0.5,s3[42,8]=0.3,s3[42,9]=0.6,s3[42,10]=-0.2,s3[42,11]=0.3,s3[42,12]=1.0,s3[42,13]=-0.7,s3[42,14]=0.6
s3[42,15]=1.0,s3[42,16]=0.4,s3[42,17]=-0.7,s3[42,18]=1.1,s3[42,19]=0.4,s3[42,20]=0.2,s3[42,21]=0.1,s3[42,22]=-0.1,s3[42,23]=0.5,s3[42,24]=-0.5,s3[42,25]=0.1,s3[42,26]=-0.7,s3[42,27]=0.4,s3[42,28]=-0.4,s3[42,29]=-0.9,s3[42,30]=0.3
s3[43,1]=0.1,s3[43,2]=-0.6,s3[43,3]=0.5,s3[43,4]=-0.4,s3[43,5]=0.6,s3[43,6]=0.3,s3[43,7]=-0.3,s3[43,8]=0.8,s3[43,9]=-1.2,s3[43,10]=-1.1,s3[43,11]=0.3,s3[43,12]=0.6,s3[43,13]=-0.6,s3[43,14]=0.0
s3[43,15]=0.1,s3[43,16]=-0.8,s3[43,17]=-0.9,s3[43,18]=-0.6,s3[43,19]=0.3,s3[43,20]=-0.6,s3[43,21]=-0.6,s3[43,22]=0.9,s3[43,23]=-0.5,s3[43,24]=1.1,s3[43,25]=-0.2,s3[43,26]=0.0,s3[43,27]=0.7,s3[43,28]=-1.2,s3[43,29]=-1.1,s3[43,30]=-0.4
s3[44,1]=1.1,s3[44,2]=0.1,s3[44,3]=-0.3,s3[44,4]=0.2,s3[44,5]=-0.6,s3[44,6]=0.1,s3[44,7]=0.0,s3[44,8]=0.0,s3[44,9]=-1.1,s3[44,10]=-1.0,s3[44,11]=0.9,s3[44,12]=0.0,s3[44,13]=-0.3,s3[44,14]=0.9
s3[44,15]=-0.2,s3[44,16]=0.1,s3[44,17]=-0.7,s3[44,18]=0.7,s3[44,19]=-0.5,s3[44,20]=0.2,s3[44,21]=0.2,s3[44,22]=-0.6,s3[44,23]=-0.5,s3[44,24]=0.9,s3[44,25]=-0.2,s3[44,26]=0.9,s3[44,27]=-0.7,s3[44,28]=-0.8,s3[44,29]=0.5,s3[44,30]=-0.8
s3[45,1]=-0.2,s3[45,2]=-0.5,s3[45,3]=0.9,s3[45,4]=-0.2,s3[45,5]=-0.7,s3[45,6]=-0.6,s3[45,7]=-0.9,s3[45,8]=0.0,s3[45,9]=-0.5,s3[45,10]=-0.2,s3[45,11]=-0.1,s3[45,12]=-0.8,s3[45,13]=-0.2,s3[45,14]=0.4
s3[45,15]=0.3,s3[45,16]=-0.3,s3[45,17]=1.1,s3[45,18]=0.3,s3[45,19]=-0.1,s3[45,20]=-0.2,s3[45,21]=-0.3,s3[45,22]=0.6,s3[45,23]=0.2,s3[45,24]=0.6,s3[45,25]=0.0,s3[45,26]=-0.6,s3[45,27]=-1.0,s3[45,28]=0.6,s3[45,29]=0.9,s3[45,30]=0.0
s3[46,1]=0.1,s3[46,2]=-0.6,s3[46,3]=0.3,s3[46,4]=-0.1,s3[46,5]=0.0,s3[46,6]=0.3,s3[46,7]=1.2,s3[46,8]=0.0,s3[46,9]=-0.1,s3[46,10]=1.2,s3[46,11]=-1.2,s3[46,12]=1.0,s3[46,13]=-0.4,s3[46,14]=-0.1
s3[46,15]=1.1,s3[46,16]=-0.1,s3[46,17]=0.6,s3[46,18]=-1.1,s3[46,19]=-0.6,s3[46,20]=1.1,s3[46,21]=0.3,s3[46,22]=0.7,s3[46,23]=-0.7,s3[46,24]=1.2,s3[46,25]=1.1,s3[46,26]=-0.5,s3[46,27]=-0.1,s3[46,28]=0.1,s3[46,29]=-1.0,s3[46,30]=-0.4
s3[47,1]=-0.6,s3[47,2]=-1.2,s3[47,3]=-1.0,s3[47,4]=-0.4,s3[47,5]=0.9,s3[47,6]=-0.2,s3[47,7]=-0.7,s3[47,8]=-0.2,s3[47,9]=0.6,s3[47,10]=0.0,s3[47,11]=0.3,s3[47,12]=0.4,s3[47,13]=0.0,s3[47,14]=-0.9
s3[47,15]=-0.1,s3[47,16]=0.3,s3[47,17]=0.0,s3[47,18]=-0.4,s3[47,19]=-0.1,s3[47,20]=-0.3,s3[47,21]=-0.4,s3[47,22]=-0.6,s3[47,23]=-1.1,s3[47,24]=-0.5,s3[47,25]=-1.1,s3[47,26]=1.2,s3[47,27]=0.0,s3[47,28]=0.1,s3[47,29]=0.7,s3[47,30]=0.4
s3[48,1]=-0.4,s3[48,2]=-0.9,s3[48,3]=-1.0,s3[48,4]=-0.4,s3[48,5]=0.0,s3[48,6]=-0.1,s3[48,7]=-0.8,s3[48,8]=-0.9,s3[48,9]=0.3,s3[48,10]=0.0,s3[48,11]=0.8,s3[48,12]=-0.3,s3[48,13]=-0.7,s3[48,14]=0.4
s3[48,15]=-0.9,s3[48,16]=-0.9,s3[48,17]=0.2,s3[48,18]=-0.6,s3[48,19]=1.2,s3[48,20]=0.7,s3[48,21]=0.1,s3[48,22]=0.6,s3[48,23]=0.0,s3[48,24]=-0.1,s3[48,25]=0.3,s3[48,26]=-0.5,s3[48,27]=-0.7,s3[48,28]=0.7,s3[48,29]=-0.7,s3[48,30]=-1.1
s3[49,1]=-0.9,s3[49,2]=-1.1,s3[49,3]=0.0,s3[49,4]=0.2,s3[49,5]=-0.9,s3[49,6]=-1.0,s3[49,7]=0.8,s3[49,8]=-0.3,s3[49,9]=-1.0,s3[49,10]=-1.0,s3[49,11]=-0.9,s3[49,12]=0.3,s3[49,13]=0.0,s3[49,14]=-0.4
s3[49,15]=-0.1,s3[49,16]=0.0,s3[49,17]=0.2,s3[49,18]=-0.4,s3[49,19]=0.1,s3[49,20]=0.5,s3[49,21]=1.1,s3[49,22]=1.0,s3[49,23]=-0.4,s3[49,24]=0.4,s3[49,25]=-0.5,s3[49,26]=0.9,s3[49,27]=0.0,s3[49,28]=0.4,s3[49,29]=0.9,s3[49,30]=-0.4
s3[50,1]=0.2,s3[50,2]=0.7,s3[50,3]=-0.2,s3[50,4]=-1.0,s3[50,5]=0.3,s3[50,6]=0.7,s3[50,7]=-0.3,s3[50,8]=0.5,s3[50,9]=0.7,s3[50,10]=-0.7,s3[50,11]=-0.1,s3[50,12]=0.1,s3[50,13]=0.5,s3[50,14]=0.6
s3[50,15]=-0.2,s3[50,16]=-0.4,s3[50,17]=-1.2,s3[50,18]=1.1,s3[50,19]=-0.3,s3[50,20]=0.9,s3[50,21]=-0.1,s3[50,22]=0.2,s3[50,23]=-0.7,s3[50,24]=0.3,s3[50,25]=-0.8,s3[50,26]=-0.5,s3[50,27]=0.5,s3[50,28]=1.2,s3[50,29]=-1.0,s3[50,30]=0.9
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float ppz = @ppz
float pxx = 0
float pyy = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
pyy = y
x = s3[@sd,1] + s3[@sd,2]*x + s3[@sd,3]*x*x + s3[@sd,4]*x*y \
+ s3[@sd,5]*x*ppz + s3[@sd,6]*y + s3[@sd,7]*y*y + \
s3[@sd,8]*y*ppz + s3[@sd,9]*ppz + s3[@sd,10]*ppz*ppz
y = s3[@sd,11] + s3[@sd,12]*pxx + s3[@sd,13]*pxx*pxx + s3[@sd,14]*pxx*y \
+ s3[@sd,15]*pxx*ppz + s3[@sd,16]*y + s3[@sd,17]*y*y + \
s3[@sd,18]*y*ppz + s3[@sd,19]*ppz + s3[@sd,20]*ppz*ppz
ppz = s3[@sd,21] + s3[@sd,22]*pxx + s3[@sd,23]*pxx*pxx + s3[@sd,24]*pxx*pyy + \
s3[@sd,25]*pxx*ppz + s3[@sd,26]*pyy + s3[@sd,27]*pyy*pyy + \
s3[@sd,28]*pyy*ppz + s3[@sd,29]*ppz + s3[@sd,30]*ppz*ppz
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y) + ppz*@pw)
float d = @distscale*|pz-m_LastZ|
return d
endfunc
private:
float s3[51,31]
default:
title = "Sprott3D"
heading
text="Sprott 3D quadratic attractors"
endheading
heading
text=" x -> Quadratic in x, y and z"
endheading
heading
text=" y -> Quadratic in x, y and z"
endheading
heading
text=" z -> Quadratic in x, y and z"
endheading
int param v_trapshapesprott3d
caption = "Version (Trap Shape Sprott3D)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesprott3d < 101
endparam
param sd
caption = "Sprott selector"
default = 0
enum = "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" \
"15" "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" \
"30" "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" \
"45" "46" "47" "48" "49" "50"
hint = "Each Sprott selector uses a different strange attractor."
endparam
heading
text = "'Initialize Height' sets the starting z value for the attractor."
endheading
float param ppz
caption = "Initialize Height"
default = 0.5
endparam
heading
text = "'Height weight' determines the weight of the final z value which is added \
to the trap distance."
endheading
complex param pw
caption = "Height weight"
default = (0.5,0)
endparam
float param distscale
caption = "Distance scale"
default = 2
endparam
float param s
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 15
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSprott3D_Cubic(common.ulb:TrapShape) {
; This shape uses a Sprott strange attractor.
; The Sprott attractors were developed by Julien C. Sprott, and are
; based upon polynomials and linear differential equations of polynomials.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSprott3D_Cubic(Generic pparent)
TrapShape.TrapShape(pparent)
s[0,1]=0.3,s[0,2]=-0.4,s[0,3]=1.0,s[0,4]=0.3,s[0,5]=0.5,s[0,6]=0.4,s[0,7]=0.7,s[0,8]=0.5,s[0,9]=0.9,s[0,10]=1.0,s[0,11]=1.2,s[0,12]=-0.4,s[0,13]=0.4,s[0,14]=-0.3,s[0,15]=-0.1,s[0,16]=-0.6,s[0,17]=-0.1,s[0,18]=1.1,s[0,19]=1.0,s[0,20]=0.6,s[0,21]=0.2,s[0,22]=0.6,s[0,23]=-1.1,s[0,24]=-1.0,s[0,25]=0.2,s[0,26]=0.4,s[0,27]=0.4,s[0,28]=0.2,s[0,29]=0.6,s[0,30]=-1.1
s[0,31]=0.6,s[0,32]=-0.4,s[0,33]=-1.1,s[0,34]=-0.1,s[0,35]=0.6,s[0,36]=-0.2,s[0,37]=-0.8,s[0,38]=-0.6,s[0,39]=0.6,s[0,40]=1.2,s[0,41]=-0.5,s[0,42]=0.3,s[0,43]=1.1,s[0,44]=-0.1,s[0,45]=0.9,s[0,46]=-1.0,s[0,47]=-0.6,s[0,48]=-0.3,s[0,49]=0.5,s[0,50]=0.4,s[0,51]=-0.8,s[0,52]=0.5,s[0,53]=-0.8,s[0,54]=-1.0,s[0,55]=0.1,s[0,56]=-0.9,s[0,57]=-1.1,s[0,58]=-0.7,s[0,59]=-0.1,s[0,60]=-0.6
s[1,1]=-0.1,s[1,2]=-0.6,s[1,3]=0.4,s[1,4]=-0.6,s[1,5]=-0.7,s[1,6]=0.3,s[1,7]=-0.7,s[1,8]=0.6,s[1,9]=-0.6,s[1,10]=-0.6,s[1,11]=0.8,s[1,12]=-0.6,s[1,13]=-0.8,s[1,14]=1.2,s[1,15]=0.4,s[1,16]=0.7,s[1,17]=0.1,s[1,18]=-0.7,s[1,19]=-0.5,s[1,20]=0.4,s[1,21]=-0.2,s[1,22]=1.0,s[1,23]=0.9,s[1,24]=0.8,s[1,25]=-1.1,s[1,26]=-0.3,s[1,27]=0.4,s[1,28]=-0.1,s[1,29]=1.1,s[1,30]=-0.2
s[1,31]=0.8,s[1,32]=0.6,s[1,33]=-0.3,s[1,34]=-0.3,s[1,35]=-1.0,s[1,36]=-0.2,s[1,37]=0.0,s[1,38]=0.3,s[1,39]=0.3,s[1,40]=0.1,s[1,41]=0.3,s[1,42]=0.9,s[1,43]=0.2,s[1,44]=0.0,s[1,45]=1.1,s[1,46]=1.0,s[1,47]=0.6,s[1,48]=-0.5,s[1,49]=-0.2,s[1,50]=0.8,s[1,51]=0.9,s[1,52]=-1.0,s[1,53]=-0.7,s[1,54]=1.1,s[1,55]=0.9,s[1,56]=-0.2,s[1,57]=-0.3,s[1,58]=0.5,s[1,59]=-0.9,s[1,60]=0.4
s[2,1]=0.7,s[2,2]=-0.3,s[2,3]=-0.3,s[2,4]=0.4,s[2,5]=0.1,s[2,6]=-0.8,s[2,7]=0.9,s[2,8]=-1.0,s[2,9]=1.1,s[2,10]=-0.1,s[2,11]=-0.4,s[2,12]=0.3,s[2,13]=-1.0,s[2,14]=-0.2,s[2,15]=0.9,s[2,16]=-1.0,s[2,17]=0.4,s[2,18]=0.4,s[2,19]=1.0,s[2,20]=0.3,s[2,21]=0.8,s[2,22]=0.2,s[2,23]=0.9,s[2,24]=-0.2,s[2,25]=0.6,s[2,26]=-0.2,s[2,27]=0.2,s[2,28]=-0.9,s[2,29]=-0.4,s[2,30]=-0.3
s[2,31]=-0.1,s[2,32]=-0.4,s[2,33]=0.3,s[2,34]=-0.2,s[2,35]=0.7,s[2,36]=0.1,s[2,37]=1.0,s[2,38]=-0.9,s[2,39]=-0.1,s[2,40]=-0.5,s[2,41]=0.0,s[2,42]=-0.8,s[2,43]=0.9,s[2,44]=1.1,s[2,45]=-1.2,s[2,46]=-0.6,s[2,47]=0.0,s[2,48]=0.5,s[2,49]=0.3,s[2,50]=-0.4,s[2,51]=-0.5,s[2,52]=0.0,s[2,53]=-0.3,s[2,54]=0.5,s[2,55]=0.5,s[2,56]=-1.2,s[2,57]=-0.2,s[2,58]=0.3,s[2,59]=-0.8,s[2,60]=1.2
s[3,1]=0.0,s[3,2]=0.6,s[3,3]=0.4,s[3,4]=-0.1,s[3,5]=-1.0,s[3,6]=0.3,s[3,7]=-0.7,s[3,8]=-0.5,s[3,9]=0.7,s[3,10]=0.7,s[3,11]=0.1,s[3,12]=-0.2,s[3,13]=-1.2,s[3,14]=-0.6,s[3,15]=0.4,s[3,16]=-0.1,s[3,17]=1.1,s[3,18]=-0.3,s[3,19]=-0.1,s[3,20]=-0.4,s[3,21]=0.4,s[3,22]=0.7,s[3,23]=-1.0,s[3,24]=0.8,s[3,25]=0.1,s[3,26]=-0.3,s[3,27]=0.9,s[3,28]=-1.2,s[3,29]=-0.4,s[3,30]=-0.7
s[3,31]=0.4,s[3,32]=0.8,s[3,33]=-0.9,s[3,34]=-0.4,s[3,35]=0.9,s[3,36]=0.4,s[3,37]=-0.5,s[3,38]=0.7,s[3,39]=0.7,s[3,40]=0.3,s[3,41]=-0.7,s[3,42]=0.5,s[3,43]=0.4,s[3,44]=0.3,s[3,45]=0.9,s[3,46]=0.8,s[3,47]=0.2,s[3,48]=-0.3,s[3,49]=0.1,s[3,50]=0.8,s[3,51]=0.5,s[3,52]=-0.6,s[3,53]=0.2,s[3,54]=1.0,s[3,55]=-0.3,s[3,56]=0.4,s[3,57]=0.7,s[3,58]=-0.4,s[3,59]=0.4,s[3,60]=0.9
s[4,1]=-0.6,s[4,2]=-0.8,s[4,3]=0.6,s[4,4]=-0.1,s[4,5]=-0.1,s[4,6]=0.2,s[4,7]=0.1,s[4,8]=0.1,s[4,9]=0.1,s[4,10]=-0.3,s[4,11]=0.2,s[4,12]=-0.7,s[4,13]=-0.1,s[4,14]=0.1,s[4,15]=-0.3,s[4,16]=-0.1,s[4,17]=-0.1,s[4,18]=-0.4,s[4,19]=-1.0,s[4,20]=-1.0,s[4,21]=0.2,s[4,22]=0.5,s[4,23]=0.8,s[4,24]=0.9,s[4,25]=-0.4,s[4,26]=0.2,s[4,27]=1.1,s[4,28]=0.5,s[4,29]=0.4,s[4,30]=0.8
s[4,31]=1.0,s[4,32]=0.1,s[4,33]=-0.6,s[4,34]=-0.3,s[4,35]=-1.2,s[4,36]=-1.0,s[4,37]=-0.3,s[4,38]=0.3,s[4,39]=1.2,s[4,40]=0.3,s[4,41]=-0.1,s[4,42]=-0.3,s[4,43]=0.0,s[4,44]=1.1,s[4,45]=-0.9,s[4,46]=-0.6,s[4,47]=-1.2,s[4,48]=0.8,s[4,49]=0.1,s[4,50]=0.1,s[4,51]=-0.6,s[4,52]=1.2,s[4,53]=-0.1,s[4,54]=-0.1,s[4,55]=1.2,s[4,56]=-0.8,s[4,57]=0.9,s[4,58]=1.0,s[4,59]=0.1,s[4,60]=-0.8
s[5,1]=-0.4,s[5,2]=0.7,s[5,3]=0.6,s[5,4]=1.2,s[5,5]=-0.6,s[5,6]=-0.5,s[5,7]=-0.1,s[5,8]=-0.8,s[5,9]=1.2,s[5,10]=-1.0,s[5,11]=1.0,s[5,12]=0.4,s[5,13]=0.2,s[5,14]=0.5,s[5,15]=0.8,s[5,16]=-0.7,s[5,17]=0.9,s[5,18]=0.7,s[5,19]=-0.3,s[5,20]=-0.7,s[5,21]=0.5,s[5,22]=-0.6,s[5,23]=-1.0,s[5,24]=-1.0,s[5,25]=-0.6,s[5,26]=1.1,s[5,27]=-0.6,s[5,28]=-0.3,s[5,29]=0.8,s[5,30]=0.6
s[5,31]=-0.2,s[5,32]=0.6,s[5,33]=-0.4,s[5,34]=0.2,s[5,35]=-1.1,s[5,36]=0.8,s[5,37]=-0.5,s[5,38]=-0.7,s[5,39]=-0.7,s[5,40]=0.8,s[5,41]=0.6,s[5,42]=-1.1,s[5,43]=0.8,s[5,44]=0.5,s[5,45]=0.1,s[5,46]=0.8,s[5,47]=-0.3,s[5,48]=1.1,s[5,49]=-1.1,s[5,50]=-0.9,s[5,51]=-0.8,s[5,52]=-1.0,s[5,53]=0.1,s[5,54]=0.9,s[5,55]=-0.2,s[5,56]=-0.1,s[5,57]=-0.3,s[5,58]=-0.7,s[5,59]=0.8,s[5,60]=-0.6
s[6,1]=-0.3,s[6,2]=-0.4,s[6,3]=0.0,s[6,4]=-0.8,s[6,5]=0.5,s[6,6]=1.1,s[6,7]=0.1,s[6,8]=0.3,s[6,9]=-0.5,s[6,10]=0.9,s[6,11]=0.7,s[6,12]=0.5,s[6,13]=-0.8,s[6,14]=0.6,s[6,15]=0.3,s[6,16]=0.5,s[6,17]=1.1,s[6,18]=-0.3,s[6,19]=1.1,s[6,20]=-0.4,s[6,21]=0.5,s[6,22]=-0.4,s[6,23]=-0.5,s[6,24]=1.0,s[6,25]=-0.4,s[6,26]=0.0,s[6,27]=-1.2,s[6,28]=-0.6,s[6,29]=0.9,s[6,30]=-0.2
s[6,31]=0.5,s[6,32]=-1.0,s[6,33]=0.2,s[6,34]=0.0,s[6,35]=1.0,s[6,36]=0.1,s[6,37]=0.6,s[6,38]=-0.2,s[6,39]=-1.2,s[6,40]=-0.3,s[6,41]=0.2,s[6,42]=0.2,s[6,43]=-1.0,s[6,44]=-0.4,s[6,45]=-0.1,s[6,46]=-0.1,s[6,47]=-0.2,s[6,48]=-0.1,s[6,49]=0.9,s[6,50]=-0.5,s[6,51]=0.1,s[6,52]=0.9,s[6,53]=0.9,s[6,54]=0.3,s[6,55]=1.1,s[6,56]=-0.6,s[6,57]=0.4,s[6,58]=-0.5,s[6,59]=0.9,s[6,60]=0.9
s[7,1]=0.6,s[7,2]=-0.5,s[7,3]=-0.6,s[7,4]=-0.5,s[7,5]=-0.9,s[7,6]=1.1,s[7,7]=0.1,s[7,8]=0.4,s[7,9]=0.0,s[7,10]=-1.1,s[7,11]=0.3,s[7,12]=1.1,s[7,13]=0.5,s[7,14]=0.0,s[7,15]=-0.9,s[7,16]=0.8,s[7,17]=0.0,s[7,18]=0.3,s[7,19]=-0.8,s[7,20]=-0.9,s[7,21]=-0.1,s[7,22]=0.3,s[7,23]=0.9,s[7,24]=-0.9,s[7,25]=0.5,s[7,26]=0.1,s[7,27]=-0.4,s[7,28]=-0.8,s[7,29]=-0.1,s[7,30]=-0.4
s[7,31]=0.0,s[7,32]=-0.4,s[7,33]=1.0,s[7,34]=-0.6,s[7,35]=0.5,s[7,36]=1.0,s[7,37]=0.0,s[7,38]=1.1,s[7,39]=0.1,s[7,40]=-0.4,s[7,41]=-0.5,s[7,42]=1.0,s[7,43]=1.0,s[7,44]=-0.9,s[7,45]=-0.5,s[7,46]=1.2,s[7,47]=0.1,s[7,48]=0.3,s[7,49]=-0.2,s[7,50]=-0.8,s[7,51]=-0.8,s[7,52]=-1.1,s[7,53]=0.0,s[7,54]=0.9,s[7,55]=-0.9,s[7,56]=0.3,s[7,57]=-0.7,s[7,58]=-0.3,s[7,59]=-0.7,s[7,60]=0.9
s[8,1]=-0.1,s[8,2]=-1.0,s[8,3]=-0.6,s[8,4]=0.8,s[8,5]=-0.3,s[8,6]=0.0,s[8,7]=0.5,s[8,8]=0.3,s[8,9]=1.1,s[8,10]=-0.7,s[8,11]=-0.3,s[8,12]=-1.0,s[8,13]=1.1,s[8,14]=0.6,s[8,15]=-1.1,s[8,16]=0.9,s[8,17]=0.3,s[8,18]=-1.1,s[8,19]=0.0,s[8,20]=-0.8,s[8,21]=0.0,s[8,22]=-0.4,s[8,23]=-0.9,s[8,24]=0.2,s[8,25]=-1.1,s[8,26]=-1.0,s[8,27]=-1.2,s[8,28]=0.9,s[8,29]=1.0,s[8,30]=0.8
s[8,31]=-0.2,s[8,32]=0.5,s[8,33]=0.6,s[8,34]=0.3,s[8,35]=1.1,s[8,36]=0.4,s[8,37]=0.5,s[8,38]=-1.0,s[8,39]=1.2,s[8,40]=-1.1,s[8,41]=0.0,s[8,42]=-0.1,s[8,43]=0.8,s[8,44]=1.2,s[8,45]=-0.6,s[8,46]=-0.8,s[8,47]=-0.6,s[8,48]=-0.6,s[8,49]=0.8,s[8,50]=1.2,s[8,51]=0.2,s[8,52]=0.5,s[8,53]=0.3,s[8,54]=0.8,s[8,55]=-0.6,s[8,56]=1.0,s[8,57]=0.5,s[8,58]=-0.5,s[8,59]=0.0,s[8,60]=0.1
s[9,1]=-0.1,s[9,2]=0.1,s[9,3]=-0.5,s[9,4]=-0.1,s[9,5]=0.6,s[9,6]=0.6,s[9,7]=0.6,s[9,8]=-0.7,s[9,9]=1.1,s[9,10]=-1.1,s[9,11]=0.0,s[9,12]=0.7,s[9,13]=-0.4,s[9,14]=-0.3,s[9,15]=-0.4,s[9,16]=-0.8,s[9,17]=0.1,s[9,18]=0.5,s[9,19]=-0.1,s[9,20]=-0.6,s[9,21]=0.0,s[9,22]=-0.1,s[9,23]=-0.4,s[9,24]=0.9,s[9,25]=0.7,s[9,26]=-1.0,s[9,27]=1.2,s[9,28]=-0.9,s[9,29]=0.1,s[9,30]=0.0
s[9,31]=0.5,s[9,32]=1.0,s[9,33]=-1.1,s[9,34]=0.4,s[9,35]=1.0,s[9,36]=0.3,s[9,37]=-1.1,s[9,38]=0.5,s[9,39]=-0.7,s[9,40]=-0.8,s[9,41]=-0.1,s[9,42]=-1.2,s[9,43]=0.5,s[9,44]=0.8,s[9,45]=-0.5,s[9,46]=0.2,s[9,47]=0.6,s[9,48]=-0.4,s[9,49]=1.2,s[9,50]=0.6,s[9,51]=0.0,s[9,52]=-1.2,s[9,53]=0.3,s[9,54]=-0.1,s[9,55]=-0.3,s[9,56]=-0.3,s[9,57]=-0.4,s[9,58]=0.3,s[9,59]=1.0,s[9,60]=-1.2
s[10,1]=-0.4,s[10,2]=-1.1,s[10,3]=-1.0,s[10,4]=-0.1,s[10,5]=0.8,s[10,6]=0.3,s[10,7]=0.7,s[10,8]=-0.6,s[10,9]=1.1,s[10,10]=0.6,s[10,11]=-0.4,s[10,12]=0.3,s[10,13]=-1.2,s[10,14]=0.7,s[10,15]=-1.1,s[10,16]=0.0,s[10,17]=-0.6,s[10,18]=0.3,s[10,19]=0.0,s[10,20]=-0.6,s[10,21]=-0.3,s[10,22]=-0.5,s[10,23]=0.5,s[10,24]=-0.7,s[10,25]=-1.2,s[10,26]=0.6,s[10,27]=-0.8,s[10,28]=0.2,s[10,29]=0.4,s[10,30]=0.9
s[10,31]=-0.6,s[10,32]=1.1,s[10,33]=0.8,s[10,34]=0.7,s[10,35]=-0.6,s[10,36]=1.2,s[10,37]=0.7,s[10,38]=0.9,s[10,39]=-0.5,s[10,40]=-1.1,s[10,41]=-0.2,s[10,42]=0.1,s[10,43]=0.7,s[10,44]=1.1,s[10,45]=-0.8,s[10,46]=-0.3,s[10,47]=0.4,s[10,48]=0.9,s[10,49]=-0.6,s[10,50]=1.2,s[10,51]=-0.8,s[10,52]=0.3,s[10,53]=0.3,s[10,54]=-0.3,s[10,55]=-0.9,s[10,56]=0.1,s[10,57]=-1.0,s[10,58]=0.6,s[10,59]=-0.4,s[10,60]=1.2
s[11,1]=1.0,s[11,2]=-0.3,s[11,3]=-0.5,s[11,4]=1.0,s[11,5]=1.1,s[11,6]=1.0,s[11,7]=-0.5,s[11,8]=-1.0,s[11,9]=-1.2,s[11,10]=-1.2,s[11,11]=-0.6,s[11,12]=-0.2,s[11,13]=-1.1,s[11,14]=-0.3,s[11,15]=0.0,s[11,16]=0.1,s[11,17]=0.3,s[11,18]=-0.5,s[11,19]=0.4,s[11,20]=-0.3,s[11,21]=-0.2,s[11,22]=-0.6,s[11,23]=0.8,s[11,24]=0.1,s[11,25]=1.2,s[11,26]=-0.7,s[11,27]=0.7,s[11,28]=-0.5,s[11,29]=-0.7,s[11,30]=-0.2
s[11,31]=1.2,s[11,32]=-0.1,s[11,33]=0.0,s[11,34]=-0.1,s[11,35]=-0.9,s[11,36]=0.8,s[11,37]=-0.5,s[11,38]=0.5,s[11,39]=0.4,s[11,40]=-0.5,s[11,41]=0.6,s[11,42]=0.3,s[11,43]=-0.3,s[11,44]=0.7,s[11,45]=0.3,s[11,46]=0.2,s[11,47]=0.7,s[11,48]=0.4,s[11,49]=0.0,s[11,50]=-0.5,s[11,51]=1.1,s[11,52]=-0.4,s[11,53]=0.5,s[11,54]=-1.0,s[11,55]=-0.7,s[11,56]=0.6,s[11,57]=1.1,s[11,58]=-1.2,s[11,59]=0.1,s[11,60]=0.3
s[12,1]=-0.2,s[12,2]=-0.9,s[12,3]=-0.8,s[12,4]=-0.2,s[12,5]=0.6,s[12,6]=-0.9,s[12,7]=0.0,s[12,8]=0.6,s[12,9]=1.1,s[12,10]=1.2,s[12,11]=-0.5,s[12,12]=0.0,s[12,13]=0.6,s[12,14]=1.0,s[12,15]=1.1,s[12,16]=-0.1,s[12,17]=-0.7,s[12,18]=-1.1,s[12,19]=-0.5,s[12,20]=0.8,s[12,21]=-0.2,s[12,22]=0.9,s[12,23]=1.1,s[12,24]=-0.1,s[12,25]=-0.4,s[12,26]=-0.3,s[12,27]=0.3,s[12,28]=1.1,s[12,29]=-0.9,s[12,30]=-0.5
s[12,31]=0.5,s[12,32]=0.3,s[12,33]=0.6,s[12,34]=0.9,s[12,35]=-0.4,s[12,36]=0.7,s[12,37]=1.1,s[12,38]=0.6,s[12,39]=-1.2,s[12,40]=0.2,s[12,41]=-0.1,s[12,42]=0.2,s[12,43]=-0.7,s[12,44]=0.8,s[12,45]=0.9,s[12,46]=0.4,s[12,47]=-0.6,s[12,48]=-0.2,s[12,49]=-1.1,s[12,50]=0.4,s[12,51]=-0.7,s[12,52]=-0.7,s[12,53]=0.5,s[12,54]=0.5,s[12,55]=0.7,s[12,56]=0.1,s[12,57]=0.4,s[12,58]=0.5,s[12,59]=-1.2,s[12,60]=0.8
s[13,1]=0.6,s[13,2]=-1.1,s[13,3]=-0.1,s[13,4]=-0.9,s[13,5]=0.0,s[13,6]=0.6,s[13,7]=-0.9,s[13,8]=0.4,s[13,9]=0.4,s[13,10]=-1.1,s[13,11]=-0.1,s[13,12]=-0.8,s[13,13]=0.5,s[13,14]=0.7,s[13,15]=-0.3,s[13,16]=-0.3,s[13,17]=-0.2,s[13,18]=1.1,s[13,19]=0.3,s[13,20]=-0.1,s[13,21]=0.0,s[13,22]=0.9,s[13,23]=-0.1,s[13,24]=-0.7,s[13,25]=-0.1,s[13,26]=0.3,s[13,27]=0.1,s[13,28]=-0.4,s[13,29]=1.0,s[13,30]=0.4
s[13,31]=-0.6,s[13,32]=-0.8,s[13,33]=0.4,s[13,34]=0.6,s[13,35]=0.5,s[13,36]=1.2,s[13,37]=0.3,s[13,38]=-0.7,s[13,39]=0.8,s[13,40]=0.9,s[13,41]=0.1,s[13,42]=0.3,s[13,43]=0.0,s[13,44]=-1.2,s[13,45]=0.0,s[13,46]=1.0,s[13,47]=1.1,s[13,48]=-1.2,s[13,49]=0.4,s[13,50]=0.0,s[13,51]=-0.8,s[13,52]=-0.9,s[13,53]=0.5,s[13,54]=1.1,s[13,55]=1.2,s[13,56]=-1.0,s[13,57]=0.2,s[13,58]=0.3,s[13,59]=0.0,s[13,60]=0.2
s[14,1]=-0.2,s[14,2]=-0.5,s[14,3]=-0.9,s[14,4]=-1.1,s[14,5]=-1.2,s[14,6]=-0.2,s[14,7]=0.5,s[14,8]=-1.1,s[14,9]=-0.7,s[14,10]=-0.4,s[14,11]=0.5,s[14,12]=0.1,s[14,13]=0.4,s[14,14]=0.1,s[14,15]=0.3,s[14,16]=0.1,s[14,17]=-1.2,s[14,18]=0.2,s[14,19]=0.2,s[14,20]=-0.3,s[14,21]=-0.2,s[14,22]=-0.2,s[14,23]=0.0,s[14,24]=-1.0,s[14,25]=0.4,s[14,26]=0.5,s[14,27]=0.7,s[14,28]=0.2,s[14,29]=-0.3,s[14,30]=0.5
s[14,31]=-0.2,s[14,32]=0.9,s[14,33]=0.8,s[14,34]=1.1,s[14,35]=-0.6,s[14,36]=-0.7,s[14,37]=-0.9,s[14,38]=-0.9,s[14,39]=1.2,s[14,40]=0.9,s[14,41]=0.1,s[14,42]=-0.9,s[14,43]=-0.6,s[14,44]=-1.0,s[14,45]=0.5,s[14,46]=1.0,s[14,47]=-0.2,s[14,48]=0.0,s[14,49]=-1.2,s[14,50]=0.1,s[14,51]=0.1,s[14,52]=-0.2,s[14,53]=0.7,s[14,54]=-0.7,s[14,55]=0.8,s[14,56]=-0.8,s[14,57]=0.8,s[14,58]=0.4,s[14,59]=-0.4,s[14,60]=-1.1
s[15,1]=-0.2,s[15,2]=0.2,s[15,3]=1.1,s[15,4]=-0.2,s[15,5]=-0.9,s[15,6]=-0.7,s[15,7]=-1.1,s[15,8]=0.7,s[15,9]=0.4,s[15,10]=-0.4,s[15,11]=-0.3,s[15,12]=-0.1,s[15,13]=-0.6,s[15,14]=0.9,s[15,15]=-0.8,s[15,16]=0.1,s[15,17]=-0.5,s[15,18]=0.9,s[15,19]=-1.0,s[15,20]=0.4,s[15,21]=0.1,s[15,22]=-0.1,s[15,23]=1.0,s[15,24]=0.9,s[15,25]=-1.1,s[15,26]=-0.1,s[15,27]=-0.3,s[15,28]=0.6,s[15,29]=-0.5,s[15,30]=1.0
s[15,31]=0.8,s[15,32]=-0.3,s[15,33]=0.3,s[15,34]=0.2,s[15,35]=-0.8,s[15,36]=0.5,s[15,37]=0.3,s[15,38]=-0.4,s[15,39]=1.1,s[15,40]=0.9,s[15,41]=0.6,s[15,42]=1.2,s[15,43]=0.8,s[15,44]=1.1,s[15,45]=1.1,s[15,46]=-0.7,s[15,47]=-0.2,s[15,48]=1.2,s[15,49]=1.0,s[15,50]=1.2,s[15,51]=-0.4,s[15,52]=-0.4,s[15,53]=-1.2,s[15,54]=-0.7,s[15,55]=-0.3,s[15,56]=-0.4,s[15,57]=0.9,s[15,58]=0.0,s[15,59]=0.7,s[15,60]=-1.0
s[16,1]=0.3,s[16,2]=-0.7,s[16,3]=-1.0,s[16,4]=0.1,s[16,5]=0.4,s[16,6]=-0.3,s[16,7]=-0.5,s[16,8]=1.0,s[16,9]=1.2,s[16,10]=-0.9,s[16,11]=-1.0,s[16,12]=-0.9,s[16,13]=-0.8,s[16,14]=0.7,s[16,15]=0.3,s[16,16]=-0.3,s[16,17]=1.2,s[16,18]=-0.2,s[16,19]=-1.0,s[16,20]=0.1,s[16,21]=0.3,s[16,22]=-0.3,s[16,23]=-0.9,s[16,24]=0.2,s[16,25]=0.7,s[16,26]=0.5,s[16,27]=-0.6,s[16,28]=-0.1,s[16,29]=-0.5,s[16,30]=-1.2
s[16,31]=0.5,s[16,32]=0.8,s[16,33]=-0.5,s[16,34]=-0.8,s[16,35]=0.5,s[16,36]=0.5,s[16,37]=-0.5,s[16,38]=-0.9,s[16,39]=0.2,s[16,40]=0.7,s[16,41]=-0.5,s[16,42]=-0.7,s[16,43]=0.3,s[16,44]=0.8,s[16,45]=-0.3,s[16,46]=-1.0,s[16,47]=-0.6,s[16,48]=-0.5,s[16,49]=-0.8,s[16,50]=0.7,s[16,51]=0.4,s[16,52]=-0.1,s[16,53]=-0.1,s[16,54]=0.2,s[16,55]=-0.1,s[16,56]=0.2,s[16,57]=0.6,s[16,58]=0.4,s[16,59]=-0.2,s[16,60]=-1.2
s[17,1]=0.9,s[17,2]=-0.9,s[17,3]=0.4,s[17,4]=-0.1,s[17,5]=0.9,s[17,6]=-0.6,s[17,7]=-0.7,s[17,8]=1.2,s[17,9]=-0.2,s[17,10]=1.2,s[17,11]=-1.2,s[17,12]=0.3,s[17,13]=-0.4,s[17,14]=0.8,s[17,15]=0.9,s[17,16]=-0.3,s[17,17]=-0.3,s[17,18]=-0.8,s[17,19]=-0.5,s[17,20]=0.1,s[17,21]=-0.2,s[17,22]=0.5,s[17,23]=0.0,s[17,24]=0.6,s[17,25]=1.1,s[17,26]=-0.1,s[17,27]=0.6,s[17,28]=-1.0,s[17,29]=0.1,s[17,30]=-0.8
s[17,31]=0.8,s[17,32]=-1.2,s[17,33]=-1.2,s[17,34]=-0.2,s[17,35]=0.5,s[17,36]=-0.6,s[17,37]=0.9,s[17,38]=-0.6,s[17,39]=1.2,s[17,40]=-0.9,s[17,41]=0.4,s[17,42]=0.6,s[17,43]=-0.3,s[17,44]=-1.2,s[17,45]=-1.0,s[17,46]=-0.5,s[17,47]=-0.7,s[17,48]=0.9,s[17,49]=0.5,s[17,50]=0.5,s[17,51]=-0.7,s[17,52]=-0.5,s[17,53]=-1.2,s[17,54]=-1.2,s[17,55]=-0.7,s[17,56]=0.0,s[17,57]=1.2,s[17,58]=0.4,s[17,59]=1.2,s[17,60]=-0.9
s[18,1]=0.1,s[18,2]=-0.5,s[18,3]=0.9,s[18,4]=1.0,s[18,5]=1.0,s[18,6]=0.8,s[18,7]=-0.9,s[18,8]=0.9,s[18,9]=-0.6,s[18,10]=1.0,s[18,11]=-0.1,s[18,12]=-0.2,s[18,13]=0.9,s[18,14]=0.9,s[18,15]=-0.3,s[18,16]=0.0,s[18,17]=0.4,s[18,18]=-0.2,s[18,19]=-0.4,s[18,20]=-0.7,s[18,21]=-0.3,s[18,22]=1.1,s[18,23]=0.9,s[18,24]=-0.7,s[18,25]=-0.1,s[18,26]=-1.2,s[18,27]=-0.1,s[18,28]=-0.1,s[18,29]=1.0,s[18,30]=-1.1
s[18,31]=1.0,s[18,32]=1.1,s[18,33]=0.2,s[18,34]=-1.1,s[18,35]=0.5,s[18,36]=-0.5,s[18,37]=0.5,s[18,38]=0.3,s[18,39]=-0.8,s[18,40]=0.8,s[18,41]=0.4,s[18,42]=0.4,s[18,43]=-0.1,s[18,44]=0.3,s[18,45]=-0.6,s[18,46]=-0.7,s[18,47]=0.6,s[18,48]=-0.6,s[18,49]=-1.2,s[18,50]=0.0,s[18,51]=0.4,s[18,52]=1.1,s[18,53]=0.2,s[18,54]=0.4,s[18,55]=1.0,s[18,56]=-0.6,s[18,57]=-0.8,s[18,58]=0.3,s[18,59]=-0.8,s[18,60]=0.8
s[19,1]=0.4,s[19,2]=-1.1,s[19,3]=-1.2,s[19,4]=0.8,s[19,5]=0.2,s[19,6]=0.6,s[19,7]=0.0,s[19,8]=-0.1,s[19,9]=-0.5,s[19,10]=0.9,s[19,11]=0.7,s[19,12]=1.1,s[19,13]=-0.8,s[19,14]=0.3,s[19,15]=0.3,s[19,16]=0.7,s[19,17]=0.1,s[19,18]=0.4,s[19,19]=-0.2,s[19,20]=-1.1,s[19,21]=0.0,s[19,22]=-0.6,s[19,23]=-0.8,s[19,24]=1.1,s[19,25]=0.3,s[19,26]=0.2,s[19,27]=0.6,s[19,28]=0.3,s[19,29]=-1.0,s[19,30]=0.7
s[19,31]=0.8,s[19,32]=-0.8,s[19,33]=-1.2,s[19,34]=-0.1,s[19,35]=-0.5,s[19,36]=0.3,s[19,37]=-1.1,s[19,38]=0.6,s[19,39]=-0.1,s[19,40]=-1.1,s[19,41]=0.1,s[19,42]=-0.5,s[19,43]=0.5,s[19,44]=1.2,s[19,45]=0.0,s[19,46]=-0.6,s[19,47]=-0.7,s[19,48]=-0.8,s[19,49]=0.5,s[19,50]=-0.2,s[19,51]=0.8,s[19,52]=0.1,s[19,53]=1.0,s[19,54]=-0.6,s[19,55]=0.5,s[19,56]=-0.9,s[19,57]=-0.1,s[19,58]=1.0,s[19,59]=-1.2,s[19,60]=-0.5
s[20,1]=0.2,s[20,2]=-1.0,s[20,3]=0.1,s[20,4]=0.7,s[20,5]=0.0,s[20,6]=0.7,s[20,7]=-0.3,s[20,8]=0.5,s[20,9]=-0.6,s[20,10]=-0.6,s[20,11]=-0.7,s[20,12]=0.7,s[20,13]=-0.7,s[20,14]=0.9,s[20,15]=1.1,s[20,16]=-0.9,s[20,17]=-0.1,s[20,18]=-0.4,s[20,19]=-0.6,s[20,20]=-0.6,s[20,21]=-0.1,s[20,22]=0.0,s[20,23]=1.0,s[20,24]=-0.7,s[20,25]=-0.6,s[20,26]=0.5,s[20,27]=0.3,s[20,28]=0.9,s[20,29]=0.9,s[20,30]=0.9
s[20,31]=-1.0,s[20,32]=0.0,s[20,33]=0.9,s[20,34]=-0.1,s[20,35]=-0.2,s[20,36]=0.9,s[20,37]=1.1,s[20,38]=-0.8,s[20,39]=0.1,s[20,40]=1.0,s[20,41]=0.0,s[20,42]=0.1,s[20,43]=0.6,s[20,44]=0.9,s[20,45]=-1.1,s[20,46]=0.4,s[20,47]=-0.9,s[20,48]=0.2,s[20,49]=-1.1,s[20,50]=1.0,s[20,51]=1.0,s[20,52]=0.9,s[20,53]=-1.0,s[20,54]=0.6,s[20,55]=-1.0,s[20,56]=-0.6,s[20,57]=-1.1,s[20,58]=0.2,s[20,59]=-0.7,s[20,60]=0.5
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float ppz = @ppz
float pxx = 0
float pyy = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
pyy = y
x = s[@sd,1] + s[@sd,2]*x + s[@sd,3]*x*x + s[@sd,4]*x*x*x + s[@sd,5]*x*x*y + s[@sd,6]*x*x*ppz + s[@sd,7]*x*y + \
s[@sd,8]*x*y*y + s[@sd,9]*x*y*ppz + s[@sd,10]*x*ppz + s[@sd,11]*x*ppz*ppz + s[@sd,12]*y + s[@sd,13]*y*y + s[@sd,14]*y*y*y + \
s[@sd,15]*y*y*ppz + s[@sd,16]*y*ppz + s[@sd,17]*y*ppz*ppz + s[@sd,18]*ppz +s[@sd,19]*ppz*ppz +s[@sd,20]*ppz*ppz*ppz
y = s[@sd,21] +s[@sd,22]*pxx +s[@sd,23]*pxx*pxx +s[@sd,24]*pxx*pxx*pxx +s[@sd,25]*pxx*pxx*y +s[@sd,26]*pxx*pxx*ppz +s[@sd,27]*pxx*y +\
s[@sd,28]*pxx*y*y +s[@sd,29]*pxx*y*ppz +s[@sd,30]*pxx*ppz +s[@sd,31]*pxx*ppz*ppz +s[@sd,32]*y +s[@sd,33]*y*y +s[@sd,34]*y*y*y + \
s[@sd,35]*y*y*ppz +s[@sd,36]*y*ppz +s[@sd,37]*y*ppz*ppz +s[@sd,38]*ppz +s[@sd,39]*ppz*ppz +s[@sd,40]*ppz*ppz*ppz
ppz = s[@sd,41] +s[@sd,42]*pxx +s[@sd,43]*pxx*pxx +s[@sd,44]*pxx*pxx*pxx +s[@sd,45]*pxx*pxx*pyy +s[@sd,46]*pxx*pxx*ppz +s[@sd,47]*pxx*pyy + \
s[@sd,48]*pxx*pyy*pyy +s[@sd,49]*pxx*pyy*ppz +s[@sd,50]*pxx*ppz +s[@sd,51]*pxx*ppz*ppz +s[@sd,52]*pyy +s[@sd,53]*pyy*pyy +s[@sd,54]*pyy*pyy*pyy + \
s[@sd,55]*pyy*pyy*ppz +s[@sd,56]*pyy*ppz +s[@sd,57]*pyy*ppz*ppz +s[@sd,58]*ppz +s[@sd,59]*ppz*ppz +s[@sd,60]*ppz*ppz*ppz
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y) + ppz*@pw)
float d = @distscale*|pz-(x + sgn*flip(y) + ppz*@pw)|
return d
endfunc
private:
float s[21,61]
default:
title = "Sprott3D_Cubic"
heading
text="Sprott 3D cubic attractors"
endheading
heading
text=" x -> Cubic in x, y and z"
endheading
heading
text=" y -> Cubic in x, y and z"
endheading
heading
text=" z -> Cubic in x, y and z"
endheading
int param v_trapshapesprott3d_Cubic
caption = "Version (Trap Shape Sprott3D_Cubic)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesprott3d_Cubic < 100
endparam
param sd
caption = "Sprott selector"
default = 0
enum = "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" \
"15" "16" "17" "18" "19" "20"
hint = "Each Sprott selector uses a different strange attractor."
endparam
heading
text = "'Initialize Height' sets the starting z value for the attractor."
endheading
float param ppz
caption = "Initialize Height"
default = 0.0
endparam
heading
text = "'Height weight' determines the weight of the final z value which is added \
to the trap distance."
endheading
complex param pw
caption = "Height weight"
default = (0.5,0)
endparam
float param distscale
caption = "Distance scale"
default = 2
endparam
float param s
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 15
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSprott3D_Cubic_ODE(common.ulb:TrapShape) {
; This shape uses a Sprott strange attractor.
; The Sprott attractors were developed by Julien C. Sprott, and are
; based upon polynomials and linear differential equations of polynomials.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSprott3D_Cubic_ODE(Generic pparent)
TrapShape.TrapShape(pparent)
s[0,1]=0.4,s[0,2]=0.7,s[0,3]=-0.5,s[0,4]=-0.3,s[0,5]=1.1,s[0,6]=-0.9,s[0,7]=0.6,s[0,8]=-0.5,s[0,9]=0.7,s[0,10]=0.1,s[0,11]=0.9,s[0,12]=1.1,s[0,13]=-0.8,s[0,14]=0.9,s[0,15]=-1.1,s[0,16]=-0.6,s[0,17]=1.0,s[0,18]=-1.2,s[0,19]=1.0,s[0,20]=0.8,s[0,21]=1.2,s[0,22]=-1.1,s[0,23]=-0.4,s[0,24]=-0.9,s[0,25]=-0.9,s[0,26]=0.8,s[0,27]=-0.5,s[0,28]=-1.1,s[0,29]=-0.2,s[0,30]=-0.6
s[0,31]=1.1,s[0,32]=0.1,s[0,33]=0.4,s[0,34]=-1.0,s[0,35]=0.3,s[0,36]=-0.7,s[0,37]=-1.2,s[0,38]=-0.5,s[0,39]=1.1,s[0,40]=1.1,s[0,41]=0.6,s[0,42]=0.9,s[0,43]=-0.3,s[0,44]=0.0,s[0,45]=1.2,s[0,46]=-1.2,s[0,47]=-0.9,s[0,48]=-0.3,s[0,49]=1.2,s[0,50]=-0.8,s[0,51]=1.2,s[0,52]=-0.1,s[0,53]=0.8,s[0,54]=-0.5,s[0,55]=-1.2,s[0,56]=0.6,s[0,57]=-0.1,s[0,58]=1.1,s[0,59]=-1.0,s[0,60]=0.3
s[1,1]=0.7,s[1,2]=0.0,s[1,3]=0.0,s[1,4]=-1.0,s[1,5]=0.6,s[1,6]=0.3,s[1,7]=0.0,s[1,8]=0.7,s[1,9]=-0.4,s[1,10]=0.5,s[1,11]=1.0,s[1,12]=-0.2,s[1,13]=0.8,s[1,14]=0.5,s[1,15]=0.3
s[1,16]=-0.8,s[1,17]=0.4,s[1,18]=0.8,s[1,19]=0.8,s[1,20]=-1.2,s[1,21]=-0.2,s[1,22]=0.6,s[1,23]=-1.1,s[1,24]=-0.9,s[1,25]=0.7,s[1,26]=0.2,s[1,27]=0.9,s[1,28]=1.1,s[1,29]=-0.2,s[1,30]=0.8
s[1,31]=0.8,s[1,32]=-0.1,s[1,33]=-0.1,s[1,34]=-0.7,s[1,35]=-0.8,s[1,36]=1.0,s[1,37]=0.8,s[1,38]=-0.7,s[1,39]=-1.1,s[1,40]=0.1,s[1,41]=-0.2,s[1,42]=0.8,s[1,43]=0.8,s[1,44]=-0.2,s[1,45]=-0.5
s[1,46]=-0.4,s[1,47]=-0.8,s[1,48]=0.1,s[1,49]=0.3,s[1,50]=0.6,s[1,51]=0.1,s[1,52]=-0.7,s[1,53]=-0.5,s[1,54]=0.5,s[1,55]=-0.3,s[1,56]=-0.1,s[1,57]=-0.3,s[1,58]=-0.6,s[1,59]=0.2,s[1,60]=-0.2
s[2,1]=-0.2,s[2,2]=0.5,s[2,3]=-1.1,s[2,4]=-1.1,s[2,5]=0.6,s[2,6]=-1.0,s[2,7]=0.0,s[2,8]=-0.2,s[2,9]=1.0,s[2,10]=-0.8,s[2,11]=0.7,s[2,12]=0.3,s[2,13]=0.8,s[2,14]=0.0,s[2,15]=-0.1
s[2,16]=0.7,s[2,17]=-0.1,s[2,18]=-0.2,s[2,19]=1.1,s[2,20]=-0.7,s[2,21]=0.1,s[2,22]=-0.8,s[2,23]=-0.1,s[2,24]=-0.7,s[2,25]=0.3,s[2,26]=-0.9,s[2,27]=1.1,s[2,28]=-0.5,s[2,29]=0.6,s[2,30]=-0.4
s[2,31]=-0.4,s[2,32]=-0.9,s[2,33]=0.3,s[2,34]=-1.2,s[2,35]=0.2,s[2,36]=-0.6,s[2,37]=0.1,s[2,38]=0.2,s[2,39]=1.2,s[2,40]=0.1,s[2,41]=1.0,s[2,42]=-0.6,s[2,43]=0.5,s[2,44]=0.6,s[2,45]=-0.1
s[2,46]=1.0,s[2,47]=-1.1,s[2,48]=-0.6,s[2,49]=-1.2,s[2,50]=0.9,s[2,51]=0.6,s[2,52]=0.5,s[2,53]=-0.6,s[2,54]=0.8,s[2,55]=0.2,s[2,56]=0.9,s[2,57]=-0.7,s[2,58]=0.6,s[2,59]=-0.1,s[2,60]=-0.2
s[3,1]=1.0,s[3,2]=-0.7,s[3,3]=0.6,s[3,4]=-0.3,s[3,5]=-0.5,s[3,6]=-0.2,s[3,7]=-0.4,s[3,8]=-0.1,s[3,9]=-0.9,s[3,10]=-0.6,s[3,11]=1.0,s[3,12]=-0.1,s[3,13]=-0.6,s[3,14]=1.2,s[3,15]=-0.4
s[3,16]=-0.5,s[3,17]=-0.2,s[3,18]=0.5,s[3,19]=0.0,s[3,20]=0.7,s[3,21]=0.5,s[3,22]=0.4,s[3,23]=-0.4,s[3,24]=-0.2,s[3,25]=0.9,s[3,26]=-0.7,s[3,27]=0.6,s[3,28]=0.1,s[3,29]=1.0,s[3,30]=-0.6
s[3,31]=-1.1,s[3,32]=-1.0,s[3,33]=0.2,s[3,34]=-1.0,s[3,35]=0.4,s[3,36]=0.0,s[3,37]=-0.3,s[3,38]=-0.5,s[3,39]=-1.1,s[3,40]=1.2,s[3,41]=0.6,s[3,42]=-0.3,s[3,43]=-1.1,s[3,44]=-0.6,s[3,45]=-0.1
s[3,46]=-0.9,s[3,47]=-0.8,s[3,48]=-0.1,s[3,49]=0.5,s[3,50]=0.5,s[3,51]=-0.4,s[3,52]=-0.2,s[3,53]=0.8,s[3,54]=0.4,s[3,55]=-0.5,s[3,56]=0.4,s[3,57]=0.6,s[3,58]=0.7,s[3,59]=-0.6,s[3,60]=-0.6
s[4,1]=0.9,s[4,2]=-0.2,s[4,3]=-1.1,s[4,4]=-1.1,s[4,5]=0.9,s[4,6]=-0.4,s[4,7]=-0.1,s[4,8]=-0.4,s[4,9]=-1.0,s[4,10]=0.0,s[4,11]=0.1,s[4,12]=-0.7,s[4,13]=-0.8,s[4,14]=-0.6,s[4,15]=-1.2
s[4,16]=0.0,s[4,17]=0.1,s[4,18]=-0.1,s[4,19]=0.9,s[4,20]=1.2,s[4,21]=-0.2,s[4,22]=-0.8,s[4,23]=-0.6,s[4,24]=0.2,s[4,25]=-0.6,s[4,26]=0.7,s[4,27]=0.1,s[4,28]=1.2,s[4,29]=-0.1,s[4,30]=-0.3
s[4,31]=-0.8,s[4,32]=-0.1,s[4,33]=-1.2,s[4,34]=-1.2,s[4,35]=1.1,s[4,36]=-0.8,s[4,37]=0.1,s[4,38]=-0.9,s[4,39]=-0.3,s[4,40]=0.5,s[4,41]=0.6,s[4,42]=0.6,s[4,43]=0.6,s[4,44]=-1.1,s[4,45]=-0.4
s[4,46]=-0.4,s[4,47]=-0.4,s[4,48]=-0.7,s[4,49]=0.1,s[4,50]=0.8,s[4,51]=0.3,s[4,52]=-0.6,s[4,53]=-0.4,s[4,54]=-1.2,s[4,55]=0.6,s[4,56]=-0.7,s[4,57]=-0.7,s[4,58]=0.8,s[4,59]=0.3,s[4,60]=-0.3
s[5,1]=1.0,s[5,2]=0.4,s[5,3]=0.7,s[5,4]=-1.1,s[5,5]=-0.3,s[5,6]=-0.9,s[5,7]=0.9,s[5,8]=-0.3,s[5,9]=-0.3,s[5,10]=-0.6,s[5,11]=-0.1,s[5,12]=0.6,s[5,13]=0.7,s[5,14]=0.6,s[5,15]=-0.3
s[5,16]=-0.8,s[5,17]=-1.1,s[5,18]=0.2,s[5,19]=0.0,s[5,20]=-0.3,s[5,21]=-0.5,s[5,22]=-0.9,s[5,23]=1.0,s[5,24]=-0.4,s[5,25]=-1.0,s[5,26]=0.4,s[5,27]=0.5,s[5,28]=1.1,s[5,29]=0.6,s[5,30]=-1.2
s[5,31]=-0.2,s[5,32]=1.1,s[5,33]=1.0,s[5,34]=-0.9,s[5,35]=-0.2,s[5,36]=-0.5,s[5,37]=-0.8,s[5,38]=0.2,s[5,39]=-1.0,s[5,40]=-1.1,s[5,41]=0.6,s[5,42]=0.9,s[5,43]=0.3,s[5,44]=-0.2,s[5,45]=-0.9
s[5,46]=0.2,s[5,47]=-0.8,s[5,48]=0.2,s[5,49]=-1.2,s[5,50]=0.3,s[5,51]=0.4,s[5,52]=0.6,s[5,53]=-0.1,s[5,54]=1.1,s[5,55]=0.0,s[5,56]=0.5,s[5,57]=0.7,s[5,58]=0.7,s[5,59]=0.3,s[5,60]=0.1
s[6,1]=0.3,s[6,2]=-0.8,s[6,3]=1.1,s[6,4]=-0.7,s[6,5]=-0.7,s[6,6]=-1.2,s[6,7]=0.3,s[6,8]=-0.9,s[6,9]=0.2,s[6,10]=1.2,s[6,11]=-1.1,s[6,12]=-0.7,s[6,13]=-1.2,s[6,14]=-0.4,s[6,15]=-0.5
s[6,16]=-0.7,s[6,17]=-0.6,s[6,18]=-1.1,s[6,19]=-0.8,s[6,20]=0.8,s[6,21]=0.2,s[6,22]=0.7,s[6,23]=-0.7,s[6,24]=-0.4,s[6,25]=-1.0,s[6,26]=0.5,s[6,27]=0.2,s[6,28]=-1.1,s[6,29]=0.7,s[6,30]=1.1
s[6,31]=1.1,s[6,32]=-0.1,s[6,33]=-0.9,s[6,34]=0.1,s[6,35]=-0.9,s[6,36]=0.0,s[6,37]=0.3,s[6,38]=-1.0,s[6,39]=-0.5,s[6,40]=0.2,s[6,41]=-0.3,s[6,42]=-0.1,s[6,43]=0.4,s[6,44]=0.1,s[6,45]=-0.9
s[6,46]=0.2,s[6,47]=-1.0,s[6,48]=-0.4,s[6,49]=0.9,s[6,50]=-0.1,s[6,51]=-1.2,s[6,52]=-0.5,s[6,53]=-0.9,s[6,54]=0.4,s[6,55]=0.5,s[6,56]=0.3,s[6,57]=0.3,s[6,58]=-0.8,s[6,59]=-0.8,s[6,60]=-1.1
s[7,1]=-0.3,s[7,2]=0.6,s[7,3]=-1.0,s[7,4]=0.7,s[7,5]=-0.3,s[7,6]=-0.9,s[7,7]=1.2,s[7,8]=1.0,s[7,9]=-0.2,s[7,10]=0.1,s[7,11]=-0.8,s[7,12]=-0.9,s[7,13]=0.1,s[7,14]=-1.0,s[7,15]=0.9
s[7,16]=-1.0,s[7,17]=-0.3,s[7,18]=-0.1,s[7,19]=-0.5,s[7,20]=-0.2,s[7,21]=-0.4,s[7,22]=0.4,s[7,23]=-1.1,s[7,24]=0.7,s[7,25]=0.4,s[7,26]=0.7,s[7,27]=0.2,s[7,28]=0.7,s[7,29]=-0.2,s[7,30]=0.3
s[7,31]=0.6,s[7,32]=-0.3,s[7,33]=1.2,s[7,34]=0.9,s[7,35]=0.2,s[7,36]=-0.2,s[7,37]=-0.2,s[7,38]=1.1,s[7,39]=-0.6,s[7,40]=-0.5,s[7,41]=-0.8,s[7,42]=-0.5,s[7,43]=-1.0,s[7,44]=-0.4,s[7,45]=-0.8
s[7,46]=-0.7,s[7,47]=-0.8,s[7,48]=0.8,s[7,49]=-1.1,s[7,50]=0.5,s[7,51]=-0.9,s[7,52]=0.7,s[7,53]=0.2,s[7,54]=0.6,s[7,55]=1.1,s[7,56]=0.6,s[7,57]=0.7,s[7,58]=0.4,s[7,59]=0.8,s[7,60]=-0.9
s[8,1]=-0.1,s[8,2]=1.0,s[8,3]=0.4,s[8,4]=-0.6,s[8,5]=0.2,s[8,6]=1.2,s[8,7]=0.2,s[8,8]=-0.5,s[8,9]=1.0,s[8,10]=0.6,s[8,11]=0.3,s[8,12]=0.9,s[8,13]=0.2,s[8,14]=-0.2,s[8,15]=0.1
s[8,16]=-0.6,s[8,17]=-1.0,s[8,18]=0.6,s[8,19]=0.8,s[8,20]=-1.0,s[8,21]=-0.2,s[8,22]=1.1,s[8,23]=0.6,s[8,24]=-0.7,s[8,25]=-0.7,s[8,26]=-0.7,s[8,27]=0.7,s[8,28]=-0.1,s[8,29]=-0.2,s[8,30]=-1.1
s[8,31]=0.1,s[8,32]=1.1,s[8,33]=0.5,s[8,34]=0.1,s[8,35]=0.8,s[8,36]=-0.4,s[8,37]=-0.4,s[8,38]=-1.0,s[8,39]=1.2,s[8,40]=0.5,s[8,41]=-1.0,s[8,42]=-1.1,s[8,43]=-0.8,s[8,44]=0.8,s[8,45]=0.0
s[8,46]=-1.2,s[8,47]=-1.0,s[8,48]=-0.9,s[8,49]=0.8,s[8,50]=-0.4,s[8,51]=-0.9,s[8,52]=1.0,s[8,53]=0.8,s[8,54]=-0.9,s[8,55]=-0.9,s[8,56]=1.1,s[8,57]=-0.8,s[8,58]=0.9,s[8,59]=0.7,s[8,60]=-1.1
s[9,1]=-0.3,s[9,2]=0.8,s[9,3]=0.4,s[9,4]=-1.0,s[9,5]=0.7,s[9,6]=1.1,s[9,7]=1.1,s[9,8]=1.1,s[9,9]=0.1,s[9,10]=0.6,s[9,11]=0.3,s[9,12]=0.0,s[9,13]=0.6,s[9,14]=0.1,s[9,15]=0.0
s[9,16]=-0.3,s[9,17]=-1.0,s[9,18]=-1.0,s[9,19]=0.0,s[9,20]=-0.8,s[9,21]=-0.5,s[9,22]=0.9,s[9,23]=-0.6,s[9,24]=0.6,s[9,25]=-0.6,s[9,26]=0.4,s[9,27]=-0.2,s[9,28]=1.2,s[9,29]=-0.5,s[9,30]=0.3
s[9,31]=-0.9,s[9,32]=-1.0,s[9,33]=0.2,s[9,34]=-0.4,s[9,35]=0.0,s[9,36]=0.4,s[9,37]=-0.5,s[9,38]=-0.1,s[9,39]=-0.7,s[9,40]=0.4,s[9,41]=1.2,s[9,42]=-0.3,s[9,43]=0.7,s[9,44]=1.0,s[9,45]=0.8
s[9,46]=-0.1,s[9,47]=-0.9,s[9,48]=-0.2,s[9,49]=-0.9,s[9,50]=0.6,s[9,51]=0.5,s[9,52]=-0.3,s[9,53]=-0.2,s[9,54]=0.3,s[9,55]=-0.2,s[9,56]=-1.0,s[9,57]=0.1,s[9,58]=-0.6,s[9,59]=0.8,s[9,60]=-0.2
s[10,1]=0.9,s[10,2]=0.1,s[10,3]=-1.1,s[10,4]=0.5,s[10,5]=1.2,s[10,6]=-0.9,s[10,7]=-0.4,s[10,8]=-1.0,s[10,9]=-0.1,s[10,10]=0.8,s[10,11]=-0.4,s[10,12]=1.2,s[10,13]=-0.9,s[10,14]=0.0,s[10,15]=0.1
s[10,16]=-0.3,s[10,17]=-0.3,s[10,18]=0.1,s[10,19]=0.2,s[10,20]=1.0,s[10,21]=-0.8,s[10,22]=0.4,s[10,23]=0.9,s[10,24]=0.2,s[10,25]=-0.9,s[10,26]=-0.4,s[10,27]=-0.6,s[10,28]=1.0,s[10,29]=0.4,s[10,30]=0.0
s[10,31]=0.8,s[10,32]=-0.9,s[10,33]=0.3,s[10,34]=-0.2,s[10,35]=-0.3,s[10,36]=0.0,s[10,37]=-0.4,s[10,38]=-0.6,s[10,39]=0.6,s[10,40]=0.9,s[10,41]=-0.1,s[10,42]=1.0,s[10,43]=0.7,s[10,44]=0.2,s[10,45]=0.3
s[10,46]=0.0,s[10,47]=0.7,s[10,48]=-0.8,s[10,49]=1.2,s[10,50]=0.8,s[10,51]=0.0,s[10,52]=-1.1,s[10,53]=0.2,s[10,54]=0.1,s[10,55]=-0.7,s[10,56]=-0.7,s[10,57]=-0.8,s[10,58]=0.3,s[10,59]=0.8,s[10,60]=-0.6
s[11,1]=-0.3,s[11,2]=-0.3,s[11,3]=-0.9,s[11,4]=-1.2,s[11,5]=-0.6,s[11,6]=1.2,s[11,7]=0.9,s[11,8]=-0.5,s[11,9]=-0.5,s[11,10]=-0.9,s[11,11]=-0.9,s[11,12]=0.0,s[11,13]=-0.7,s[11,14]=0.0,s[11,15]=0.1
s[11,16]=-0.5,s[11,17]=0.1,s[11,18]=1.2,s[11,19]=-1.2,s[11,20]=-0.7,s[11,21]=-0.4,s[11,22]=-0.6,s[11,23]=0.3,s[11,24]=-1.2,s[11,25]=-1.2,s[11,26]=-0.2,s[11,27]=1.2,s[11,28]=1.1,s[11,29]=0.0,s[11,30]=0.4
s[11,31]=-1.2,s[11,32]=-0.2,s[11,33]=-1.1,s[11,34]=-1.1,s[11,35]=0.5,s[11,36]=-0.2,s[11,37]=0.0,s[11,38]=0.9,s[11,39]=-0.9,s[11,40]=0.9,s[11,41]=-0.4,s[11,42]=-0.5,s[11,43]=-0.9,s[11,44]=-0.6,s[11,45]=1.1
s[11,46]=-0.2,s[11,47]=0.7,s[11,48]=0.7,s[11,49]=-0.9,s[11,50]=-0.9,s[11,51]=-1.1,s[11,52]=0.9,s[11,53]=-0.8,s[11,54]=-1.0,s[11,55]=-0.6,s[11,56]=-0.8,s[11,57]=0.3,s[11,58]=0.8,s[11,59]=0.7,s[11,60]=-0.3
s[12,1]=0.5,s[12,2]=-1.0,s[12,3]=-0.4,s[12,4]=-0.7,s[12,5]=0.9,s[12,6]=0.9,s[12,7]=-0.9,s[12,8]=0.7,s[12,9]=0.9,s[12,10]=-1.2,s[12,11]=0.8,s[12,12]=0.2,s[12,13]=-0.4,s[12,14]=-1.0,s[12,15]=-0.9
s[12,16]=0.5,s[12,17]=-0.5,s[12,18]=0.0,s[12,19]=0.9,s[12,20]=-1.0,s[12,21]=0.8,s[12,22]=-0.9,s[12,23]=-0.9,s[12,24]=0.2,s[12,25]=0.4,s[12,26]=1.2,s[12,27]=0.8,s[12,28]=1.0,s[12,29]=-1.0,s[12,30]=0.3
s[12,31]=0.2,s[12,32]=-1.2,s[12,33]=-0.2,s[12,34]=-1.0,s[12,35]=-0.5,s[12,36]=-0.4,s[12,37]=-0.3,s[12,38]=-0.9,s[12,39]=-0.2,s[12,40]=0.2,s[12,41]=-0.9,s[12,42]=-0.3,s[12,43]=-1.2,s[12,44]=0.8,s[12,45]=1.1
s[12,46]=1.1,s[12,47]=-0.9,s[12,48]=0.1,s[12,49]=0.6,s[12,50]=-0.5,s[12,51]=-0.2,s[12,52]=0.2,s[12,53]=-0.3,s[12,54]=-0.9,s[12,55]=-0.6,s[12,56]=0.3,s[12,57]=0.6,s[12,58]=-0.1,s[12,59]=0.7,s[12,60]=-0.9
s[13,1]=-0.9,s[13,2]=-0.9,s[13,3]=-0.8,s[13,4]=0.3,s[13,5]=-0.9,s[13,6]=-1.1,s[13,7]=1.0,s[13,8]=0.0,s[13,9]=0.7,s[13,10]=-0.8,s[13,11]=1.0,s[13,12]=0.0,s[13,13]=-0.7,s[13,14]=-1.1,s[13,15]=-1.1
s[13,16]=-1.2,s[13,17]=0.7,s[13,18]=-0.7,s[13,19]=-0.1,s[13,20]=-1.1,s[13,21]=-1.0,s[13,22]=0.6,s[13,23]=-1.0,s[13,24]=0.5,s[13,25]=-0.7,s[13,26]=0.2,s[13,27]=-0.9,s[13,28]=-1.1,s[13,29]=0.6,s[13,30]=0.9
s[13,31]=0.6,s[13,32]=-1.1,s[13,33]=-0.1,s[13,34]=-0.5,s[13,35]=1.0,s[13,36]=-1.1,s[13,37]=-1.2,s[13,38]=-0.8,s[13,39]=0.7,s[13,40]=-0.8,s[13,41]=-0.7,s[13,42]=-0.8,s[13,43]=-0.8,s[13,44]=0.5,s[13,45]=0.6
s[13,46]=0.2,s[13,47]=-0.2,s[13,48]=0.7,s[13,49]=0.8,s[13,50]=0.0,s[13,51]=-1.2,s[13,52]=-0.3,s[13,53]=1.1,s[13,54]=-0.9,s[13,55]=0.1,s[13,56]=0.3,s[13,57]=-0.6,s[13,58]=-0.8,s[13,59]=0.1,s[13,60]=0.3
s[14,1]=-0.4,s[14,2]=-0.2,s[14,3]=0.5,s[14,4]=-1.0,s[14,5]=-0.2,s[14,6]=0.8,s[14,7]=-0.1,s[14,8]=0.7,s[14,9]=0.7,s[14,10]=-0.4,s[14,11]=0.4,s[14,12]=0.0,s[14,13]=0.7,s[14,14]=-0.1,s[14,15]=0.3
s[14,16]=-0.4,s[14,17]=-0.1,s[14,18]=-1.0,s[14,19]=0.3,s[14,20]=1.1,s[14,21]=1.2,s[14,22]=0.8,s[14,23]=0.2,s[14,24]=0.1,s[14,25]=-0.7,s[14,26]=-0.9,s[14,27]=-0.5,s[14,28]=1.1,s[14,29]=-1.1,s[14,30]=-0.2
s[14,31]=0.2,s[14,32]=0.5,s[14,33]=-0.8,s[14,34]=-1.1,s[14,35]=-1.1,s[14,36]=-0.2,s[14,37]=0.7,s[14,38]=0.8,s[14,39]=0.2,s[14,40]=0.0,s[14,41]=-0.4,s[14,42]=0.7,s[14,43]=0.6,s[14,44]=-0.3,s[14,45]=0.9
s[14,46]=-1.1,s[14,47]=-0.7,s[14,48]=0.3,s[14,49]=1.0,s[14,50]=0.3,s[14,51]=-0.7,s[14,52]=0.0,s[14,53]=0.6,s[14,54]=0.0,s[14,55]=0.8,s[14,56]=0.5,s[14,57]=0.4,s[14,58]=1.2,s[14,59]=1.0,s[14,60]=-0.7
s[15,1]=0.1,s[15,2]=0.0,s[15,3]=-0.7,s[15,4]=-0.8,s[15,5]=0.5,s[15,6]=1.0,s[15,7]=-0.6,s[15,8]=-0.8,s[15,9]=-0.7,s[15,10]=0.8,s[15,11]=1.0,s[15,12]=0.0,s[15,13]=0.2,s[15,14]=0.7,s[15,15]=0.6
s[15,16]=-0.3,s[15,17]=-1.0,s[15,18]=-1.0,s[15,19]=-0.1,s[15,20]=-0.5,s[15,21]=0.4,s[15,22]=-1.1,s[15,23]=-0.2,s[15,24]=0.3,s[15,25]=-1.1,s[15,26]=0.6,s[15,27]=0.4,s[15,28]=0.1,s[15,29]=-0.7,s[15,30]=-0.2
s[15,31]=-0.4,s[15,32]=-0.9,s[15,33]=0.0,s[15,34]=-0.1,s[15,35]=-0.1,s[15,36]=1.1,s[15,37]=0.2,s[15,38]=-0.5,s[15,39]=-0.5,s[15,40]=-0.7,s[15,41]=-1.0,s[15,42]=-0.5,s[15,43]=0.9,s[15,44]=0.8,s[15,45]=0.6
s[15,46]=0.1,s[15,47]=-0.2,s[15,48]=-1.0,s[15,49]=-0.5,s[15,50]=0.5,s[15,51]=-0.9,s[15,52]=0.7,s[15,53]=0.8,s[15,54]=-0.5,s[15,55]=-0.5,s[15,56]=-0.3,s[15,57]=1.1,s[15,58]=0.5,s[15,59]=0.9,s[15,60]=0.1
s[16,1]=-1.1,s[16,2]=0.2,s[16,3]=0.6,s[16,4]=-0.4,s[16,5]=-0.2,s[16,6]=1.0,s[16,7]=0.8,s[16,8]=-0.6,s[16,9]=-1.2,s[16,10]=-1.0,s[16,11]=0.1,s[16,12]=-0.5,s[16,13]=0.0,s[16,14]=0.1,s[16,15]=1.1
s[16,16]=1.2,s[16,17]=0.3,s[16,18]=1.1,s[16,19]=-0.7,s[16,20]=-0.6,s[16,21]=0.5,s[16,22]=-0.5,s[16,23]=-1.0,s[16,24]=0.9,s[16,25]=-1.0,s[16,26]=0.4,s[16,27]=1.2,s[16,28]=-0.2,s[16,29]=0.7,s[16,30]=0.5
s[16,31]=-1.0,s[16,32]=1.1,s[16,33]=1.1,s[16,34]=0.6,s[16,35]=0.0,s[16,36]=1.2,s[16,37]=0.1,s[16,38]=0.5,s[16,39]=0.9,s[16,40]=0.6,s[16,41]=0.5,s[16,42]=0.2,s[16,43]=0.2,s[16,44]=1.1,s[16,45]=-0.1
s[16,46]=-0.3,s[16,47]=-0.4,s[16,48]=0.9,s[16,49]=0.5,s[16,50]=0.8,s[16,51]=0.3,s[16,52]=-0.2,s[16,53]=-1.2,s[16,54]=1.1,s[16,55]=0.3,s[16,56]=0.5,s[16,57]=0.0,s[16,58]=-1.1,s[16,59]=0.2,s[16,60]=-0.5
s[17,1]=0.1,s[17,2]=0.9,s[17,3]=0.0,s[17,4]=-1.0,s[17,5]=0.2,s[17,6]=-0.7,s[17,7]=0.3,s[17,8]=1.0,s[17,9]=-0.5,s[17,10]=0.4,s[17,11]=0.4,s[17,12]=0.8,s[17,13]=-0.7,s[17,14]=-0.5,s[17,15]=-0.9
s[17,16]=0.2,s[17,17]=0.0,s[17,18]=0.1,s[17,19]=1.0,s[17,20]=0.9,s[17,21]=-0.4,s[17,22]=-0.2,s[17,23]=0.7,s[17,24]=-1.1,s[17,25]=-0.8,s[17,26]=-0.7,s[17,27]=0.3,s[17,28]=-0.7,s[17,29]=-0.7,s[17,30]=0.3
s[17,31]=1.2,s[17,32]=0.7,s[17,33]=0.6,s[17,34]=-1.2,s[17,35]=-0.1,s[17,36]=0.3,s[17,37]=0.1,s[17,38]=-0.1,s[17,39]=-0.1,s[17,40]=-1.0,s[17,41]=0.2,s[17,42]=0.4,s[17,43]=-0.8,s[17,44]=-0.1,s[17,45]=0.7
s[17,46]=-0.8,s[17,47]=-0.6,s[17,48]=-0.4,s[17,49]=-0.8,s[17,50]=0.7,s[17,51]=0.3,s[17,52]=1.1,s[17,53]=-0.5,s[17,54]=0.9,s[17,55]=0.9,s[17,56]=-1.0,s[17,57]=-0.9,s[17,58]=-1.0,s[17,59]=0.8,s[17,60]=-1.2
s[18,1]=0.0,s[18,2]=-0.7,s[18,3]=-0.1,s[18,4]=1.1,s[18,5]=-1.2,s[18,6]=0.8,s[18,7]=1.0,s[18,8]=-0.1,s[18,9]=0.2,s[18,10]=0.0,s[18,11]=-0.5,s[18,12]=-0.3,s[18,13]=0.1,s[18,14]=0.9,s[18,15]=1.2
s[18,16]=0.8,s[18,17]=0.6,s[18,18]=-1.2,s[18,19]=-0.8,s[18,20]=1.0,s[18,21]=0.4,s[18,22]=-0.6,s[18,23]=-0.7,s[18,24]=-0.2,s[18,25]=0.7,s[18,26]=0.0,s[18,27]=-0.6,s[18,28]=1.1,s[18,29]=1.2,s[18,30]=-0.6
s[18,31]=0.9,s[18,32]=1.1,s[18,33]=-0.2,s[18,34]=-1.2,s[18,35]=0.2,s[18,36]=0.5,s[18,37]=-0.2,s[18,38]=-1.1,s[18,39]=-0.5,s[18,40]=0.9,s[18,41]=0.5,s[18,42]=0.0,s[18,43]=1.0,s[18,44]=-0.7,s[18,45]=0.6
s[18,46]=-0.4,s[18,47]=0.0,s[18,48]=-0.9,s[18,49]=1.0,s[18,50]=-0.6,s[18,51]=-0.3,s[18,52]=-0.4,s[18,53]=0.0,s[18,54]=-0.9,s[18,55]=0.9,s[18,56]=0.5,s[18,57]=-0.3,s[18,58]=-1.2,s[18,59]=-0.1,s[18,60]=-1.1
s[19,1]=-1.1,s[19,2]=0.6,s[19,3]=0.6,s[19,4]=0.0,s[19,5]=-0.4,s[19,6]=-0.4,s[19,7]=-0.1,s[19,8]=-1.2,s[19,9]=-1.0,s[19,10]=1.2,s[19,11]=0.1,s[19,12]=-1.2,s[19,13]=-1.1,s[19,14]=0.6,s[19,15]=1.1
s[19,16]=1.1,s[19,17]=-0.6,s[19,18]=0.3,s[19,19]=0.4,s[19,20]=0.3,s[19,21]=1.1,s[19,22]=0.9,s[19,23]=-0.4,s[19,24]=1.1,s[19,25]=-0.3,s[19,26]=-1.1,s[19,27]=-0.9,s[19,28]=-1.2,s[19,29]=0.3,s[19,30]=0.3
s[19,31]=-1.1,s[19,32]=0.2,s[19,33]=-0.2,s[19,34]=-1.0,s[19,35]=-1.1,s[19,36]=0.9,s[19,37]=0.4,s[19,38]=-0.6,s[19,39]=1.1,s[19,40]=-0.1,s[19,41]=-0.7,s[19,42]=0.9,s[19,43]=-0.4,s[19,44]=-0.3,s[19,45]=0.7
s[19,46]=-0.8,s[19,47]=-1.2,s[19,48]=-0.1,s[19,49]=-0.3,s[19,50]=-0.6,s[19,51]=-1.1,s[19,52]=-0.2,s[19,53]=-1.2,s[19,54]=-1.1,s[19,55]=1.1,s[19,56]=-0.5,s[19,57]=0.9,s[19,58]=-0.3,s[19,59]=0.9,s[19,60]=-1.2
s[20,1]=-0.2,s[20,2]=-0.1,s[20,3]=0.6,s[20,4]=-0.1,s[20,5]=0.7,s[20,6]=0.2,s[20,7]=0.8,s[20,8]=-0.3,s[20,9]=0.7,s[20,10]=-0.9,s[20,11]=-0.1,s[20,12]=0.6,s[20,13]=-0.4,s[20,14]=-1.1,s[20,15]=0.8
s[20,16]=1.0,s[20,17]=-0.7,s[20,18]=-0.1,s[20,19]=-0.3,s[20,20]=-0.1,s[20,21]=-0.6,s[20,22]=0.1,s[20,23]=-0.5,s[20,24]=-0.4,s[20,25]=-1.2,s[20,26]=-1.2,s[20,27]=0.6,s[20,28]=-0.9,s[20,29]=0.8,s[20,30]=0.4
s[20,31]=1.1,s[20,32]=-0.9,s[20,33]=0.9,s[20,34]=-0.8,s[20,35]=0.5,s[20,36]=0.1,s[20,37]=0.3,s[20,38]=-1.2,s[20,39]=0.2,s[20,40]=-0.9,s[20,41]=-0.5,s[20,42]=-0.3,s[20,43]=1.1,s[20,44]=1.1,s[20,45]=0.8
s[20,46]=-0.4,s[20,47]=0.1,s[20,48]=-0.6,s[20,49]=0.7,s[20,50]=-0.8,s[20,51]=1.0,s[20,52]=-0.4,s[20,53]=-0.4,s[20,54]=0.9,s[20,55]=-0.1,s[20,56]=0.3,s[20,57]=-0.4,s[20,58]=-0.1,s[20,59]=-0.3,s[20,60]=-0.3
s[21,1]=-0.2,s[21,2]=-0.3,s[21,3]=-0.2,s[21,4]=0.9,s[21,5]=1.0,s[21,6]=-0.1,s[21,7]=0.0,s[21,8]=0.0,s[21,9]=0.6,s[21,10]=-1.0,s[21,11]=-1.2,s[21,12]=-0.7,s[21,13]=-0.5,s[21,14]=-0.1,s[21,15]=-0.6
s[21,16]=-0.6,s[21,17]=-0.2,s[21,18]=0.6,s[21,19]=-0.9,s[21,20]=-0.2,s[21,21]=-0.6,s[21,22]=0.7,s[21,23]=1.1,s[21,24]=-0.3,s[21,25]=0.6,s[21,26]=-1.1,s[21,27]=-0.9,s[21,28]=0.3,s[21,29]=0.2,s[21,30]=0.7
s[21,31]=0.3,s[21,32]=-1.2,s[21,33]=-0.9,s[21,34]=-0.1,s[21,35]=0.1,s[21,36]=1.2,s[21,37]=-1.2,s[21,38]=-1.1,s[21,39]=0.4,s[21,40]=0.3,s[21,41]=0.8,s[21,42]=-0.8,s[21,43]=1.1,s[21,44]=-0.4,s[21,45]=-1.2
s[21,46]=-0.5,s[21,47]=-0.3,s[21,48]=0.9,s[21,49]=0.5,s[21,50]=0.6,s[21,51]=-1.2,s[21,52]=-0.8,s[21,53]=0.4,s[21,54]=0.9,s[21,55]=0.4,s[21,56]=1.1,s[21,57]=0.2,s[21,58]=1.2,s[21,59]=0.3,s[21,60]=-1.1
s[22,1]=0.1,s[22,2]=0.7,s[22,3]=-0.9,s[22,4]=0.0,s[22,5]=0.3,s[22,6]=-0.8,s[22,7]=-1.1,s[22,8]=-0.5,s[22,9]=0.4,s[22,10]=-1.0,s[22,11]=0.2,s[22,12]=-0.3,s[22,13]=-1.0,s[22,14]=1.0,s[22,15]=-0.5
s[22,16]=-1.1,s[22,17]=0.4,s[22,18]=-0.9,s[22,19]=0.6,s[22,20]=0.5,s[22,21]=1.0,s[22,22]=-0.2,s[22,23]=-0.4,s[22,24]=0.4,s[22,25]=0.5,s[22,26]=0.1,s[22,27]=0.0,s[22,28]=-0.7,s[22,29]=-0.9,s[22,30]=-0.9
s[22,31]=-0.1,s[22,32]=0.6,s[22,33]=-0.8,s[22,34]=-0.4,s[22,35]=-1.1,s[22,36]=-1.0,s[22,37]=-1.2,s[22,38]=0.1,s[22,39]=-0.1,s[22,40]=-1.2,s[22,41]=-0.4,s[22,42]=0.8,s[22,43]=0.5,s[22,44]=0.2,s[22,45]=-1.1
s[22,46]=0.7,s[22,47]=0.2,s[22,48]=-0.7,s[22,49]=-0.2,s[22,50]=-1.2,s[22,51]=1.2,s[22,52]=0.5,s[22,53]=-0.8,s[22,54]=0.8,s[22,55]=-0.7,s[22,56]=0.7,s[22,57]=-1.2,s[22,58]=0.4,s[22,59]=1.2,s[22,60]=-1.1
s[23,1]=0.7,s[23,2]=-0.6,s[23,3]=-0.3,s[23,4]=-0.5,s[23,5]=-0.1,s[23,6]=1.2,s[23,7]=-0.2,s[23,8]=0.4,s[23,9]=0.7,s[23,10]=-1.2,s[23,11]=-0.4,s[23,12]=0.1,s[23,13]=0.0,s[23,14]=-0.5,s[23,15]=0.4
s[23,16]=-0.4,s[23,17]=-0.6,s[23,18]=-0.9,s[23,19]=1.1,s[23,20]=-1.1,s[23,21]=0.8,s[23,22]=-1.0,s[23,23]=-0.1,s[23,24]=-0.3,s[23,25]=0.9,s[23,26]=-0.4,s[23,27]=0.5,s[23,28]=-1.0,s[23,29]=1.1,s[23,30]=-0.4
s[23,31]=-0.1,s[23,32]=0.1,s[23,33]=0.2,s[23,34]=-0.2,s[23,35]=-1.2,s[23,36]=0.8,s[23,37]=-0.9,s[23,38]=0.1,s[23,39]=-0.3,s[23,40]=-0.7,s[23,41]=-0.1,s[23,42]=-1.0,s[23,43]=0.5,s[23,44]=-0.8,s[23,45]=1.1
s[23,46]=0.4,s[23,47]=-0.9,s[23,48]=-0.2,s[23,49]=-0.7,s[23,50]=1.0,s[23,51]=-1.2,s[23,52]=-0.3,s[23,53]=-0.7,s[23,54]=1.2,s[23,55]=0.5,s[23,56]=-0.1,s[23,57]=0.6,s[23,58]=-0.7,s[23,59]=0.9,s[23,60]=-1.2
s[24,1]=0.3,s[24,2]=0.9,s[24,3]=-0.9,s[24,4]=-0.7,s[24,5]=-1.1,s[24,6]=1.2,s[24,7]=-1.1,s[24,8]=1.0,s[24,9]=0.7,s[24,10]=1.2,s[24,11]=-0.7,s[24,12]=0.3,s[24,13]=1.2,s[24,14]=1.2,s[24,15]=0.3
s[24,16]=-0.1,s[24,17]=-0.6,s[24,18]=-1.2,s[24,19]=1.2,s[24,20]=1.2,s[24,21]=-0.9,s[24,22]=-0.2,s[24,23]=0.2,s[24,24]=-0.5,s[24,25]=-1.1,s[24,26]=-1.0,s[24,27]=-1.2,s[24,28]=-0.5,s[24,29]=0.2,s[24,30]=-0.2
s[24,31]=0.3,s[24,32]=-0.9,s[24,33]=0.4,s[24,34]=-0.9,s[24,35]=-0.5,s[24,36]=-1.0,s[24,37]=0.3,s[24,38]=0.6,s[24,39]=-0.5,s[24,40]=-1.0,s[24,41]=-0.8,s[24,42]=-0.1,s[24,43]=-1.0,s[24,44]=1.1,s[24,45]=-0.3
s[24,46]=-0.1,s[24,47]=0.2,s[24,48]=0.7,s[24,49]=-0.6,s[24,50]=1.0,s[24,51]=0.0,s[24,52]=-1.0,s[24,53]=0.5,s[24,54]=-0.4,s[24,55]=-0.9,s[24,56]=-0.8,s[24,57]=-0.2,s[24,58]=0.3,s[24,59]=-0.7,s[24,60]=-0.5
s[25,1]=1.2,s[25,2]=-0.9,s[25,3]=-0.5,s[25,4]=0.1,s[25,5]=0.2,s[25,6]=-0.8,s[25,7]=0.0,s[25,8]=1.2,s[25,9]=-0.5,s[25,10]=-0.1,s[25,11]=0.9,s[25,12]=-0.9,s[25,13]=-0.8,s[25,14]=0.1,s[25,15]=-0.9
s[25,16]=0.3,s[25,17]=-0.9,s[25,18]=-0.4,s[25,19]=-0.5,s[25,20]=-0.6,s[25,21]=-1.1,s[25,22]=-0.9,s[25,23]=-0.9,s[25,24]=0.9,s[25,25]=1.1,s[25,26]=0.6,s[25,27]=-0.3,s[25,28]=-0.1,s[25,29]=-1.2,s[25,30]=-1.1
s[25,31]=0.0,s[25,32]=0.1,s[25,33]=-0.7,s[25,34]=-0.7,s[25,35]=0.5,s[25,36]=-0.4,s[25,37]=1.0,s[25,38]=0.2,s[25,39]=0.7,s[25,40]=-0.5,s[25,41]=-0.4,s[25,42]=-0.1,s[25,43]=-0.1,s[25,44]=0.2,s[25,45]=0.2
s[25,46]=-0.7,s[25,47]=0.8,s[25,48]=1.1,s[25,49]=-0.1,s[25,50]=-0.6,s[25,51]=0.1,s[25,52]=0.5,s[25,53]=-0.5,s[25,54]=-0.4,s[25,55]=0.2,s[25,56]=1.0,s[25,57]=1.1,s[25,58]=0.0,s[25,59]=-0.1,s[25,60]=-1.2
s[26,1]=-0.6,s[26,2]=0.1,s[26,3]=-0.4,s[26,4]=-1.1,s[26,5]=-0.6,s[26,6]=0.1,s[26,7]=-1.0,s[26,8]=-1.0,s[26,9]=-0.6,s[26,10]=0.1,s[26,11]=-0.7,s[26,12]=0.9,s[26,13]=-0.4,s[26,14]=-0.1,s[26,15]=-1.0
s[26,16]=0.7,s[26,17]=0.9,s[26,18]=0.9,s[26,19]=0.7,s[26,20]=0.9,s[26,21]=1.2,s[26,22]=0.8,s[26,23]=0.1,s[26,24]=-1.2,s[26,25]=0.4,s[26,26]=0.8,s[26,27]=-0.8,s[26,28]=-0.2,s[26,29]=-0.7,s[26,30]=-0.8
s[26,31]=-1.2,s[26,32]=0.5,s[26,33]=0.3,s[26,34]=-0.4,s[26,35]=-0.6,s[26,36]=1.2,s[26,37]=-1.1,s[26,38]=0.1,s[26,39]=-0.6,s[26,40]=1.0,s[26,41]=-1.1,s[26,42]=-0.3,s[26,43]=0.2,s[26,44]=-0.6,s[26,45]=0.4
s[26,46]=-1.1,s[26,47]=-0.6,s[26,48]=0.9,s[26,49]=0.1,s[26,50]=-0.2,s[26,51]=-0.8,s[26,52]=-0.3,s[26,53]=-0.5,s[26,54]=0.0,s[26,55]=-1.2,s[26,56]=1.0,s[26,57]=-0.3,s[26,58]=-0.6,s[26,59]=0.3,s[26,60]=1.0
s[27,1]=0.1,s[27,2]=1.1,s[27,3]=0.1,s[27,4]=-0.9,s[27,5]=-0.4,s[27,6]=0.7,s[27,7]=0.1,s[27,8]=0.6,s[27,9]=0.9,s[27,10]=0.1,s[27,11]=0.9,s[27,12]=-0.1,s[27,13]=-0.9,s[27,14]=-0.6,s[27,15]=1.2
s[27,16]=0.1,s[27,17]=-0.6,s[27,18]=-0.5,s[27,19]=0.4,s[27,20]=-0.8,s[27,21]=-0.5,s[27,22]=0.7,s[27,23]=-0.8,s[27,24]=0.6,s[27,25]=-1.1,s[27,26]=-0.1,s[27,27]=-0.3,s[27,28]=-1.1,s[27,29]=-0.1,s[27,30]=0.3
s[27,31]=0.2,s[27,32]=-1.1,s[27,33]=-0.5,s[27,34]=1.1,s[27,35]=-0.1,s[27,36]=-0.6,s[27,37]=-0.6,s[27,38]=-1.1,s[27,39]=0.0,s[27,40]=-0.2,s[27,41]=-0.8,s[27,42]=0.1,s[27,43]=-0.6,s[27,44]=-0.4,s[27,45]=1.2
s[27,46]=0.9,s[27,47]=1.2,s[27,48]=0.3,s[27,49]=0.5,s[27,50]=0.7,s[27,51]=0.9,s[27,52]=-1.1,s[27,53]=0.1,s[27,54]=1.2,s[27,55]=-0.5,s[27,56]=-0.3,s[27,57]=-0.8,s[27,58]=0.1,s[27,59]=-1.2,s[27,60]=-0.7
s[28,1]=0.4,s[28,2]=-0.8,s[28,3]=-0.4,s[28,4]=0.1,s[28,5]=-0.2,s[28,6]=0.2,s[28,7]=1.0,s[28,8]=-0.5,s[28,9]=1.0,s[28,10]=0.5,s[28,11]=-0.7,s[28,12]=-0.5,s[28,13]=-0.8,s[28,14]=0.1,s[28,15]=0.7
s[28,16]=-0.8,s[28,17]=1.1,s[28,18]=1.0,s[28,19]=0.3,s[28,20]=0.0,s[28,21]=1.2,s[28,22]=-0.5,s[28,23]=-1.1,s[28,24]=-0.2,s[28,25]=0.2,s[28,26]=-0.8,s[28,27]=0.4,s[28,28]=-0.7,s[28,29]=0.7,s[28,30]=-1.1
s[28,31]=-1.1,s[28,32]=1.1,s[28,33]=-1.2,s[28,34]=-1.1,s[28,35]=-0.7,s[28,36]=0.6,s[28,37]=-1.2,s[28,38]=0.5,s[28,39]=0.9,s[28,40]=-1.0,s[28,41]=-0.4,s[28,42]=0.2,s[28,43]=-0.9,s[28,44]=0.5,s[28,45]=-1.2
s[28,46]=-0.2,s[28,47]=-0.4,s[28,48]=-0.8,s[28,49]=0.4,s[28,50]=-0.6,s[28,51]=0.0,s[28,52]=0.7,s[28,53]=-0.7,s[28,54]=1.2,s[28,55]=-0.1,s[28,56]=-0.7,s[28,57]=-1.1,s[28,58]=-0.3,s[28,59]=0.9,s[28,60]=-1.1
s[29,1]=-0.4,s[29,2]=-0.9,s[29,3]=-0.1,s[29,4]=0.0,s[29,5]=-0.9,s[29,6]=-0.2,s[29,7]=-0.3,s[29,8]=-0.4,s[29,9]=-0.3,s[29,10]=-0.9,s[29,11]=0.9,s[29,12]=-1.0,s[29,13]=0.8,s[29,14]=0.5,s[29,15]=-0.2
s[29,16]=0.4,s[29,17]=-0.9,s[29,18]=-0.1,s[29,19]=-1.2,s[29,20]=-0.8,s[29,21]=0.1,s[29,22]=0.5,s[29,23]=0.6,s[29,24]=0.6,s[29,25]=1.0,s[29,26]=-0.2,s[29,27]=-0.2,s[29,28]=0.1,s[29,29]=0.3,s[29,30]=-0.3
s[29,31]=-0.7,s[29,32]=-1.0,s[29,33]=-0.2,s[29,34]=-0.5,s[29,35]=-0.6,s[29,36]=0.7,s[29,37]=-1.1,s[29,38]=1.2,s[29,39]=-0.6,s[29,40]=0.4,s[29,41]=0.5,s[29,42]=-0.5,s[29,43]=-0.8,s[29,44]=0.4,s[29,45]=1.1
s[29,46]=0.1,s[29,47]=-0.3,s[29,48]=-0.2,s[29,49]=0.0,s[29,50]=-0.8,s[29,51]=-1.2,s[29,52]=0.1,s[29,53]=-0.4,s[29,54]=-1.2,s[29,55]=-1.1,s[29,56]=0.0,s[29,57]=-0.8,s[29,58]=-0.3,s[29,59]=-0.5,s[29,60]=-1.2
s[30,1]=0.3,s[30,2]=-0.8,s[30,3]=-0.8,s[30,4]=-1.0,s[30,5]=0.9,s[30,6]=1.2,s[30,7]=-1.0,s[30,8]=-0.3,s[30,9]=-1.0,s[30,10]=-0.8,s[30,11]=-1.0,s[30,12]=0.6,s[30,13]=0.8,s[30,14]=0.6,s[30,15]=0.8
s[30,16]=-0.4,s[30,17]=0.2,s[30,18]=0.7,s[30,19]=-1.1,s[30,20]=0.0,s[30,21]=-1.1,s[30,22]=-0.2,s[30,23]=0.1,s[30,24]=1.0,s[30,25]=-0.8,s[30,26]=-0.5,s[30,27]=1.0,s[30,28]=-0.5,s[30,29]=0.0,s[30,30]=-0.5
s[30,31]=0.2,s[30,32]=0.4,s[30,33]=-0.3,s[30,34]=-0.2,s[30,35]=-1.2,s[30,36]=1.2,s[30,37]=-1.0,s[30,38]=0.2,s[30,39]=1.0,s[30,40]=0.4,s[30,41]=0.0,s[30,42]=-0.7,s[30,43]=1.1,s[30,44]=-0.8,s[30,45]=0.2
s[30,46]=-0.8,s[30,47]=-1.2,s[30,48]=1.0,s[30,49]=0.9,s[30,50]=0.9,s[30,51]=0.7,s[30,52]=0.8,s[30,53]=0.9,s[30,54]=-1.2,s[30,55]=0.6,s[30,56]=-1.0,s[30,57]=0.5,s[30,58]=-1.1,s[30,59]=-0.5,s[30,60]=-0.8
s[31,1]=-0.3,s[31,2]=-0.2,s[31,3]=0.8,s[31,4]=-1.1,s[31,5]=-0.8,s[31,6]=0.0,s[31,7]=-1.0,s[31,8]=-0.9,s[31,9]=-1.0,s[31,10]=0.4,s[31,11]=-0.6,s[31,12]=-0.9,s[31,13]=-0.9,s[31,14]=0.0,s[31,15]=0.0
s[31,16]=-0.3,s[31,17]=0.6,s[31,18]=0.2,s[31,19]=0.1,s[31,20]=1.1,s[31,21]=1.1,s[31,22]=-1.0,s[31,23]=0.6,s[31,24]=1.2,s[31,25]=0.8,s[31,26]=1.2,s[31,27]=0.6,s[31,28]=0.4,s[31,29]=0.9,s[31,30]=0.1
s[31,31]=-1.0,s[31,32]=-1.0,s[31,33]=-0.4,s[31,34]=0.1,s[31,35]=0.2,s[31,36]=0.9,s[31,37]=0.4,s[31,38]=-0.8,s[31,39]=-0.8,s[31,40]=-0.3,s[31,41]=0.9,s[31,42]=-0.3,s[31,43]=-0.5,s[31,44]=0.0,s[31,45]=0.6
s[31,46]=0.1,s[31,47]=-1.0,s[31,48]=0.3,s[31,49]=-1.2,s[31,50]=-1.1,s[31,51]=-0.8,s[31,52]=0.3,s[31,53]=0.0,s[31,54]=0.8,s[31,55]=-0.9,s[31,56]=-0.6,s[31,57]=-0.1,s[31,58]=0.4,s[31,59]=0.9,s[31,60]=-0.7
s[32,1]=-0.2,s[32,2]=-0.5,s[32,3]=-0.7,s[32,4]=-0.6,s[32,5]=0.9,s[32,6]=0.0,s[32,7]=-0.2,s[32,8]=1.1,s[32,9]=1.0,s[32,10]=-0.5,s[32,11]=-1.2,s[32,12]=0.8,s[32,13]=-0.1,s[32,14]=-1.2,s[32,15]=-0.1
s[32,16]=0.2,s[32,17]=-1.0,s[32,18]=-0.6,s[32,19]=-0.9,s[32,20]=0.7,s[32,21]=-0.6,s[32,22]=0.8,s[32,23]=-0.6,s[32,24]=-0.5,s[32,25]=-1.0,s[32,26]=-1.0,s[32,27]=1.1,s[32,28]=1.0,s[32,29]=-0.6,s[32,30]=0.0
s[32,31]=-0.2,s[32,32]=1.0,s[32,33]=0.3,s[32,34]=-1.2,s[32,35]=0.1,s[32,36]=0.2,s[32,37]=-1.2,s[32,38]=1.1,s[32,39]=-1.1,s[32,40]=0.6,s[32,41]=-0.6,s[32,42]=0.4,s[32,43]=-0.3,s[32,44]=-1.2,s[32,45]=0.1
s[32,46]=-1.0,s[32,47]=0.5,s[32,48]=-0.5,s[32,49]=0.8,s[32,50]=0.0,s[32,51]=-1.1,s[32,52]=-0.7,s[32,53]=-0.7,s[32,54]=-0.8,s[32,55]=0.6,s[32,56]=0.1,s[32,57]=-0.9,s[32,58]=-0.6,s[32,59]=-0.7,s[32,60]=0.2
s[33,1]=0.9,s[33,2]=-0.2,s[33,3]=-1.1,s[33,4]=0.2,s[33,5]=0.6,s[33,6]=0.8,s[33,7]=0.0,s[33,8]=1.0,s[33,9]=0.2,s[33,10]=-0.5,s[33,11]=-0.1,s[33,12]=-0.7,s[33,13]=-0.4,s[33,14]=0.6,s[33,15]=-0.6
s[33,16]=0.4,s[33,17]=-0.6,s[33,18]=0.0,s[33,19]=1.1,s[33,20]=-0.9,s[33,21]=-0.7,s[33,22]=-0.8,s[33,23]=0.3,s[33,24]=-0.2,s[33,25]=1.0,s[33,26]=-0.6,s[33,27]=-0.2,s[33,28]=1.0,s[33,29]=-0.5,s[33,30]=0.6
s[33,31]=0.6,s[33,32]=-0.1,s[33,33]=-0.7,s[33,34]=-0.2,s[33,35]=1.1,s[33,36]=1.1,s[33,37]=0.4,s[33,38]=-0.9,s[33,39]=0.1,s[33,40]=1.2,s[33,41]=1.0,s[33,42]=-1.1,s[33,43]=0.0,s[33,44]=0.0,s[33,45]=-1.0
s[33,46]=-1.1,s[33,47]=0.7,s[33,48]=-0.7,s[33,49]=1.0,s[33,50]=-1.0,s[33,51]=-0.2,s[33,52]=-1.0,s[33,53]=-0.7,s[33,54]=-0.7,s[33,55]=0.9,s[33,56]=-0.9,s[33,57]=0.0,s[33,58]=0.2,s[33,59]=0.6,s[33,60]=-1.1
s[34,1]=0.3,s[34,2]=-0.5,s[34,3]=1.1,s[34,4]=0.2,s[34,5]=-1.1,s[34,6]=-0.1,s[34,7]=1.0,s[34,8]=0.7,s[34,9]=-0.4,s[34,10]=-1.0,s[34,11]=0.6,s[34,12]=-0.6,s[34,13]=0.2,s[34,14]=-1.0,s[34,15]=0.1
s[34,16]=-0.5,s[34,17]=-0.7,s[34,18]=-0.6,s[34,19]=0.5,s[34,20]=-0.7,s[34,21]=0.6,s[34,22]=0.3,s[34,23]=1.0,s[34,24]=0.8,s[34,25]=-0.5,s[34,26]=-0.8,s[34,27]=-1.2,s[34,28]=1.1,s[34,29]=0.7,s[34,30]=0.5
s[34,31]=0.7,s[34,32]=0.3,s[34,33]=-0.7,s[34,34]=-0.5,s[34,35]=1.0,s[34,36]=-1.2,s[34,37]=-0.2,s[34,38]=0.0,s[34,39]=-0.5,s[34,40]=1.0,s[34,41]=0.3,s[34,42]=-0.1,s[34,43]=-0.1,s[34,44]=-0.7,s[34,45]=0.0
s[34,46]=-1.0,s[34,47]=0.1,s[34,48]=0.3,s[34,49]=-1.1,s[34,50]=1.0,s[34,51]=0.5,s[34,52]=-0.5,s[34,53]=-0.5,s[34,54]=-0.4,s[34,55]=-0.9,s[34,56]=-0.8,s[34,57]=0.6,s[34,58]=0.2,s[34,59]=-0.8,s[34,60]=-0.6
s[35,1]=1.1,s[35,2]=-0.5,s[35,3]=-0.2,s[35,4]=-0.8,s[35,5]=0.6,s[35,6]=-1.2,s[35,7]=1.2,s[35,8]=-0.7,s[35,9]=-0.9,s[35,10]=-0.1,s[35,11]=0.5,s[35,12]=-0.5,s[35,13]=-0.5,s[35,14]=-0.1,s[35,15]=-0.6
s[35,16]=-0.9,s[35,17]=-0.1,s[35,18]=0.2,s[35,19]=-0.8,s[35,20]=-0.7,s[35,21]=0.5,s[35,22]=0.6,s[35,23]=-0.2,s[35,24]=0.0,s[35,25]=-0.8,s[35,26]=-0.8,s[35,27]=0.7,s[35,28]=0.7,s[35,29]=0.5,s[35,30]=-0.1
s[35,31]=-1.1,s[35,32]=-0.8,s[35,33]=-0.4,s[35,34]=0.0,s[35,35]=-0.8,s[35,36]=-1.1,s[35,37]=0.1,s[35,38]=-0.1,s[35,39]=-0.5,s[35,40]=-0.4,s[35,41]=-0.9,s[35,42]=0.4,s[35,43]=0.6,s[35,44]=1.2,s[35,45]=1.1
s[35,46]=0.8,s[35,47]=-1.1,s[35,48]=0.3,s[35,49]=-1.0,s[35,50]=0.7,s[35,51]=0.2,s[35,52]=-0.2,s[35,53]=-1.1,s[35,54]=1.0,s[35,55]=-1.0,s[35,56]=0.3,s[35,57]=-0.4,s[35,58]=-0.5,s[35,59]=0.1,s[35,60]=0.2
s[36,1]=-0.7,s[36,2]=1.0,s[36,3]=0.7,s[36,4]=0.0,s[36,5]=0.7,s[36,6]=-0.4,s[36,7]=0.8,s[36,8]=0.9,s[36,9]=-0.8,s[36,10]=-1.1,s[36,11]=1.0,s[36,12]=0.3,s[36,13]=0.2,s[36,14]=-0.3,s[36,15]=0.8
s[36,16]=-1.2,s[36,17]=-0.1,s[36,18]=1.0,s[36,19]=-0.7,s[36,20]=0.9,s[36,21]=0.1,s[36,22]=0.8,s[36,23]=0.1,s[36,24]=0.1,s[36,25]=-1.2,s[36,26]=-0.5,s[36,27]=0.8,s[36,28]=-0.6,s[36,29]=1.0,s[36,30]=-1.0
s[36,31]=0.2,s[36,32]=1.1,s[36,33]=-0.5,s[36,34]=0.3,s[36,35]=-1.2,s[36,36]=0.9,s[36,37]=0.3,s[36,38]=-1.1,s[36,39]=0.4,s[36,40]=-1.2,s[36,41]=-0.2,s[36,42]=-0.2,s[36,43]=-0.2,s[36,44]=-0.1,s[36,45]=0.9
s[36,46]=0.7,s[36,47]=-0.5,s[36,48]=0.2,s[36,49]=0.8,s[36,50]=0.3,s[36,51]=-1.2,s[36,52]=0.3,s[36,53]=-0.3,s[36,54]=-0.9,s[36,55]=-0.4,s[36,56]=-0.9,s[36,57]=0.0,s[36,58]=-0.7,s[36,59]=0.0,s[36,60]=-1.2
s[37,1]=-1.0,s[37,2]=0.7,s[37,3]=-0.8,s[37,4]=-0.5,s[37,5]=1.0,s[37,6]=-1.0,s[37,7]=0.8,s[37,8]=0.6,s[37,9]=0.3,s[37,10]=0.0,s[37,11]=0.9,s[37,12]=0.5,s[37,13]=0.0,s[37,14]=0.6,s[37,15]=1.2
s[37,16]=-0.6,s[37,17]=0.6,s[37,18]=-1.0,s[37,19]=0.8,s[37,20]=-0.9,s[37,21]=-1.0,s[37,22]=1.2,s[37,23]=-0.8,s[37,24]=-0.1,s[37,25]=0.4,s[37,26]=-1.0,s[37,27]=0.1,s[37,28]=-0.7,s[37,29]=-0.5,s[37,30]=-0.8
s[37,31]=0.8,s[37,32]=0.4,s[37,33]=-0.4,s[37,34]=-0.6,s[37,35]=-0.9,s[37,36]=1.2,s[37,37]=-0.1,s[37,38]=-0.5,s[37,39]=-0.4,s[37,40]=0.6,s[37,41]=-1.2,s[37,42]=-0.6,s[37,43]=0.1,s[37,44]=0.1,s[37,45]=0.8
s[37,46]=-1.1,s[37,47]=0.4,s[37,48]=0.2,s[37,49]=-0.2,s[37,50]=0.9,s[37,51]=-0.3,s[37,52]=0.0,s[37,53]=0.6,s[37,54]=0.7,s[37,55]=-1.1,s[37,56]=0.1,s[37,57]=0.0,s[37,58]=0.2,s[37,59]=-0.6,s[37,60]=0.4
s[38,1]=0.3,s[38,2]=0.0,s[38,3]=-0.4,s[38,4]=-0.6,s[38,5]=1.1,s[38,6]=0.4,s[38,7]=1.2,s[38,8]=0.1,s[38,9]=-0.6,s[38,10]=0.5,s[38,11]=-0.8,s[38,12]=-0.9,s[38,13]=0.2,s[38,14]=-0.7,s[38,15]=-0.7
s[38,16]=0.2,s[38,17]=0.0,s[38,18]=1.0,s[38,19]=1.0,s[38,20]=1.2,s[38,21]=0.8,s[38,22]=0.4,s[38,23]=-1.0,s[38,24]=-0.1,s[38,25]=-0.2,s[38,26]=0.6,s[38,27]=0.5,s[38,28]=0.2,s[38,29]=-0.8,s[38,30]=1.0
s[38,31]=-0.5,s[38,32]=1.1,s[38,33]=-0.9,s[38,34]=-0.2,s[38,35]=0.4,s[38,36]=0.0,s[38,37]=-0.3,s[38,38]=-0.6,s[38,39]=-0.8,s[38,40]=-1.2,s[38,41]=-0.2,s[38,42]=-0.7,s[38,43]=-0.6,s[38,44]=-0.2,s[38,45]=-0.7
s[38,46]=0.0,s[38,47]=-1.2,s[38,48]=-0.4,s[38,49]=-0.2,s[38,50]=0.6,s[38,51]=0.1,s[38,52]=0.8,s[38,53]=-0.3,s[38,54]=0.4,s[38,55]=-0.7,s[38,56]=-1.0,s[38,57]=-0.5,s[38,58]=0.8,s[38,59]=-0.8,s[38,60]=-0.2
s[39,1]=-0.6,s[39,2]=0.8,s[39,3]=-0.9,s[39,4]=0.1,s[39,5]=0.0,s[39,6]=0.8,s[39,7]=0.3,s[39,8]=-0.8,s[39,9]=0.2,s[39,10]=0.7,s[39,11]=0.0,s[39,12]=0.7,s[39,13]=1.2,s[39,14]=-1.1,s[39,15]=0.4
s[39,16]=0.9,s[39,17]=-1.0,s[39,18]=1.2,s[39,19]=-0.5,s[39,20]=-0.8,s[39,21]=0.1,s[39,22]=-1.1,s[39,23]=0.6,s[39,24]=0.8,s[39,25]=-0.6,s[39,26]=-0.6,s[39,27]=1.0,s[39,28]=-0.6,s[39,29]=0.8,s[39,30]=0.2
s[39,31]=0.9,s[39,32]=-0.9,s[39,33]=0.5,s[39,34]=-1.2,s[39,35]=1.1,s[39,36]=0.1,s[39,37]=1.2,s[39,38]=1.2,s[39,39]=-0.5,s[39,40]=0.7,s[39,41]=1.0,s[39,42]=0.9,s[39,43]=-0.4,s[39,44]=-0.6,s[39,45]=0.5
s[39,46]=0.4,s[39,47]=-0.8,s[39,48]=0.5,s[39,49]=-0.8,s[39,50]=-0.2,s[39,51]=1.1,s[39,52]=1.1,s[39,53]=-0.8,s[39,54]=-1.2,s[39,55]=-0.5,s[39,56]=-0.4,s[39,57]=0.1,s[39,58]=0.8,s[39,59]=-0.9,s[39,60]=0.1
s[40,1]=0.0,s[40,2]=0.8,s[40,3]=0.3,s[40,4]=-0.7,s[40,5]=0.3,s[40,6]=0.0,s[40,7]=-1.2,s[40,8]=0.3,s[40,9]=-0.8,s[40,10]=-0.2,s[40,11]=0.4,s[40,12]=-0.6,s[40,13]=-0.9,s[40,14]=-0.2,s[40,15]=-0.9
s[40,16]=-0.4,s[40,17]=-0.4,s[40,18]=-0.9,s[40,19]=0.1,s[40,20]=-1.2,s[40,21]=1.2,s[40,22]=-0.3,s[40,23]=-0.4,s[40,24]=-0.1,s[40,25]=-0.9,s[40,26]=-1.0,s[40,27]=0.8,s[40,28]=0.8,s[40,29]=-0.6,s[40,30]=-0.9
s[40,31]=0.9,s[40,32]=-1.1,s[40,33]=-0.5,s[40,34]=-0.3,s[40,35]=-0.9,s[40,36]=0.6,s[40,37]=0.9,s[40,38]=0.9,s[40,39]=-0.9,s[40,40]=1.2,s[40,41]=-0.9,s[40,42]=-1.2,s[40,43]=0.5,s[40,44]=-0.1,s[40,45]=0.9
s[40,46]=-1.0,s[40,47]=1.2,s[40,48]=-0.7,s[40,49]=-0.9,s[40,50]=1.1,s[40,51]=0.1,s[40,52]=-0.6,s[40,53]=0.9,s[40,54]=0.7,s[40,55]=0.0,s[40,56]=-0.2,s[40,57]=-1.0,s[40,58]=0.6,s[40,59]=1.1,s[40,60]=-0.7
s[41,1]=-0.6,s[41,2]=-0.9,s[41,3]=-0.9,s[41,4]=-0.3,s[41,5]=-0.6,s[41,6]=-0.4,s[41,7]=0.8,s[41,8]=0.4,s[41,9]=0.8,s[41,10]=-0.7,s[41,11]=-0.4,s[41,12]=-0.4,s[41,13]=-0.1,s[41,14]=0.6,s[41,15]=0.3
s[41,16]=0.2,s[41,17]=-1.0,s[41,18]=0.7,s[41,19]=-1.1,s[41,20]=0.8,s[41,21]=-0.1,s[41,22]=-0.1,s[41,23]=-0.8,s[41,24]=-0.4,s[41,25]=0.7,s[41,26]=-1.1,s[41,27]=0.6,s[41,28]=-0.3,s[41,29]=0.1,s[41,30]=0.3
s[41,31]=1.2,s[41,32]=-0.4,s[41,33]=0.6,s[41,34]=-1.2,s[41,35]=-0.2,s[41,36]=0.4,s[41,37]=-0.7,s[41,38]=0.6,s[41,39]=0.7,s[41,40]=0.8,s[41,41]=0.7,s[41,42]=-0.6,s[41,43]=-0.2,s[41,44]=0.1,s[41,45]=-0.3
s[41,46]=0.4,s[41,47]=1.2,s[41,48]=-1.1,s[41,49]=-0.1,s[41,50]=-0.7,s[41,51]=0.4,s[41,52]=-0.3,s[41,53]=-0.2,s[41,54]=-0.2,s[41,55]=-0.7,s[41,56]=-1.1,s[41,57]=0.2,s[41,58]=0.5,s[41,59]=0.5,s[41,60]=-0.2
s[42,1]=0.1,s[42,2]=-0.2,s[42,3]=-0.2,s[42,4]=-0.6,s[42,5]=0.6,s[42,6]=-1.0,s[42,7]=1.0,s[42,8]=0.7,s[42,9]=-1.1,s[42,10]=-1.2,s[42,11]=-0.3,s[42,12]=-1.1,s[42,13]=-0.7,s[42,14]=0.3,s[42,15]=-0.1
s[42,16]=-0.5,s[42,17]=-1.2,s[42,18]=0.6,s[42,19]=0.9,s[42,20]=-0.5,s[42,21]=0.3,s[42,22]=-1.1,s[42,23]=-0.9,s[42,24]=-0.1,s[42,25]=-0.1,s[42,26]=0.9,s[42,27]=0.7,s[42,28]=0.4,s[42,29]=-0.4,s[42,30]=-0.3
s[42,31]=-0.9,s[42,32]=1.1,s[42,33]=0.3,s[42,34]=-0.1,s[42,35]=-1.0,s[42,36]=0.7,s[42,37]=-0.5,s[42,38]=1.2,s[42,39]=-0.6,s[42,40]=1.2,s[42,41]=-1.0,s[42,42]=-0.8,s[42,43]=-0.9,s[42,44]=0.1,s[42,45]=-0.3
s[42,46]=-0.4,s[42,47]=1.1,s[42,48]=0.6,s[42,49]=-1.2,s[42,50]=-0.3,s[42,51]=0.0,s[42,52]=-0.2,s[42,53]=0.1,s[42,54]=-0.9,s[42,55]=0.5,s[42,56]=0.1,s[42,57]=0.0,s[42,58]=-1.1,s[42,59]=-0.1,s[42,60]=-1.2
s[43,1]=1.0,s[43,2]=-0.9,s[43,3]=-0.9,s[43,4]=0.5,s[43,5]=-0.8,s[43,6]=-1.1,s[43,7]=-1.1,s[43,8]=-1.2,s[43,9]=0.9,s[43,10]=1.2,s[43,11]=1.0,s[43,12]=-0.9,s[43,13]=-1.1,s[43,14]=-0.9,s[43,15]=0.1
s[43,16]=0.5,s[43,17]=0.2,s[43,18]=-0.6,s[43,19]=0.6,s[43,20]=-1.1,s[43,21]=-0.1,s[43,22]=0.0,s[43,23]=-1.0,s[43,24]=-0.7,s[43,25]=1.1,s[43,26]=-0.6,s[43,27]=0.1,s[43,28]=0.9,s[43,29]=1.1,s[43,30]=0.9
s[43,31]=1.1,s[43,32]=0.4,s[43,33]=1.1,s[43,34]=-0.1,s[43,35]=-0.7,s[43,36]=-0.4,s[43,37]=-0.6,s[43,38]=0.1,s[43,39]=0.6,s[43,40]=-0.6,s[43,41]=-0.2,s[43,42]=0.1,s[43,43]=-0.8,s[43,44]=0.3,s[43,45]=1.2
s[43,46]=0.6,s[43,47]=-1.0,s[43,48]=1.1,s[43,49]=0.3,s[43,50]=-0.7,s[43,51]=0.0,s[43,52]=-0.1,s[43,53]=1.2,s[43,54]=-0.2,s[43,55]=-1.0,s[43,56]=-0.2,s[43,57]=0.1,s[43,58]=0.9,s[43,59]=-1.2,s[43,60]=0.1
s[44,1]=1.0,s[44,2]=-1.0,s[44,3]=0.9,s[44,4]=-1.2,s[44,5]=0.5,s[44,6]=0.3,s[44,7]=-0.1,s[44,8]=-0.1,s[44,9]=-0.8,s[44,10]=1.0,s[44,11]=-0.3,s[44,12]=1.0,s[44,13]=-0.2,s[44,14]=1.1,s[44,15]=-0.7
s[44,16]=-0.8,s[44,17]=-0.6,s[44,18]=-1.0,s[44,19]=0.1,s[44,20]=0.1,s[44,21]=0.3,s[44,22]=1.2,s[44,23]=0.9,s[44,24]=0.5,s[44,25]=0.2,s[44,26]=0.8,s[44,27]=-0.5,s[44,28]=-0.6,s[44,29]=-0.3,s[44,30]=-0.3
s[44,31]=-0.1,s[44,32]=0.7,s[44,33]=0.7,s[44,34]=-0.3,s[44,35]=0.3,s[44,36]=-1.1,s[44,37]=-1.1,s[44,38]=-0.1,s[44,39]=-1.1,s[44,40]=-0.9,s[44,41]=-1.1,s[44,42]=-0.5,s[44,43]=1.0,s[44,44]=0.5,s[44,45]=0.0
s[44,46]=-0.5,s[44,47]=-0.5,s[44,48]=0.6,s[44,49]=-0.8,s[44,50]=-0.3,s[44,51]=1.1,s[44,52]=-0.5,s[44,53]=-0.5,s[44,54]=0.4,s[44,55]=-1.2,s[44,56]=0.1,s[44,57]=0.4,s[44,58]=0.0,s[44,59]=-1.1,s[44,60]=-1.2
s[45,1]=-1.0,s[45,2]=0.5,s[45,3]=1.2,s[45,4]=-0.6,s[45,5]=-0.1,s[45,6]=-0.4,s[45,7]=0.8,s[45,8]=-0.8,s[45,9]=0.6,s[45,10]=-0.2,s[45,11]=0.2,s[45,12]=0.1,s[45,13]=0.2,s[45,14]=0.5,s[45,15]=0.6
s[45,16]=1.1,s[45,17]=0.4,s[45,18]=-0.4,s[45,19]=-0.1,s[45,20]=0.2,s[45,21]=0.8,s[45,22]=0.0,s[45,23]=-0.9,s[45,24]=-0.6,s[45,25]=0.1,s[45,26]=0.1,s[45,27]=-1.0,s[45,28]=1.0,s[45,29]=-0.4,s[45,30]=0.1
s[45,31]=0.0,s[45,32]=-0.4,s[45,33]=1.1,s[45,34]=-1.2,s[45,35]=0.6,s[45,36]=-0.8,s[45,37]=-0.1,s[45,38]=0.5,s[45,39]=1.2,s[45,40]=0.9,s[45,41]=0.9,s[45,42]=0.7,s[45,43]=0.5,s[45,44]=0.2,s[45,45]=-0.3
s[45,46]=0.2,s[45,47]=-1.2,s[45,48]=-1.1,s[45,49]=-0.2,s[45,50]=0.6,s[45,51]=-1.2,s[45,52]=-0.7,s[45,53]=-1.2,s[45,54]=0.4,s[45,55]=0.1,s[45,56]=-0.6,s[45,57]=0.8,s[45,58]=0.4,s[45,59]=1.0,s[45,60]=-0.7
s[46,1]=-0.4,s[46,2]=0.4,s[46,3]=0.6,s[46,4]=-0.6,s[46,5]=-0.4,s[46,6]=-1.1,s[46,7]=-0.2,s[46,8]=-0.9,s[46,9]=0.0,s[46,10]=0.3,s[46,11]=-0.1,s[46,12]=0.8,s[46,13]=-0.9,s[46,14]=0.5,s[46,15]=-0.7
s[46,16]=0.7,s[46,17]=-0.5,s[46,18]=-1.2,s[46,19]=-0.1,s[46,20]=1.1,s[46,21]=-1.2,s[46,22]=-0.6,s[46,23]=1.1,s[46,24]=0.4,s[46,25]=-0.7,s[46,26]=0.4,s[46,27]=1.2,s[46,28]=-1.1,s[46,29]=-0.2,s[46,30]=-0.8
s[46,31]=-0.3,s[46,32]=-0.6,s[46,33]=0.0,s[46,34]=-0.7,s[46,35]=-0.6,s[46,36]=-0.8,s[46,37]=-1.2,s[46,38]=-0.7,s[46,39]=0.2,s[46,40]=0.4,s[46,41]=-0.3,s[46,42]=1.2,s[46,43]=-0.9,s[46,44]=-0.8,s[46,45]=1.0
s[46,46]=-0.6,s[46,47]=-0.1,s[46,48]=-0.9,s[46,49]=0.0,s[46,50]=0.2,s[46,51]=0.5,s[46,52]=-0.8,s[46,53]=-0.7,s[46,54]=0.2,s[46,55]=-0.6,s[46,56]=0.5,s[46,57]=0.3,s[46,58]=-0.3,s[46,59]=-0.2,s[46,60]=-0.1
s[47,1]=0.4,s[47,2]=-0.5,s[47,3]=0.4,s[47,4]=-0.1,s[47,5]=0.8,s[47,6]=-0.1,s[47,7]=-1.1,s[47,8]=0.2,s[47,9]=0.8,s[47,10]=1.1,s[47,11]=-0.1,s[47,12]=-1.2,s[47,13]=0.2,s[47,14]=1.1,s[47,15]=-0.5
s[47,16]=-0.1,s[47,17]=-1.0,s[47,18]=-0.1,s[47,19]=0.3,s[47,20]=0.1,s[47,21]=1.0,s[47,22]=-0.2,s[47,23]=1.1,s[47,24]=0.9,s[47,25]=-0.6,s[47,26]=0.8,s[47,27]=-0.6,s[47,28]=-1.2,s[47,29]=0.3,s[47,30]=0.0
s[47,31]=1.1,s[47,32]=0.2,s[47,33]=1.0,s[47,34]=0.0,s[47,35]=0.6,s[47,36]=0.8,s[47,37]=-0.3,s[47,38]=-0.8,s[47,39]=0.6,s[47,40]=0.1,s[47,41]=-0.7,s[47,42]=-1.0,s[47,43]=-0.5,s[47,44]=-0.5,s[47,45]=-0.3
s[47,46]=-0.5,s[47,47]=-0.6,s[47,48]=0.9,s[47,49]=1.2,s[47,50]=-0.2,s[47,51]=0.0,s[47,52]=-0.1,s[47,53]=-1.1,s[47,54]=0.6,s[47,55]=-0.9,s[47,56]=1.1,s[47,57]=-1.1,s[47,58]=-0.1,s[47,59]=-0.4,s[47,60]=-0.3
s[48,1]=1.2,s[48,2]=-1.2,s[48,3]=-0.7,s[48,4]=-1.0,s[48,5]=-0.1,s[48,6]=0.2,s[48,7]=0.6,s[48,8]=1.2,s[48,9]=1.0,s[48,10]=-0.5,s[48,11]=0.1,s[48,12]=0.6,s[48,13]=0.3,s[48,14]=0.3,s[48,15]=-0.3
s[48,16]=1.0,s[48,17]=0.0,s[48,18]=-1.2,s[48,19]=-0.4,s[48,20]=0.7,s[48,21]=-0.7,s[48,22]=-0.7,s[48,23]=0.4,s[48,24]=0.4,s[48,25]=-0.3,s[48,26]=-1.2,s[48,27]=-0.6,s[48,28]=-0.5,s[48,29]=1.1,s[48,30]=0.5
s[48,31]=-0.1,s[48,32]=-0.8,s[48,33]=-1.2,s[48,34]=-0.5,s[48,35]=0.2,s[48,36]=0.2,s[48,37]=-0.4,s[48,38]=-0.4,s[48,39]=-1.2,s[48,40]=-0.1,s[48,41]=0.3,s[48,42]=0.1,s[48,43]=0.3,s[48,44]=-0.2,s[48,45]=1.0
s[48,46]=-0.6,s[48,47]=0.6,s[48,48]=0.6,s[48,49]=1.2,s[48,50]=-1.2,s[48,51]=-1.1,s[48,52]=-0.7,s[48,53]=-0.4,s[48,54]=-0.1,s[48,55]=-0.7,s[48,56]=-0.9,s[48,57]=0.3,s[48,58]=0.9,s[48,59]=0.6,s[48,60]=-0.5
s[49,1]=-0.2,s[49,2]=-0.3,s[49,3]=0.2,s[49,4]=-0.3,s[49,5]=-0.8,s[49,6]=-0.9,s[49,7]=-0.5,s[49,8]=-0.4,s[49,9]=-1.1,s[49,10]=0.9,s[49,11]=0.3,s[49,12]=-0.3,s[49,13]=-0.7,s[49,14]=-0.5,s[49,15]=0.6
s[49,16]=0.1,s[49,17]=-0.3,s[49,18]=0.0,s[49,19]=-0.5,s[49,20]=0.7,s[49,21]=0.0,s[49,22]=0.6,s[49,23]=-0.7,s[49,24]=1.2,s[49,25]=-1.1,s[49,26]=-0.8,s[49,27]=0.7,s[49,28]=0.9,s[49,29]=-1.2,s[49,30]=-0.2
s[49,31]=0.9,s[49,32]=0.3,s[49,33]=-1.2,s[49,34]=-1.1,s[49,35]=0.7,s[49,36]=1.0,s[49,37]=-1.2,s[49,38]=-1.1,s[49,39]=1.2,s[49,40]=0.0,s[49,41]=-0.9,s[49,42]=0.8,s[49,43]=-0.3,s[49,44]=-1.1,s[49,45]=-0.7
s[49,46]=-0.9,s[49,47]=1.2,s[49,48]=0.4,s[49,49]=0.2,s[49,50]=-1.2,s[49,51]=1.1,s[49,52]=-1.1,s[49,53]=-0.3,s[49,54]=-0.5,s[49,55]=-0.6,s[49,56]=0.2,s[49,57]=-0.5,s[49,58]=-0.6,s[49,59]=-0.8,s[49,60]=-0.2
s[50,1]=0.5,s[50,2]=-0.2,s[50,3]=-0.5,s[50,4]=-0.8,s[50,5]=1.2,s[50,6]=-0.4,s[50,7]=-0.6,s[50,8]=-0.8,s[50,9]=-0.8,s[50,10]=1.2,s[50,11]=0.1,s[50,12]=0.3,s[50,13]=0.4,s[50,14]=0.3,s[50,15]=-0.3
s[50,16]=-1.1,s[50,17]=-0.9,s[50,18]=0.5,s[50,19]=1.1,s[50,20]=-1.2,s[50,21]=0.2,s[50,22]=-0.7,s[50,23]=0.7,s[50,24]=-0.7,s[50,25]=0.1,s[50,26]=-0.4,s[50,27]=-0.5,s[50,28]=1.2,s[50,29]=-0.1,s[50,30]=-1.0
s[50,31]=0.8,s[50,32]=-0.3,s[50,33]=0.0,s[50,34]=-0.5,s[50,35]=-0.6,s[50,36]=-0.2,s[50,37]=0.3,s[50,38]=0.1,s[50,39]=-0.9,s[50,40]=-0.1,s[50,41]=0.6,s[50,42]=0.7,s[50,43]=0.8,s[50,44]=-0.4,s[50,45]=-0.2
s[50,46]=0.6,s[50,47]=-0.5,s[50,48]=1.1,s[50,49]=-0.4,s[50,50]=0.4,s[50,51]=0.9,s[50,52]=-0.2,s[50,53]=-1.2,s[50,54]=-0.2,s[50,55]=0.0,s[50,56]=-0.1,s[50,57]=0.0,s[50,58]=0.5,s[50,59]=0.0,s[50,60]=-1.1
s[51,1]=-0.3,s[51,2]=0.1,s[51,3]=-0.1,s[51,4]=-0.5,s[51,5]=0.4,s[51,6]=-0.5,s[51,7]=0.4,s[51,8]=-0.5,s[51,9]=1.0,s[51,10]=0.4,s[51,11]=0.2,s[51,12]=0.8,s[51,13]=-0.4,s[51,14]=0.7,s[51,15]=-0.7
s[51,16]=-0.6,s[51,17]=-0.1,s[51,18]=-0.1,s[51,19]=-0.3,s[51,20]=-1.0,s[51,21]=-0.8,s[51,22]=1.2,s[51,23]=0.7,s[51,24]=-0.9,s[51,25]=0.4,s[51,26]=1.0,s[51,27]=0.1,s[51,28]=-0.1,s[51,29]=1.2,s[51,30]=0.7
s[51,31]=0.7,s[51,32]=1.0,s[51,33]=1.0,s[51,34]=-0.5,s[51,35]=-1.1,s[51,36]=-0.5,s[51,37]=-0.5,s[51,38]=-0.4,s[51,39]=-0.9,s[51,40]=1.2,s[51,41]=-0.7,s[51,42]=0.6,s[51,43]=0.3,s[51,44]=0.4,s[51,45]=0.1
s[51,46]=-0.2,s[51,47]=-0.5,s[51,48]=1.0,s[51,49]=-0.7,s[51,50]=0.6,s[51,51]=-0.4,s[51,52]=0.9,s[51,53]=0.0,s[51,54]=-0.1,s[51,55]=-0.9,s[51,56]=1.2,s[51,57]=1.1,s[51,58]=0.7,s[51,59]=-0.3,s[51,60]=-0.3
s[52,1]=-0.6,s[52,2]=-0.8,s[52,3]=-1.1,s[52,4]=-0.9,s[52,5]=-1.1,s[52,6]=1.0,s[52,7]=1.0,s[52,8]=-1.1,s[52,9]=0.5,s[52,10]=-1.0,s[52,11]=1.0,s[52,12]=1.2,s[52,13]=-0.7,s[52,14]=-0.1,s[52,15]=0.0
s[52,16]=0.4,s[52,17]=-0.7,s[52,18]=0.4,s[52,19]=-1.2,s[52,20]=0.2,s[52,21]=0.0,s[52,22]=0.9,s[52,23]=-0.3,s[52,24]=1.0,s[52,25]=-1.0,s[52,26]=-0.1,s[52,27]=-0.5,s[52,28]=0.9,s[52,29]=0.6,s[52,30]=0.6
s[52,31]=-0.4,s[52,32]=0.8,s[52,33]=0.5,s[52,34]=-0.4,s[52,35]=0.3,s[52,36]=1.2,s[52,37]=-0.8,s[52,38]=0.2,s[52,39]=0.2,s[52,40]=-0.5,s[52,41]=0.4,s[52,42]=0.6,s[52,43]=-0.8,s[52,44]=-0.2,s[52,45]=-1.2
s[52,46]=-1.2,s[52,47]=-1.1,s[52,48]=0.3,s[52,49]=1.2,s[52,50]=-1.1,s[52,51]=-0.1,s[52,52]=1.1,s[52,53]=0.5,s[52,54]=0.0,s[52,55]=0.0,s[52,56]=0.6,s[52,57]=-0.7,s[52,58]=-0.8,s[52,59]=-0.1,s[52,60]=0.4
s[53,1]=1.0,s[53,2]=0.3,s[53,3]=0.2,s[53,4]=-0.7,s[53,5]=-0.7,s[53,6]=0.9,s[53,7]=-0.7,s[53,8]=-0.1,s[53,9]=-0.8,s[53,10]=0.6,s[53,11]=-0.2,s[53,12]=-0.2,s[53,13]=0.1,s[53,14]=-0.9,s[53,15]=-1.2
s[53,16]=-1.2,s[53,17]=-1.1,s[53,18]=0.2,s[53,19]=-1.0,s[53,20]=0.1,s[53,21]=1.2,s[53,22]=-0.2,s[53,23]=-1.1,s[53,24]=0.7,s[53,25]=0.9,s[53,26]=0.6,s[53,27]=-0.2,s[53,28]=0.6,s[53,29]=0.4,s[53,30]=0.2
s[53,31]=-1.1,s[53,32]=0.1,s[53,33]=1.2,s[53,34]=-0.4,s[53,35]=1.0,s[53,36]=-1.0,s[53,37]=-0.6,s[53,38]=0.3,s[53,39]=-0.7,s[53,40]=0.6,s[53,41]=-0.5,s[53,42]=-1.1,s[53,43]=0.0,s[53,44]=-0.3,s[53,45]=-1.1
s[53,46]=0.6,s[53,47]=-1.1,s[53,48]=0.9,s[53,49]=-0.8,s[53,50]=0.3,s[53,51]=-0.1,s[53,52]=-0.1,s[53,53]=0.7,s[53,54]=-0.8,s[53,55]=-1.0,s[53,56]=0.0,s[53,57]=-0.9,s[53,58]=-1.1,s[53,59]=0.4,s[53,60]=-0.9
s[54,1]=0.1,s[54,2]=-0.1,s[54,3]=0.9,s[54,4]=-1.0,s[54,5]=1.1,s[54,6]=0.1,s[54,7]=0.0,s[54,8]=-1.2,s[54,9]=-1.1,s[54,10]=-0.1,s[54,11]=0.1,s[54,12]=1.2,s[54,13]=-0.4,s[54,14]=0.8,s[54,15]=0.4
s[54,16]=1.2,s[54,17]=0.1,s[54,18]=-0.7,s[54,19]=-0.8,s[54,20]=1.0,s[54,21]=1.0,s[54,22]=-0.7,s[54,23]=-1.2,s[54,24]=0.7,s[54,25]=-1.1,s[54,26]=0.9,s[54,27]=0.9,s[54,28]=0.3,s[54,29]=0.4,s[54,30]=-0.9
s[54,31]=0.4,s[54,32]=1.0,s[54,33]=1.1,s[54,34]=-0.8,s[54,35]=-0.9,s[54,36]=-0.4,s[54,37]=-0.9,s[54,38]=0.6,s[54,39]=1.2,s[54,40]=0.7,s[54,41]=0.7,s[54,42]=1.0,s[54,43]=0.8,s[54,44]=-1.1,s[54,45]=-0.3
s[54,46]=-0.3,s[54,47]=1.0,s[54,48]=-0.9,s[54,49]=0.5,s[54,50]=1.2,s[54,51]=1.0,s[54,52]=0.4,s[54,53]=-1.2,s[54,54]=-0.5,s[54,55]=0.0,s[54,56]=-0.4,s[54,57]=1.2,s[54,58]=-0.5,s[54,59]=-0.4,s[54,60]=-0.1
s[55,1]=-0.3,s[55,2]=1.0,s[55,3]=-0.4,s[55,4]=0.0,s[55,5]=-1.2,s[55,6]=0.2,s[55,7]=-0.9,s[55,8]=0.1,s[55,9]=-0.3,s[55,10]=1.2,s[55,11]=-0.8,s[55,12]=1.2,s[55,13]=1.2,s[55,14]=-0.1,s[55,15]=-0.5
s[55,16]=-1.1,s[55,17]=1.1,s[55,18]=-0.8,s[55,19]=-0.9,s[55,20]=-1.1,s[55,21]=-0.9,s[55,22]=-0.4,s[55,23]=0.6,s[55,24]=0.4,s[55,25]=0.7,s[55,26]=0.2,s[55,27]=-0.9,s[55,28]=1.0,s[55,29]=-0.1,s[55,30]=0.1
s[55,31]=1.0,s[55,32]=-1.0,s[55,33]=0.9,s[55,34]=-0.4,s[55,35]=0.0,s[55,36]=-0.8,s[55,37]=-1.1,s[55,38]=-0.9,s[55,39]=1.1,s[55,40]=-0.1,s[55,41]=0.5,s[55,42]=0.4,s[55,43]=0.5,s[55,44]=0.7,s[55,45]=1.2
s[55,46]=-0.7,s[55,47]=-0.3,s[55,48]=0.1,s[55,49]=0.4,s[55,50]=1.1,s[55,51]=0.6,s[55,52]=0.8,s[55,53]=-0.5,s[55,54]=-0.2,s[55,55]=0.7,s[55,56]=-0.8,s[55,57]=-0.4,s[55,58]=-0.2,s[55,59]=-0.4,s[55,60]=-1.0
s[56,1]=-0.5,s[56,2]=0.5,s[56,3]=0.6,s[56,4]=-1.1,s[56,5]=-0.5,s[56,6]=1.2,s[56,7]=0.6,s[56,8]=-1.0,s[56,9]=0.2,s[56,10]=0.4,s[56,11]=0.1,s[56,12]=-0.6,s[56,13]=-0.4,s[56,14]=-0.8,s[56,15]=-1.2
s[56,16]=0.2,s[56,17]=1.1,s[56,18]=-0.4,s[56,19]=0.0,s[56,20]=-0.8,s[56,21]=1.2,s[56,22]=-0.2,s[56,23]=0.0,s[56,24]=-0.5,s[56,25]=0.2,s[56,26]=0.9,s[56,27]=0.0,s[56,28]=0.6,s[56,29]=0.6,s[56,30]=-0.2
s[56,31]=1.1,s[56,32]=0.4,s[56,33]=1.1,s[56,34]=0.0,s[56,35]=0.6,s[56,36]=1.1,s[56,37]=-0.1,s[56,38]=-0.5,s[56,39]=1.2,s[56,40]=0.3,s[56,41]=-0.5,s[56,42]=-0.5,s[56,43]=0.8,s[56,44]=0.7,s[56,45]=-0.1
s[56,46]=-1.2,s[56,47]=-0.1,s[56,48]=-0.2,s[56,49]=1.1,s[56,50]=0.6,s[56,51]=-0.9,s[56,52]=-0.7,s[56,53]=0.5,s[56,54]=-1.2,s[56,55]=1.0,s[56,56]=1.1,s[56,57]=0.0,s[56,58]=-0.5,s[56,59]=0.0,s[56,60]=-1.2
s[57,1]=-0.5,s[57,2]=-1.2,s[57,3]=-0.7,s[57,4]=-0.4,s[57,5]=0.1,s[57,6]=0.0,s[57,7]=-0.5,s[57,8]=0.9,s[57,9]=0.0,s[57,10]=-0.7,s[57,11]=0.6,s[57,12]=-1.0,s[57,13]=0.2,s[57,14]=-0.5,s[57,15]=0.2
s[57,16]=-0.2,s[57,17]=-1.0,s[57,18]=-0.2,s[57,19]=0.3,s[57,20]=0.4,s[57,21]=-1.0,s[57,22]=0.7,s[57,23]=0.1,s[57,24]=0.1,s[57,25]=-1.0,s[57,26]=0.1,s[57,27]=-0.5,s[57,28]=-0.1,s[57,29]=-0.4,s[57,30]=-0.1
s[57,31]=0.5,s[57,32]=-0.4,s[57,33]=-1.0,s[57,34]=0.0,s[57,35]=0.3,s[57,36]=0.2,s[57,37]=-0.6,s[57,38]=-0.8,s[57,39]=1.1,s[57,40]=1.0,s[57,41]=0.1,s[57,42]=-1.1,s[57,43]=-0.1,s[57,44]=0.6,s[57,45]=-1.1
s[57,46]=-1.1,s[57,47]=-1.1,s[57,48]=1.2,s[57,49]=-0.2,s[57,50]=-0.1,s[57,51]=-0.5,s[57,52]=-1.0,s[57,53]=-0.5,s[57,54]=0.0,s[57,55]=0.9,s[57,56]=0.5,s[57,57]=-0.5,s[57,58]=-1.0,s[57,59]=0.6,s[57,60]=-0.4
s[58,1]=1.2,s[58,2]=0.3,s[58,3]=-0.7,s[58,4]=-1.2,s[58,5]=0.9,s[58,6]=0.6,s[58,7]=-0.3,s[58,8]=0.0,s[58,9]=0.8,s[58,10]=-0.2,s[58,11]=0.6,s[58,12]=-1.1,s[58,13]=-0.9,s[58,14]=-1.0,s[58,15]=-0.4
s[58,16]=0.8,s[58,17]=0.5,s[58,18]=0.1,s[58,19]=0.3,s[58,20]=-1.2,s[58,21]=1.0,s[58,22]=0.4,s[58,23]=0.0,s[58,24]=1.1,s[58,25]=-0.3,s[58,26]=-0.2,s[58,27]=0.3,s[58,28]=1.2,s[58,29]=-0.6,s[58,30]=-0.4
s[58,31]=-0.9,s[58,32]=0.9,s[58,33]=-0.8,s[58,34]=-0.4,s[58,35]=0.2,s[58,36]=1.0,s[58,37]=-0.1,s[58,38]=0.5,s[58,39]=-0.4,s[58,40]=0.1,s[58,41]=-0.7,s[58,42]=-0.6,s[58,43]=0.9,s[58,44]=0.3,s[58,45]=0.8
s[58,46]=-0.6,s[58,47]=1.1,s[58,48]=1.2,s[58,49]=0.0,s[58,50]=0.5,s[58,51]=-0.4,s[58,52]=-0.8,s[58,53]=-1.0,s[58,54]=-1.2,s[58,55]=1.1,s[58,56]=-1.1,s[58,57]=-0.5,s[58,58]=-1.0,s[58,59]=-1.1,s[58,60]=-0.8
s[59,1]=0.4,s[59,2]=-1.2,s[59,3]=0.1,s[59,4]=-1.1,s[59,5]=-0.6,s[59,6]=0.3,s[59,7]=1.1,s[59,8]=-0.8,s[59,9]=-0.1,s[59,10]=0.6,s[59,11]=0.3,s[59,12]=0.2,s[59,13]=0.4,s[59,14]=-0.8,s[59,15]=1.0
s[59,16]=0.7,s[59,17]=0.3,s[59,18]=1.2,s[59,19]=0.3,s[59,20]=-0.4,s[59,21]=-0.2,s[59,22]=-1.1,s[59,23]=0.9,s[59,24]=0.7,s[59,25]=-0.6,s[59,26]=-0.4,s[59,27]=-0.7,s[59,28]=-0.3,s[59,29]=-1.0,s[59,30]=0.5
s[59,31]=1.1,s[59,32]=0.6,s[59,33]=-0.3,s[59,34]=0.1,s[59,35]=-0.8,s[59,36]=0.0,s[59,37]=-0.1,s[59,38]=-0.4,s[59,39]=0.6,s[59,40]=0.4,s[59,41]=-0.8,s[59,42]=-0.3,s[59,43]=-0.6,s[59,44]=0.8,s[59,45]=-0.9
s[59,46]=-1.2,s[59,47]=0.7,s[59,48]=1.0,s[59,49]=0.1,s[59,50]=-0.4,s[59,51]=0.5,s[59,52]=1.1,s[59,53]=-0.7,s[59,54]=-0.4,s[59,55]=-0.8,s[59,56]=0.1,s[59,57]=0.8,s[59,58]=1.1,s[59,59]=0.3,s[59,60]=-0.5
s[60,1]=1.2,s[60,2]=-0.8,s[60,3]=-0.1,s[60,4]=-0.5,s[60,5]=-0.2,s[60,6]=-0.5,s[60,7]=0.8,s[60,8]=-0.7,s[60,9]=0.3,s[60,10]=0.3,s[60,11]=-0.3,s[60,12]=-0.3,s[60,13]=-0.7,s[60,14]=0.8,s[60,15]=-0.5
s[60,16]=0.0,s[60,17]=0.2,s[60,18]=0.0,s[60,19]=-1.1,s[60,20]=0.0,s[60,21]=0.8,s[60,22]=0.7,s[60,23]=0.3,s[60,24]=-1.2,s[60,25]=0.5,s[60,26]=0.9,s[60,27]=0.9,s[60,28]=-0.8,s[60,29]=-0.1,s[60,30]=-1.2
s[60,31]=-0.6,s[60,32]=0.2,s[60,33]=0.0,s[60,34]=-0.6,s[60,35]=-0.3,s[60,36]=0.9,s[60,37]=0.9,s[60,38]=-0.2,s[60,39]=0.8,s[60,40]=-0.8,s[60,41]=0.4,s[60,42]=-0.3,s[60,43]=-0.5,s[60,44]=-0.1,s[60,45]=1.0
s[60,46]=0.6,s[60,47]=0.0,s[60,48]=-0.5,s[60,49]=-1.0,s[60,50]=0.7,s[60,51]=0.5,s[60,52]=-0.5,s[60,53]=0.9,s[60,54]=-1.1,s[60,55]=-0.3,s[60,56]=0.0,s[60,57]=-0.8,s[60,58]=-1.0,s[60,59]=0.0,s[60,60]=-1.2
s[61,1]=0.0,s[61,2]=0.7,s[61,3]=0.9,s[61,4]=0.4,s[61,5]=-1.0,s[61,6]=0.3,s[61,7]=-1.2,s[61,8]=1.1,s[61,9]=-0.3,s[61,10]=0.1,s[61,11]=-0.8,s[61,12]=-0.3,s[61,13]=-0.1,s[61,14]=-1.1,s[61,15]=-0.3
s[61,16]=-0.8,s[61,17]=0.1,s[61,18]=-0.8,s[61,19]=0.2,s[61,20]=0.7,s[61,21]=0.0,s[61,22]=1.1,s[61,23]=-0.5,s[61,24]=0.8,s[61,25]=0.1,s[61,26]=-0.4,s[61,27]=1.0,s[61,28]=-0.5,s[61,29]=-0.8,s[61,30]=-0.2
s[61,31]=1.0,s[61,32]=1.2,s[61,33]=0.3,s[61,34]=-0.1,s[61,35]=0.3,s[61,36]=-1.2,s[61,37]=-1.1,s[61,38]=-0.9,s[61,39]=1.2,s[61,40]=0.4,s[61,41]=-0.8,s[61,42]=-0.9,s[61,43]=-0.6,s[61,44]=-0.9,s[61,45]=1.2
s[61,46]=0.0,s[61,47]=0.3,s[61,48]=-0.3,s[61,49]=0.4,s[61,50]=1.0,s[61,51]=0.1,s[61,52]=0.8,s[61,53]=1.1,s[61,54]=1.2,s[61,55]=0.8,s[61,56]=-0.8,s[61,57]=0.9,s[61,58]=-0.2,s[61,59]=0.5,s[61,60]=-1.1
s[62,1]=0.8,s[62,2]=-1.2,s[62,3]=-0.7,s[62,4]=0.3,s[62,5]=-0.6,s[62,6]=1.1,s[62,7]=-0.4,s[62,8]=-0.3,s[62,9]=-0.8,s[62,10]=0.7,s[62,11]=-0.9,s[62,12]=0.3,s[62,13]=0.7,s[62,14]=1.2,s[62,15]=-0.5
s[62,16]=-1.1,s[62,17]=-0.7,s[62,18]=1.0,s[62,19]=-0.1,s[62,20]=0.0,s[62,21]=-1.2,s[62,22]=-0.9,s[62,23]=-0.3,s[62,24]=-0.3,s[62,25]=-0.1,s[62,26]=1.0,s[62,27]=-1.0,s[62,28]=0.7,s[62,29]=1.1,s[62,30]=-0.4
s[62,31]=0.7,s[62,32]=-0.9,s[62,33]=-0.3,s[62,34]=-0.7,s[62,35]=0.4,s[62,36]=1.0,s[62,37]=0.5,s[62,38]=-0.2,s[62,39]=0.8,s[62,40]=0.9,s[62,41]=-1.2,s[62,42]=1.1,s[62,43]=0.4,s[62,44]=-0.9,s[62,45]=0.7
s[62,46]=-0.5,s[62,47]=-0.5,s[62,48]=-0.6,s[62,49]=-0.7,s[62,50]=0.8,s[62,51]=1.1,s[62,52]=-1.2,s[62,53]=-0.4,s[62,54]=-0.8,s[62,55]=-0.7,s[62,56]=0.2,s[62,57]=-0.2,s[62,58]=0.4,s[62,59]=-1.1,s[62,60]=-0.7
s[63,1]=-1.2,s[63,2]=0.9,s[63,3]=0.6,s[63,4]=-0.6,s[63,5]=-0.6,s[63,6]=0.9,s[63,7]=-0.3,s[63,8]=-0.8,s[63,9]=0.5,s[63,10]=0.5,s[63,11]=0.3,s[63,12]=-0.3,s[63,13]=1.0,s[63,14]=-0.2,s[63,15]=-0.3
s[63,16]=0.2,s[63,17]=-0.9,s[63,18]=0.2,s[63,19]=0.7,s[63,20]=0.4,s[63,21]=-0.8,s[63,22]=-1.0,s[63,23]=0.7,s[63,24]=0.4,s[63,25]=0.9,s[63,26]=0.4,s[63,27]=-0.2,s[63,28]=-0.7,s[63,29]=0.4,s[63,30]=-0.7
s[63,31]=1.0,s[63,32]=0.8,s[63,33]=0.3,s[63,34]=-1.1,s[63,35]=-0.1,s[63,36]=0.0,s[63,37]=0.0,s[63,38]=0.0,s[63,39]=0.0,s[63,40]=-0.4,s[63,41]=0.0,s[63,42]=-0.2,s[63,43]=0.4,s[63,44]=0.6,s[63,45]=0.8
s[63,46]=-0.5,s[63,47]=0.4,s[63,48]=-0.6,s[63,49]=-0.9,s[63,50]=-1.0,s[63,51]=-0.9,s[63,52]=-1.2,s[63,53]=0.1,s[63,54]=0.4,s[63,55]=-0.5,s[63,56]=0.1,s[63,57]=1.1,s[63,58]=-0.8,s[63,59]=-0.5,s[63,60]=-0.6
s[64,1]=-0.2,s[64,2]=0.2,s[64,3]=-0.3,s[64,4]=0.0,s[64,5]=0.4,s[64,6]=-1.0,s[64,7]=-0.1,s[64,8]=-0.9,s[64,9]=1.2,s[64,10]=-0.6,s[64,11]=-0.7,s[64,12]=-0.4,s[64,13]=1.1,s[64,14]=0.6,s[64,15]=-1.0
s[64,16]=0.7,s[64,17]=0.2,s[64,18]=-0.1,s[64,19]=-1.1,s[64,20]=0.8,s[64,21]=-0.7,s[64,22]=1.2,s[64,23]=0.6,s[64,24]=-0.9,s[64,25]=0.0,s[64,26]=-1.0,s[64,27]=-0.4,s[64,28]=-0.6,s[64,29]=0.1,s[64,30]=0.8
s[64,31]=-1.0,s[64,32]=1.2,s[64,33]=-0.2,s[64,34]=-1.1,s[64,35]=0.3,s[64,36]=-0.4,s[64,37]=0.7,s[64,38]=1.2,s[64,39]=0.1,s[64,40]=-0.6,s[64,41]=-0.1,s[64,42]=-0.4,s[64,43]=-0.5,s[64,44]=-1.0,s[64,45]=0.7
s[64,46]=1.1,s[64,47]=-0.1,s[64,48]=-0.1,s[64,49]=-0.7,s[64,50]=0.2,s[64,51]=-0.7,s[64,52]=0.1,s[64,53]=0.9,s[64,54]=0.7,s[64,55]=-1.0,s[64,56]=0.2,s[64,57]=0.0,s[64,58]=0.1,s[64,59]=0.9,s[64,60]=-1.0
s[65,1]=-1.1,s[65,2]=0.7,s[65,3]=-1.0,s[65,4]=-0.3,s[65,5]=-0.7,s[65,6]=0.6,s[65,7]=0.6,s[65,8]=-0.2,s[65,9]=-0.4,s[65,10]=0.5,s[65,11]=-0.9,s[65,12]=0.7,s[65,13]=0.0,s[65,14]=-1.2,s[65,15]=1.0
s[65,16]=-0.9,s[65,17]=-0.8,s[65,18]=0.6,s[65,19]=0.4,s[65,20]=0.4,s[65,21]=-1.2,s[65,22]=0.7,s[65,23]=0.4,s[65,24]=0.1,s[65,25]=-0.9,s[65,26]=0.1,s[65,27]=-0.2,s[65,28]=0.2,s[65,29]=0.4,s[65,30]=-0.2
s[65,31]=-0.1,s[65,32]=0.7,s[65,33]=0.8,s[65,34]=0.1,s[65,35]=-1.1,s[65,36]=0.0,s[65,37]=-0.2,s[65,38]=-1.0,s[65,39]=1.1,s[65,40]=0.7,s[65,41]=0.1,s[65,42]=-1.1,s[65,43]=0.8,s[65,44]=0.3,s[65,45]=-0.1
s[65,46]=-1.1,s[65,47]=0.1,s[65,48]=-0.8,s[65,49]=1.2,s[65,50]=-0.1,s[65,51]=-0.6,s[65,52]=0.8,s[65,53]=-0.1,s[65,54]=0.7,s[65,55]=1.1,s[65,56]=-0.3,s[65,57]=-0.7,s[65,58]=-0.3,s[65,59]=0.0,s[65,60]=-1.0
s[66,1]=0.1,s[66,2]=-0.3,s[66,3]=-0.5,s[66,4]=-0.9,s[66,5]=0.5,s[66,6]=-1.0,s[66,7]=0.3,s[66,8]=-0.7,s[66,9]=-0.7,s[66,10]=-0.4,s[66,11]=-0.4,s[66,12]=-0.4,s[66,13]=1.1,s[66,14]=-0.8,s[66,15]=-0.9
s[66,16]=0.7,s[66,17]=0.9,s[66,18]=-0.1,s[66,19]=0.5,s[66,20]=-0.1,s[66,21]=0.5,s[66,22]=0.8,s[66,23]=-0.6,s[66,24]=-0.4,s[66,25]=-0.1,s[66,26]=-0.7,s[66,27]=-0.7,s[66,28]=1.1,s[66,29]=-0.6,s[66,30]=-0.5
s[66,31]=0.6,s[66,32]=-0.7,s[66,33]=-0.2,s[66,34]=-0.5,s[66,35]=0.2,s[66,36]=0.3,s[66,37]=0.3,s[66,38]=-0.1,s[66,39]=0.8,s[66,40]=1.1,s[66,41]=0.3,s[66,42]=-1.1,s[66,43]=-0.2,s[66,44]=0.8,s[66,45]=-0.7
s[66,46]=0.1,s[66,47]=0.5,s[66,48]=0.4,s[66,49]=0.6,s[66,50]=1.2,s[66,51]=-0.4,s[66,52]=0.5,s[66,53]=-0.6,s[66,54]=0.9,s[66,55]=-0.2,s[66,56]=0.6,s[66,57]=-0.3,s[66,58]=-0.1,s[66,59]=0.0,s[66,60]=-1.2
s[67,1]=-0.3,s[67,2]=0.7,s[67,3]=-0.9,s[67,4]=-1.0,s[67,5]=-1.0,s[67,6]=0.5,s[67,7]=-0.9,s[67,8]=-1.2,s[67,9]=0.3,s[67,10]=0.8,s[67,11]=1.2,s[67,12]=-0.2,s[67,13]=0.1,s[67,14]=-0.6,s[67,15]=-1.1
s[67,16]=0.4,s[67,17]=0.1,s[67,18]=-1.1,s[67,19]=-0.6,s[67,20]=0.8,s[67,21]=-1.2,s[67,22]=-0.4,s[67,23]=-0.8,s[67,24]=1.2,s[67,25]=0.3,s[67,26]=0.3,s[67,27]=0.6,s[67,28]=0.9,s[67,29]=0.1,s[67,30]=-0.9
s[67,31]=1.0,s[67,32]=-0.9,s[67,33]=-0.6,s[67,34]=-1.1,s[67,35]=-0.9,s[67,36]=1.0,s[67,37]=-1.2,s[67,38]=0.2,s[67,39]=-0.7,s[67,40]=0.1,s[67,41]=0.6,s[67,42]=-0.7,s[67,43]=-0.5,s[67,44]=0.4,s[67,45]=-0.9
s[67,46]=-1.2,s[67,47]=-0.2,s[67,48]=-0.9,s[67,49]=1.2,s[67,50]=0.7,s[67,51]=0.3,s[67,52]=-1.2,s[67,53]=0.6,s[67,54]=0.2,s[67,55]=0.5,s[67,56]=1.1,s[67,57]=1.0,s[67,58]=1.2,s[67,59]=-0.1,s[67,60]=0.1
s[68,1]=0.8,s[68,2]=-1.0,s[68,3]=-1.0,s[68,4]=-0.7,s[68,5]=0.2,s[68,6]=0.3,s[68,7]=-0.7,s[68,8]=0.1,s[68,9]=0.9,s[68,10]=-0.8,s[68,11]=1.0,s[68,12]=-0.5,s[68,13]=1.0,s[68,14]=-0.9,s[68,15]=-0.1
s[68,16]=0.8,s[68,17]=1.0,s[68,18]=1.0,s[68,19]=-1.2,s[68,20]=-0.6,s[68,21]=-0.9,s[68,22]=0.6,s[68,23]=0.1,s[68,24]=0.4,s[68,25]=-1.2,s[68,26]=-0.2,s[68,27]=0.4,s[68,28]=-0.3,s[68,29]=1.1,s[68,30]=-1.0
s[68,31]=-1.2,s[68,32]=-0.6,s[68,33]=0.2,s[68,34]=-0.5,s[68,35]=1.0,s[68,36]=-0.6,s[68,37]=0.7,s[68,38]=0.0,s[68,39]=1.1,s[68,40]=0.3,s[68,41]=0.7,s[68,42]=0.7,s[68,43]=0.5,s[68,44]=-0.9,s[68,45]=-0.2
s[68,46]=0.7,s[68,47]=-0.4,s[68,48]=-0.5,s[68,49]=-0.4,s[68,50]=0.8,s[68,51]=1.0,s[68,52]=-1.1,s[68,53]=-1.0,s[68,54]=-0.4,s[68,55]=-0.4,s[68,56]=-1.1,s[68,57]=-0.9,s[68,58]=1.1,s[68,59]=1.1,s[68,60]=-0.9
s[69,1]=0.5,s[69,2]=1.1,s[69,3]=-0.2,s[69,4]=-0.2,s[69,5]=1.1,s[69,6]=-0.2,s[69,7]=-1.2,s[69,8]=-1.0,s[69,9]=-1.0,s[69,10]=-0.2,s[69,11]=0.5,s[69,12]=-1.0,s[69,13]=-0.3,s[69,14]=-0.8,s[69,15]=-1.2
s[69,16]=1.2,s[69,17]=0.2,s[69,18]=-0.7,s[69,19]=-0.5,s[69,20]=-0.7,s[69,21]=-0.5,s[69,22]=0.1,s[69,23]=-0.3,s[69,24]=-0.6,s[69,25]=-0.9,s[69,26]=-0.8,s[69,27]=1.2,s[69,28]=0.1,s[69,29]=0.3,s[69,30]=0.0
s[69,31]=0.8,s[69,32]=-0.2,s[69,33]=-1.2,s[69,34]=-0.3,s[69,35]=1.2,s[69,36]=-0.5,s[69,37]=0.4,s[69,38]=1.1,s[69,39]=-0.3,s[69,40]=0.3,s[69,41]=0.0,s[69,42]=-0.3,s[69,43]=0.4,s[69,44]=0.3,s[69,45]=-0.2
s[69,46]=0.7,s[69,47]=0.8,s[69,48]=0.5,s[69,49]=0.5,s[69,50]=0.2,s[69,51]=-0.2,s[69,52]=1.0,s[69,53]=0.0,s[69,54]=-0.6,s[69,55]=0.8,s[69,56]=0.8,s[69,57]=0.3,s[69,58]=0.7,s[69,59]=-0.4,s[69,60]=-1.1
s[70,1]=-0.3,s[70,2]=0.3,s[70,3]=-0.1,s[70,4]=0.7,s[70,5]=0.0,s[70,6]=-1.0,s[70,7]=-1.2,s[70,8]=-0.1,s[70,9]=0.2,s[70,10]=-1.2,s[70,11]=-0.5,s[70,12]=-1.0,s[70,13]=1.1,s[70,14]=-0.2,s[70,15]=0.1
s[70,16]=1.0,s[70,17]=0.0,s[70,18]=1.0,s[70,19]=-1.1,s[70,20]=0.6,s[70,21]=-1.2,s[70,22]=0.6,s[70,23]=0.7,s[70,24]=-0.6,s[70,25]=0.9,s[70,26]=-0.7,s[70,27]=0.4,s[70,28]=-0.3,s[70,29]=0.8,s[70,30]=0.4
s[70,31]=0.4,s[70,32]=-1.2,s[70,33]=1.0,s[70,34]=-0.3,s[70,35]=-0.7,s[70,36]=-0.3,s[70,37]=0.8,s[70,38]=0.9,s[70,39]=0.2,s[70,40]=-0.1,s[70,41]=1.2,s[70,42]=0.4,s[70,43]=-0.4,s[70,44]=-0.3,s[70,45]=-0.3
s[70,46]=0.6,s[70,47]=-0.7,s[70,48]=-0.9,s[70,49]=0.2,s[70,50]=-0.8,s[70,51]=-0.7,s[70,52]=-0.5,s[70,53]=0.7,s[70,54]=-0.3,s[70,55]=0.6,s[70,56]=-0.6,s[70,57]=-0.6,s[70,58]=0.5,s[70,59]=1.2,s[70,60]=-0.5
s[71,1]=0.9,s[71,2]=0.1,s[71,3]=0.0,s[71,4]=-1.0,s[71,5]=-0.5,s[71,6]=-0.7,s[71,7]=-1.2,s[71,8]=0.2,s[71,9]=0.0,s[71,10]=-0.3,s[71,11]=0.8,s[71,12]=1.0,s[71,13]=-0.9,s[71,14]=-1.0,s[71,15]=-1.2
s[71,16]=-0.2,s[71,17]=-0.7,s[71,18]=-0.9,s[71,19]=-1.2,s[71,20]=-1.1,s[71,21]=-1.1,s[71,22]=0.4,s[71,23]=0.7,s[71,24]=-0.8,s[71,25]=-0.8,s[71,26]=-0.5,s[71,27]=-1.1,s[71,28]=0.7,s[71,29]=0.8,s[71,30]=0.4
s[71,31]=-0.5,s[71,32]=1.2,s[71,33]=-0.7,s[71,34]=-0.9,s[71,35]=0.4,s[71,36]=1.1,s[71,37]=-0.2,s[71,38]=0.9,s[71,39]=1.0,s[71,40]=-0.3,s[71,41]=-1.2,s[71,42]=0.0,s[71,43]=-1.0,s[71,44]=0.5,s[71,45]=-0.5
s[71,46]=0.9,s[71,47]=-1.2,s[71,48]=-0.3,s[71,49]=-0.8,s[71,50]=0.9,s[71,51]=1.2,s[71,52]=-0.3,s[71,53]=0.5,s[71,54]=-0.7,s[71,55]=-0.2,s[71,56]=-0.2,s[71,57]=-0.6,s[71,58]=0.9,s[71,59]=0.1,s[71,60]=-1.0
s[72,1]=-0.5,s[72,2]=-0.3,s[72,3]=-0.1,s[72,4]=0.2,s[72,5]=0.7,s[72,6]=-0.1,s[72,7]=-0.1,s[72,8]=-0.9,s[72,9]=-0.3,s[72,10]=0.3,s[72,11]=1.1,s[72,12]=-1.2,s[72,13]=0.2,s[72,14]=0.7,s[72,15]=-0.2
s[72,16]=-1.2,s[72,17]=1.0,s[72,18]=-1.1,s[72,19]=0.5,s[72,20]=0.4,s[72,21]=0.1,s[72,22]=-0.6,s[72,23]=0.5,s[72,24]=-0.8,s[72,25]=-0.6,s[72,26]=0.9,s[72,27]=-1.0,s[72,28]=0.9,s[72,29]=0.4,s[72,30]=-0.2
s[72,31]=0.5,s[72,32]=-0.8,s[72,33]=-0.8,s[72,34]=-1.0,s[72,35]=-1.2,s[72,36]=-0.1,s[72,37]=0.7,s[72,38]=0.6,s[72,39]=1.1,s[72,40]=0.3,s[72,41]=-1.1,s[72,42]=-0.4,s[72,43]=0.0,s[72,44]=-0.1,s[72,45]=1.2
s[72,46]=-0.7,s[72,47]=0.9,s[72,48]=-1.1,s[72,49]=-0.7,s[72,50]=0.3,s[72,51]=-0.8,s[72,52]=-0.9,s[72,53]=-1.0,s[72,54]=-1.0,s[72,55]=-0.8,s[72,56]=-1.0,s[72,57]=-0.1,s[72,58]=-1.2,s[72,59]=-1.2,s[72,60]=-1.1
s[73,1]=0.9,s[73,2]=-1.2,s[73,3]=0.7,s[73,4]=-0.8,s[73,5]=0.8,s[73,6]=1.1,s[73,7]=-1.1,s[73,8]=-0.3,s[73,9]=0.2,s[73,10]=-0.3,s[73,11]=-1.2,s[73,12]=0.6,s[73,13]=0.3,s[73,14]=-0.9,s[73,15]=1.1
s[73,16]=0.7,s[73,17]=-0.3,s[73,18]=1.1,s[73,19]=-0.8,s[73,20]=1.0,s[73,21]=1.1,s[73,22]=0.9,s[73,23]=-1.2,s[73,24]=0.8,s[73,25]=0.5,s[73,26]=1.2,s[73,27]=-1.1,s[73,28]=0.3,s[73,29]=0.2,s[73,30]=-0.6
s[73,31]=0.4,s[73,32]=-0.5,s[73,33]=0.2,s[73,34]=0.4,s[73,35]=0.6,s[73,36]=-0.3,s[73,37]=1.2,s[73,38]=0.3,s[73,39]=0.0,s[73,40]=0.3,s[73,41]=1.0,s[73,42]=-1.2,s[73,43]=-1.2,s[73,44]=-1.1,s[73,45]=-0.4
s[73,46]=0.7,s[73,47]=-1.2,s[73,48]=-0.6,s[73,49]=0.5,s[73,50]=-0.4,s[73,51]=0.3,s[73,52]=0.8,s[73,53]=-0.4,s[73,54]=-0.9,s[73,55]=-0.4,s[73,56]=-1.1,s[73,57]=-0.5,s[73,58]=0.1,s[73,59]=0.4,s[73,60]=-1.1
s[74,1]=0.6,s[74,2]=0.0,s[74,3]=-0.1,s[74,4]=-0.9,s[74,5]=0.7,s[74,6]=-1.0,s[74,7]=-1.1,s[74,8]=0.3,s[74,9]=-0.3,s[74,10]=-0.6,s[74,11]=-0.2,s[74,12]=-0.7,s[74,13]=-0.3,s[74,14]=-1.1,s[74,15]=-0.8
s[74,16]=-0.2,s[74,17]=0.0,s[74,18]=-0.7,s[74,19]=-0.4,s[74,20]=0.1,s[74,21]=-0.4,s[74,22]=1.1,s[74,23]=0.0,s[74,24]=0.0,s[74,25]=-0.4,s[74,26]=-0.7,s[74,27]=1.2,s[74,28]=-0.8,s[74,29]=0.1,s[74,30]=0.7
s[74,31]=-0.7,s[74,32]=1.2,s[74,33]=0.4,s[74,34]=-0.8,s[74,35]=-0.1,s[74,36]=0.1,s[74,37]=-0.6,s[74,38]=-0.9,s[74,39]=1.2,s[74,40]=0.1,s[74,41]=0.2,s[74,42]=-1.1,s[74,43]=-0.7,s[74,44]=-0.3,s[74,45]=-0.7
s[74,46]=-0.9,s[74,47]=1.1,s[74,48]=0.6,s[74,49]=0.9,s[74,50]=0.0,s[74,51]=-1.2,s[74,52]=-0.5,s[74,53]=0.2,s[74,54]=1.0,s[74,55]=0.2,s[74,56]=-0.3,s[74,57]=-0.6,s[74,58]=-0.6,s[74,59]=-1.0,s[74,60]=-1.2
s[75,1]=0.2,s[75,2]=-1.0,s[75,3]=-1.1,s[75,4]=-0.7,s[75,5]=0.0,s[75,6]=0.7,s[75,7]=-1.1,s[75,8]=0.6,s[75,9]=0.8,s[75,10]=0.7,s[75,11]=1.0,s[75,12]=-0.2,s[75,13]=-1.0,s[75,14]=0.0,s[75,15]=-0.8
s[75,16]=-1.0,s[75,17]=-0.2,s[75,18]=0.4,s[75,19]=0.9,s[75,20]=1.2,s[75,21]=-0.7,s[75,22]=-0.1,s[75,23]=1.2,s[75,24]=0.1,s[75,25]=-0.5,s[75,26]=0.7,s[75,27]=-0.7,s[75,28]=-1.0,s[75,29]=1.1,s[75,30]=1.2
s[75,31]=1.1,s[75,32]=0.1,s[75,33]=0.5,s[75,34]=0.1,s[75,35]=1.1,s[75,36]=-0.3,s[75,37]=0.0,s[75,38]=0.1,s[75,39]=0.4,s[75,40]=-1.0,s[75,41]=0.1,s[75,42]=-0.5,s[75,43]=1.2,s[75,44]=-0.8,s[75,45]=1.1
s[75,46]=0.4,s[75,47]=0.9,s[75,48]=0.3,s[75,49]=-0.3,s[75,50]=0.1,s[75,51]=-1.0,s[75,52]=0.0,s[75,53]=-1.2,s[75,54]=-1.0,s[75,55]=0.5,s[75,56]=0.4,s[75,57]=0.5,s[75,58]=-0.2,s[75,59]=0.3,s[75,60]=-0.6
s[76,1]=0.7,s[76,2]=-0.4,s[76,3]=-0.2,s[76,4]=0.4,s[76,5]=0.2,s[76,6]=0.9,s[76,7]=-0.1,s[76,8]=-1.2,s[76,9]=0.1,s[76,10]=-1.2,s[76,11]=-0.3,s[76,12]=1.1,s[76,13]=-0.7,s[76,14]=0.5,s[76,15]=1.0
s[76,16]=-1.2,s[76,17]=0.2,s[76,18]=1.2,s[76,19]=-1.1,s[76,20]=0.9,s[76,21]=1.2,s[76,22]=-0.2,s[76,23]=1.2,s[76,24]=-0.5,s[76,25]=-0.2,s[76,26]=-0.2,s[76,27]=-0.4,s[76,28]=0.3,s[76,29]=-0.4,s[76,30]=0.5
s[76,31]=0.3,s[76,32]=1.0,s[76,33]=-1.2,s[76,34]=-0.6,s[76,35]=1.1,s[76,36]=-1.1,s[76,37]=-0.5,s[76,38]=-1.2,s[76,39]=-0.1,s[76,40]=-1.0,s[76,41]=0.1,s[76,42]=0.4,s[76,43]=-1.1,s[76,44]=-0.3,s[76,45]=1.2
s[76,46]=0.2,s[76,47]=0.6,s[76,48]=-1.0,s[76,49]=-1.0,s[76,50]=0.5,s[76,51]=-0.9,s[76,52]=1.2,s[76,53]=-0.1,s[76,54]=0.0,s[76,55]=-0.8,s[76,56]=-0.2,s[76,57]=0.3,s[76,58]=-1.2,s[76,59]=-1.1,s[76,60]=-1.0
s[77,1]=-0.1,s[77,2]=0.9,s[77,3]=0.8,s[77,4]=-1.1,s[77,5]=-0.1,s[77,6]=0.6,s[77,7]=-0.5,s[77,8]=0.1,s[77,9]=-0.1,s[77,10]=0.8,s[77,11]=-1.1,s[77,12]=0.3,s[77,13]=1.2,s[77,14]=1.2,s[77,15]=-1.2
s[77,16]=0.5,s[77,17]=0.8,s[77,18]=-0.8,s[77,19]=-1.0,s[77,20]=1.0,s[77,21]=0.9,s[77,22]=1.1,s[77,23]=0.9,s[77,24]=0.6,s[77,25]=-0.1,s[77,26]=1.2,s[77,27]=0.7,s[77,28]=-1.0,s[77,29]=1.0,s[77,30]=0.8
s[77,31]=-0.8,s[77,32]=-0.3,s[77,33]=0.2,s[77,34]=0.0,s[77,35]=-0.7,s[77,36]=0.4,s[77,37]=0.6,s[77,38]=-0.5,s[77,39]=-0.2,s[77,40]=0.5,s[77,41]=-0.7,s[77,42]=0.1,s[77,43]=-0.1,s[77,44]=0.2,s[77,45]=-0.4
s[77,46]=-0.2,s[77,47]=-1.0,s[77,48]=-0.6,s[77,49]=0.6,s[77,50]=1.2,s[77,51]=-0.1,s[77,52]=0.4,s[77,53]=0.0,s[77,54]=-1.2,s[77,55]=1.0,s[77,56]=0.2,s[77,57]=-1.0,s[77,58]=0.1,s[77,59]=0.7,s[77,60]=-0.3
s[78,1]=0.4,s[78,2]=-0.3,s[78,3]=-0.6,s[78,4]=-0.7,s[78,5]=1.0,s[78,6]=-0.8,s[78,7]=-1.1,s[78,8]=0.2,s[78,9]=1.1,s[78,10]=-1.0,s[78,11]=1.0,s[78,12]=-0.8,s[78,13]=0.6,s[78,14]=-0.1,s[78,15]=-1.0
s[78,16]=-0.9,s[78,17]=1.1,s[78,18]=1.2,s[78,19]=-0.7,s[78,20]=0.6,s[78,21]=0.5,s[78,22]=-0.6,s[78,23]=-0.1,s[78,24]=-0.4,s[78,25]=-0.5,s[78,26]=-0.9,s[78,27]=0.1,s[78,28]=0.1,s[78,29]=0.0,s[78,30]=0.4
s[78,31]=0.4,s[78,32]=-1.2,s[78,33]=-0.2,s[78,34]=-1.0,s[78,35]=-0.4,s[78,36]=0.1,s[78,37]=0.1,s[78,38]=0.1,s[78,39]=0.3,s[78,40]=0.8,s[78,41]=-1.2,s[78,42]=0.6,s[78,43]=0.0,s[78,44]=-1.0,s[78,45]=0.5
s[78,46]=0.6,s[78,47]=0.7,s[78,48]=0.2,s[78,49]=0.0,s[78,50]=-0.2,s[78,51]=-0.8,s[78,52]=1.0,s[78,53]=0.1,s[78,54]=-1.1,s[78,55]=-0.3,s[78,56]=0.6,s[78,57]=0.7,s[78,58]=-0.7,s[78,59]=-0.5,s[78,60]=0.5
s[79,1]=-1.0,s[79,2]=-0.2,s[79,3]=0.1,s[79,4]=-0.8,s[79,5]=-0.6,s[79,6]=-0.5,s[79,7]=0.5,s[79,8]=-0.7,s[79,9]=-1.1,s[79,10]=-0.7,s[79,11]=0.4,s[79,12]=1.1,s[79,13]=1.0,s[79,14]=1.2,s[79,15]=-0.5
s[79,16]=0.1,s[79,17]=-0.5,s[79,18]=0.4,s[79,19]=0.8,s[79,20]=-0.8,s[79,21]=-0.6,s[79,22]=-0.3,s[79,23]=-0.7,s[79,24]=-0.5,s[79,25]=1.0,s[79,26]=0.8,s[79,27]=-0.6,s[79,28]=0.3,s[79,29]=-1.0,s[79,30]=1.1
s[79,31]=0.5,s[79,32]=-0.6,s[79,33]=-0.8,s[79,34]=-0.7,s[79,35]=-0.9,s[79,36]=-1.2,s[79,37]=1.0,s[79,38]=0.2,s[79,39]=-0.6,s[79,40]=-0.7,s[79,41]=-1.2,s[79,42]=-1.1,s[79,43]=-0.6,s[79,44]=-0.2,s[79,45]=-0.1
s[79,46]=-0.7,s[79,47]=0.2,s[79,48]=-0.5,s[79,49]=-0.1,s[79,50]=0.6,s[79,51]=0.0,s[79,52]=-1.2,s[79,53]=0.9,s[79,54]=1.1,s[79,55]=-0.3,s[79,56]=0.9,s[79,57]=-0.3,s[79,58]=0.5,s[79,59]=-0.8,s[79,60]=-0.8
s[80,1]=-0.8,s[80,2]=1.2,s[80,3]=0.1,s[80,4]=0.0,s[80,5]=0.7,s[80,6]=-0.9,s[80,7]=0.5,s[80,8]=-1.1,s[80,9]=-0.5,s[80,10]=0.7,s[80,11]=-0.6,s[80,12]=-0.6,s[80,13]=0.1,s[80,14]=-1.1,s[80,15]=0.7
s[80,16]=-0.5,s[80,17]=-0.4,s[80,18]=-0.7,s[80,19]=0.4,s[80,20]=0.5,s[80,21]=0.7,s[80,22]=0.8,s[80,23]=-0.7,s[80,24]=0.8,s[80,25]=-0.9,s[80,26]=0.0,s[80,27]=0.4,s[80,28]=0.0,s[80,29]=-0.4,s[80,30]=0.5
s[80,31]=1.0,s[80,32]=-1.1,s[80,33]=0.8,s[80,34]=0.0,s[80,35]=0.5,s[80,36]=0.3,s[80,37]=0.3,s[80,38]=0.5,s[80,39]=1.1,s[80,40]=-0.2,s[80,41]=1.0,s[80,42]=-0.7,s[80,43]=-1.0,s[80,44]=-0.9,s[80,45]=1.1
s[80,46]=-0.5,s[80,47]=-0.3,s[80,48]=1.0,s[80,49]=-0.2,s[80,50]=1.2,s[80,51]=-0.9,s[80,52]=1.0,s[80,53]=-0.1,s[80,54]=0.5,s[80,55]=0.8,s[80,56]=-0.4,s[80,57]=-0.5,s[80,58]=1.0,s[80,59]=-0.1,s[80,60]=-0.9
s[81,1]=0.6,s[81,2]=0.5,s[81,3]=0.7,s[81,4]=-1.0,s[81,5]=0.3,s[81,6]=0.8,s[81,7]=1.2,s[81,8]=-0.7,s[81,9]=-0.7,s[81,10]=-0.9,s[81,11]=-1.1,s[81,12]=0.0,s[81,13]=-0.6,s[81,14]=0.4,s[81,15]=1.0
s[81,16]=-0.6,s[81,17]=0.8,s[81,18]=0.0,s[81,19]=-1.1,s[81,20]=0.0,s[81,21]=0.1,s[81,22]=-0.5,s[81,23]=-0.2,s[81,24]=0.4,s[81,25]=1.1,s[81,26]=0.0,s[81,27]=0.4,s[81,28]=1.1,s[81,29]=-1.2,s[81,30]=0.7
s[81,31]=0.5,s[81,32]=-0.3,s[81,33]=0.4,s[81,34]=-1.1,s[81,35]=0.3,s[81,36]=0.2,s[81,37]=0.4,s[81,38]=-1.0,s[81,39]=-0.9,s[81,40]=-1.1,s[81,41]=0.2,s[81,42]=-1.2,s[81,43]=0.3,s[81,44]=-1.1,s[81,45]=1.2
s[81,46]=0.1,s[81,47]=0.5,s[81,48]=1.1,s[81,49]=0.9,s[81,50]=-0.7,s[81,51]=-0.5,s[81,52]=0.8,s[81,53]=1.1,s[81,54]=0.8,s[81,55]=-1.0,s[81,56]=0.2,s[81,57]=0.2,s[81,58]=0.3,s[81,59]=-0.4,s[81,60]=0.4
s[82,1]=-0.5,s[82,2]=0.3,s[82,3]=0.6,s[82,4]=-1.1,s[82,5]=0.1,s[82,6]=-1.2,s[82,7]=-0.9,s[82,8]=1.1,s[82,9]=1.1,s[82,10]=1.1,s[82,11]=-0.2,s[82,12]=0.5,s[82,13]=0.7,s[82,14]=-0.7,s[82,15]=-1.2
s[82,16]=-0.7,s[82,17]=0.4,s[82,18]=1.1,s[82,19]=-0.3,s[82,20]=-0.6,s[82,21]=0.2,s[82,22]=-0.4,s[82,23]=-0.8,s[82,24]=0.1,s[82,25]=-0.8,s[82,26]=-0.1,s[82,27]=-0.6,s[82,28]=0.3,s[82,29]=-0.7,s[82,30]=1.0
s[82,31]=0.1,s[82,32]=-0.5,s[82,33]=1.1,s[82,34]=-1.2,s[82,35]=-1.2,s[82,36]=-0.6,s[82,37]=1.2,s[82,38]=0.9,s[82,39]=0.7,s[82,40]=-0.3,s[82,41]=1.2,s[82,42]=0.3,s[82,43]=1.2,s[82,44]=0.8,s[82,45]=0.3
s[82,46]=0.1,s[82,47]=1.0,s[82,48]=-0.8,s[82,49]=-0.9,s[82,50]=0.4,s[82,51]=0.1,s[82,52]=0.2,s[82,53]=-0.1,s[82,54]=-0.2,s[82,55]=0.0,s[82,56]=0.0,s[82,57]=-0.8,s[82,58]=0.1,s[82,59]=1.0,s[82,60]=-0.7
s[83,1]=-0.7,s[83,2]=0.5,s[83,3]=-0.8,s[83,4]=-0.1,s[83,5]=0.4,s[83,6]=1.2,s[83,7]=0.4,s[83,8]=0.1,s[83,9]=0.1,s[83,10]=0.2,s[83,11]=0.6,s[83,12]=0.8,s[83,13]=0.2,s[83,14]=-0.8,s[83,15]=-0.3
s[83,16]=0.2,s[83,17]=0.2,s[83,18]=0.7,s[83,19]=-0.1,s[83,20]=-0.4,s[83,21]=-0.7,s[83,22]=-1.0,s[83,23]=0.5,s[83,24]=1.2,s[83,25]=-0.3,s[83,26]=-1.2,s[83,27]=0.5,s[83,28]=-0.6,s[83,29]=1.2,s[83,30]=0.7
s[83,31]=0.5,s[83,32]=-0.8,s[83,33]=1.1,s[83,34]=-0.4,s[83,35]=-0.6,s[83,36]=-1.1,s[83,37]=0.1,s[83,38]=1.2,s[83,39]=0.1,s[83,40]=-0.7,s[83,41]=-0.4,s[83,42]=-0.9,s[83,43]=1.0,s[83,44]=0.7,s[83,45]=-1.2
s[83,46]=1.0,s[83,47]=0.1,s[83,48]=-0.4,s[83,49]=1.1,s[83,50]=0.0,s[83,51]=-0.4,s[83,52]=0.7,s[83,53]=-0.1,s[83,54]=1.0,s[83,55]=-1.2,s[83,56]=-0.1,s[83,57]=0.2,s[83,58]=-0.5,s[83,59]=-0.3,s[83,60]=-1.1
s[84,1]=0.9,s[84,2]=1.1,s[84,3]=-0.1,s[84,4]=-0.6,s[84,5]=0.8,s[84,6]=0.1,s[84,7]=0.1,s[84,8]=0.1,s[84,9]=-0.6,s[84,10]=0.1,s[84,11]=1.1,s[84,12]=0.2,s[84,13]=-0.5,s[84,14]=-0.3,s[84,15]=-0.1
s[84,16]=-0.2,s[84,17]=1.0,s[84,18]=-0.5,s[84,19]=1.1,s[84,20]=0.1,s[84,21]=-0.9,s[84,22]=-0.5,s[84,23]=0.7,s[84,24]=-0.4,s[84,25]=-1.0,s[84,26]=0.3,s[84,27]=-0.8,s[84,28]=0.6,s[84,29]=-0.4,s[84,30]=0.4
s[84,31]=0.5,s[84,32]=0.1,s[84,33]=0.5,s[84,34]=-0.4,s[84,35]=1.2,s[84,36]=-0.4,s[84,37]=1.0,s[84,38]=-1.1,s[84,39]=0.7,s[84,40]=-0.5,s[84,41]=0.6,s[84,42]=1.1,s[84,43]=0.6,s[84,44]=0.2,s[84,45]=-0.1
s[84,46]=-0.7,s[84,47]=0.1,s[84,48]=0.2,s[84,49]=-0.4,s[84,50]=1.2,s[84,51]=-0.1,s[84,52]=-0.8,s[84,53]=0.3,s[84,54]=0.0,s[84,55]=0.1,s[84,56]=-0.3,s[84,57]=0.2,s[84,58]=1.1,s[84,59]=-0.6,s[84,60]=-1.2
s[85,1]=0.7,s[85,2]=0.2,s[85,3]=0.2,s[85,4]=-0.2,s[85,5]=0.8,s[85,6]=-1.0,s[85,7]=-0.5,s[85,8]=0.2,s[85,9]=-1.2,s[85,10]=0.8,s[85,11]=0.4,s[85,12]=1.0,s[85,13]=1.2,s[85,14]=-0.4,s[85,15]=-1.1
s[85,16]=0.7,s[85,17]=0.2,s[85,18]=-0.3,s[85,19]=0.9,s[85,20]=1.0,s[85,21]=-1.2,s[85,22]=0.0,s[85,23]=-1.2,s[85,24]=0.2,s[85,25]=-0.8,s[85,26]=-0.6,s[85,27]=-1.1,s[85,28]=0.5,s[85,29]=-0.8,s[85,30]=0.0
s[85,31]=0.5,s[85,32]=-0.6,s[85,33]=-0.3,s[85,34]=0.2,s[85,35]=-0.7,s[85,36]=-0.2,s[85,37]=-0.8,s[85,38]=1.0,s[85,39]=-1.1,s[85,40]=1.0,s[85,41]=-0.1,s[85,42]=-0.2,s[85,43]=-0.6,s[85,44]=-1.1,s[85,45]=-0.5
s[85,46]=0.4,s[85,47]=-1.2,s[85,48]=-0.2,s[85,49]=-1.1,s[85,50]=-1.2,s[85,51]=0.9,s[85,52]=0.0,s[85,53]=0.4,s[85,54]=-0.3,s[85,55]=-0.8,s[85,56]=0.9,s[85,57]=-1.0,s[85,58]=-0.2,s[85,59]=0.2,s[85,60]=0.2
s[86,1]=-1.0,s[86,2]=0.1,s[86,3]=-0.9,s[86,4]=0.0,s[86,5]=-0.6,s[86,6]=0.5,s[86,7]=-1.2,s[86,8]=1.1,s[86,9]=-0.3,s[86,10]=0.8,s[86,11]=-1.1,s[86,12]=0.4,s[86,13]=0.0,s[86,14]=0.7,s[86,15]=0.6
s[86,16]=0.1,s[86,17]=0.4,s[86,18]=0.7,s[86,19]=1.1,s[86,20]=0.9,s[86,21]=0.2,s[86,22]=0.5,s[86,23]=1.1,s[86,24]=0.4,s[86,25]=-1.1,s[86,26]=0.8,s[86,27]=1.0,s[86,28]=0.9,s[86,29]=-0.8,s[86,30]=0.2
s[86,31]=-1.2,s[86,32]=0.5,s[86,33]=0.5,s[86,34]=1.2,s[86,35]=0.0,s[86,36]=-1.0,s[86,37]=-0.9,s[86,38]=-0.5,s[86,39]=-1.0,s[86,40]=-0.8,s[86,41]=-0.5,s[86,42]=1.0,s[86,43]=-0.2,s[86,44]=-1.2,s[86,45]=-0.5
s[86,46]=-0.8,s[86,47]=-0.7,s[86,48]=0.6,s[86,49]=-0.1,s[86,50]=-0.7,s[86,51]=0.9,s[86,52]=1.2,s[86,53]=-0.7,s[86,54]=-0.8,s[86,55]=-1.0,s[86,56]=-0.8,s[86,57]=0.0,s[86,58]=-1.2,s[86,59]=0.4,s[86,60]=-0.3
s[87,1]=-0.2,s[87,2]=1.2,s[87,3]=0.1,s[87,4]=-0.6,s[87,5]=-0.2,s[87,6]=0.6,s[87,7]=-1.2,s[87,8]=-0.1,s[87,9]=0.5,s[87,10]=0.9,s[87,11]=-1.2,s[87,12]=-0.6,s[87,13]=-0.3,s[87,14]=0.3,s[87,15]=-0.6
s[87,16]=0.7,s[87,17]=-1.1,s[87,18]=-0.6,s[87,19]=0.0,s[87,20]=0.6,s[87,21]=-0.9,s[87,22]=0.4,s[87,23]=-0.9,s[87,24]=0.9,s[87,25]=-0.9,s[87,26]=-1.2,s[87,27]=0.0,s[87,28]=0.4,s[87,29]=0.5,s[87,30]=-0.8
s[87,31]=-0.5,s[87,32]=0.2,s[87,33]=-0.6,s[87,34]=-0.6,s[87,35]=-0.1,s[87,36]=0.1,s[87,37]=0.9,s[87,38]=1.2,s[87,39]=0.5,s[87,40]=-0.8,s[87,41]=0.3,s[87,42]=0.5,s[87,43]=0.5,s[87,44]=-0.5,s[87,45]=1.2
s[87,46]=0.3,s[87,47]=0.7,s[87,48]=0.6,s[87,49]=0.3,s[87,50]=-0.5,s[87,51]=0.9,s[87,52]=-0.1,s[87,53]=0.5,s[87,54]=0.2,s[87,55]=-1.2,s[87,56]=-0.5,s[87,57]=-0.6,s[87,58]=-0.6,s[87,59]=0.7,s[87,60]=0.0
s[88,1]=0.2,s[88,2]=0.7,s[88,3]=0.0,s[88,4]=-1.2,s[88,5]=-0.6,s[88,6]=0.0,s[88,7]=-0.7,s[88,8]=1.2,s[88,9]=0.7,s[88,10]=0.4,s[88,11]=0.4,s[88,12]=0.6,s[88,13]=-0.2,s[88,14]=0.6,s[88,15]=-1.1
s[88,16]=0.3,s[88,17]=-0.9,s[88,18]=-0.6,s[88,19]=0.6,s[88,20]=0.5,s[88,21]=-0.5,s[88,22]=-0.7,s[88,23]=0.8,s[88,24]=-0.1,s[88,25]=-1.1,s[88,26]=-0.3,s[88,27]=0.6,s[88,28]=0.8,s[88,29]=-0.8,s[88,30]=-0.2
s[88,31]=-0.8,s[88,32]=0.9,s[88,33]=0.6,s[88,34]=-1.1,s[88,35]=0.4,s[88,36]=0.6,s[88,37]=-1.0,s[88,38]=1.1,s[88,39]=0.1,s[88,40]=0.7,s[88,41]=-0.6,s[88,42]=1.0,s[88,43]=-0.7,s[88,44]=1.1,s[88,45]=0.3
s[88,46]=0.5,s[88,47]=0.8,s[88,48]=0.8,s[88,49]=0.1,s[88,50]=1.2,s[88,51]=-1.0,s[88,52]=0.8,s[88,53]=-0.2,s[88,54]=-0.8,s[88,55]=1.1,s[88,56]=1.1,s[88,57]=-0.9,s[88,58]=0.1,s[88,59]=-1.0,s[88,60]=-0.9
s[89,1]=-0.8,s[89,2]=-1.0,s[89,3]=1.2,s[89,4]=0.6,s[89,5]=-0.5,s[89,6]=-0.3,s[89,7]=-0.2,s[89,8]=-1.0,s[89,9]=-0.7,s[89,10]=-0.2,s[89,11]=-0.6,s[89,12]=-0.4,s[89,13]=-0.3,s[89,14]=-1.0,s[89,15]=0.8
s[89,16]=0.5,s[89,17]=-0.2,s[89,18]=-0.4,s[89,19]=-0.6,s[89,20]=1.2,s[89,21]=-0.9,s[89,22]=-1.1,s[89,23]=0.7,s[89,24]=-0.3,s[89,25]=-0.4,s[89,26]=-0.7,s[89,27]=1.0,s[89,28]=0.2,s[89,29]=-0.5,s[89,30]=-0.6
s[89,31]=0.0,s[89,32]=0.6,s[89,33]=1.1,s[89,34]=0.0,s[89,35]=0.1,s[89,36]=0.5,s[89,37]=0.5,s[89,38]=0.9,s[89,39]=-0.9,s[89,40]=-0.1,s[89,41]=-0.5,s[89,42]=-0.6,s[89,43]=0.1,s[89,44]=-0.3,s[89,45]=-0.1
s[89,46]=-0.3,s[89,47]=-1.1,s[89,48]=-0.3,s[89,49]=0.4,s[89,50]=0.9,s[89,51]=-0.5,s[89,52]=-0.1,s[89,53]=-0.1,s[89,54]=0.2,s[89,55]=1.1,s[89,56]=-1.2,s[89,57]=0.4,s[89,58]=-0.8,s[89,59]=-0.3,s[89,60]=-1.2
s[90,1]=0.6,s[90,2]=-1.2,s[90,3]=-0.6,s[90,4]=-0.8,s[90,5]=-0.1,s[90,6]=-1.0,s[90,7]=0.1,s[90,8]=-0.6,s[90,9]=0.8,s[90,10]=0.9,s[90,11]=-0.4,s[90,12]=0.2,s[90,13]=0.3,s[90,14]=0.0,s[90,15]=0.0
s[90,16]=1.2,s[90,17]=0.1,s[90,18]=0.1,s[90,19]=-0.6,s[90,20]=0.2,s[90,21]=0.9,s[90,22]=-0.3,s[90,23]=0.5,s[90,24]=0.0,s[90,25]=-0.3,s[90,26]=-0.4,s[90,27]=-1.0,s[90,28]=-0.8,s[90,29]=-0.6,s[90,30]=0.0
s[90,31]=0.6,s[90,32]=-0.5,s[90,33]=-0.3,s[90,34]=-0.6,s[90,35]=0.4,s[90,36]=-0.9,s[90,37]=1.1,s[90,38]=0.6,s[90,39]=-0.5,s[90,40]=-1.1,s[90,41]=0.4,s[90,42]=-1.1,s[90,43]=1.1,s[90,44]=-1.2,s[90,45]=0.5
s[90,46]=1.0,s[90,47]=0.6,s[90,48]=1.1,s[90,49]=0.2,s[90,50]=0.4,s[90,51]=0.7,s[90,52]=0.0,s[90,53]=0.0,s[90,54]=0.0,s[90,55]=-1.2,s[90,56]=-0.4,s[90,57]=-0.5,s[90,58]=1.2,s[90,59]=0.5,s[90,60]=-0.4
s[91,1]=-0.5,s[91,2]=0.4,s[91,3]=0.6,s[91,4]=0.2,s[91,5]=0.8,s[91,6]=-0.6,s[91,7]=0.1,s[91,8]=1.0,s[91,9]=-1.0,s[91,10]=0.4,s[91,11]=-0.6,s[91,12]=0.4,s[91,13]=1.0,s[91,14]=-0.7,s[91,15]=-0.5,s[91,16]=1.0,s[91,17]=-0.5,s[91,18]=0.7,s[91,19]=-0.2,s[91,20]=0.4,s[91,21]=0.0,s[91,22]=-1.1,s[91,23]=-1.0,s[91,24]=0.6,s[91,25]=-0.6,s[91,26]=-0.6,s[91,27]=0.2,s[91,28]=0.8,s[91,29]=0.7,s[91,30]=-1.1
s[91,31]=0.8,s[91,32]=0.7,s[91,33]=0.2,s[91,34]=-1.1,s[91,35]=0.1,s[91,36]=0.9,s[91,37]=0.4,s[91,38]=0.5,s[91,39]=-0.1,s[91,40]=0.0,s[91,41]=-1.1,s[91,42]=-0.4,s[91,43]=0.6,s[91,44]=0.9,s[91,45]=1.0,s[91,46]=-0.1,s[91,47]=-0.9,s[91,48]=0.1,s[91,49]=0.6,s[91,50]=-0.8,s[91,51]=-0.9,s[91,52]=0.0,s[91,53]=-0.1,s[91,54]=0.6,s[91,55]=-0.5,s[91,56]=-0.7,s[91,57]=-0.9,s[91,58]=-1.0,s[91,59]=0.2,s[91,60]=-1.1
s[92,1]=0.7,s[92,2]=-0.1,s[92,3]=0.5,s[92,4]=-0.7,s[92,5]=1.1,s[92,6]=-1.2,s[92,7]=-1.0,s[92,8]=-1.1,s[92,9]=-1.2,s[92,10]=0.1,s[92,11]=-0.4,s[92,12]=1.0,s[92,13]=0.0,s[92,14]=-0.1,s[92,15]=-0.4,s[92,16]=-0.1,s[92,17]=0.8,s[92,18]=-0.2,s[92,19]=-0.4,s[92,20]=0.7,s[92,21]=0.8,s[92,22]=0.3,s[92,23]=1.2,s[92,24]=-0.7,s[92,25]=-0.2,s[92,26]=-0.5,s[92,27]=-1.1,s[92,28]=-0.5,s[92,29]=0.7,s[92,30]=0.7
s[92,31]=-1.1,s[92,32]=0.7,s[92,33]=0.5,s[92,34]=-0.7,s[92,35]=-0.2,s[92,36]=0.1,s[92,37]=0.8,s[92,38]=-1.1,s[92,39]=-0.3,s[92,40]=0.0,s[92,41]=-0.3,s[92,42]=-1.0,s[92,43]=0.3,s[92,44]=-1.0,s[92,45]=-0.4,s[92,46]=0.6,s[92,47]=1.1,s[92,48]=-0.3,s[92,49]=-0.3,s[92,50]=-1.2,s[92,51]=0.9,s[92,52]=0.5,s[92,53]=-1.1,s[92,54]=-0.1,s[92,55]=0.1,s[92,56]=-1.2,s[92,57]=0.1,s[92,58]=-1.0,s[92,59]=0.2,s[92,60]=-0.9
s[93,1]=0.0,s[93,2]=0.7,s[93,3]=-0.3,s[93,4]=-0.8,s[93,5]=-1.2,s[93,6]=-0.5,s[93,7]=-0.2,s[93,8]=-1.1,s[93,9]=-0.4,s[93,10]=-0.3,s[93,11]=0.6,s[93,12]=-1.2,s[93,13]=0.0,s[93,14]=0.1,s[93,15]=1.2,s[93,16]=0.2,s[93,17]=0.8,s[93,18]=1.2,s[93,19]=-0.6,s[93,20]=0.6,s[93,21]=1.1,s[93,22]=1.0,s[93,23]=0.2,s[93,24]=0.3,s[93,25]=-1.0,s[93,26]=0.9,s[93,27]=-0.4,s[93,28]=-1.1,s[93,29]=1.0,s[93,30]=0.1
s[93,31]=0.3,s[93,32]=0.4,s[93,33]=-0.8,s[93,34]=-0.3,s[93,35]=0.1,s[93,36]=0.9,s[93,37]=-0.9,s[93,38]=-0.6,s[93,39]=-0.6,s[93,40]=0.4,s[93,41]=-0.7,s[93,42]=-0.3,s[93,43]=0.3,s[93,44]=-0.7,s[93,45]=0.3,s[93,46]=-1.2,s[93,47]=-0.6,s[93,48]=0.4,s[93,49]=0.1,s[93,50]=-0.1,s[93,51]=-1.1,s[93,52]=0.1,s[93,53]=-0.7,s[93,54]=0.2,s[93,55]=-1.1,s[93,56]=0.6,s[93,57]=-0.1,s[93,58]=0.9,s[93,59]=0.5,s[93,60]=-0.5
s[94,1]=-1.0,s[94,2]=-1.0,s[94,3]=-1.2,s[94,4]=-1.0,s[94,5]=0.5,s[94,6]=-0.9,s[94,7]=0.2,s[94,8]=1.0,s[94,9]=0.4,s[94,10]=0.7,s[94,11]=-0.2,s[94,12]=0.3,s[94,13]=1.2,s[94,14]=0.4,s[94,15]=1.0,s[94,16]=0.1,s[94,17]=0.1,s[94,18]=-0.8,s[94,19]=1.0,s[94,20]=0.3,s[94,21]=-0.1,s[94,22]=-0.3,s[94,23]=0.5,s[94,24]=0.5,s[94,25]=0.5,s[94,26]=0.1,s[94,27]=-0.2,s[94,28]=-0.8,s[94,29]=-0.9,s[94,30]=1.0
s[94,31]=0.0,s[94,32]=-0.8,s[94,33]=-0.6,s[94,34]=-1.0,s[94,35]=-0.2,s[94,36]=0.3,s[94,37]=0.0,s[94,38]=0.6,s[94,39]=-0.1,s[94,40]=0.4,s[94,41]=-0.4,s[94,42]=0.1,s[94,43]=-1.2,s[94,44]=1.0,s[94,45]=-0.4,s[94,46]=0.1,s[94,47]=-0.4,s[94,48]=-1.0,s[94,49]=-0.1,s[94,50]=0.8,s[94,51]=-1.1,s[94,52]=-0.4,s[94,53]=-0.5,s[94,54]=0.1,s[94,55]=0.8,s[94,56]=0.6,s[94,57]=0.9,s[94,58]=0.1,s[94,59]=0.2,s[94,60]=-0.4
s[95,1]=0.3,s[95,2]=-0.5,s[95,3]=0.8,s[95,4]=-1.1,s[95,5]=-0.4,s[95,6]=-0.6,s[95,7]=0.4,s[95,8]=-0.1,s[95,9]=-0.5,s[95,10]=-0.5,s[95,11]=1.1,s[95,12]=-1.1,s[95,13]=-0.9,s[95,14]=-0.3,s[95,15]=-0.9,s[95,16]=-0.7,s[95,17]=0.6,s[95,18]=-0.9,s[95,19]=-0.4,s[95,20]=-0.3,s[95,21]=-0.3,s[95,22]=0.5,s[95,23]=0.8,s[95,24]=0.8,s[95,25]=1.0,s[95,26]=-0.7,s[95,27]=-1.1,s[95,28]=0.0,s[95,29]=-1.2,s[95,30]=0.2
s[95,31]=0.2,s[95,32]=0.9,s[95,33]=-1.0,s[95,34]=-1.0,s[95,35]=-1.1,s[95,36]=0.4,s[95,37]=0.6,s[95,38]=1.1,s[95,39]=0.9,s[95,40]=-0.1,s[95,41]=0.1,s[95,42]=0.2,s[95,43]=0.4,s[95,44]=0.5,s[95,45]=0.0,s[95,46]=-1.2,s[95,47]=0.2,s[95,48]=0.7,s[95,49]=-0.3,s[95,50]=-0.8,s[95,51]=-0.1,s[95,52]=0.3,s[95,53]=0.3,s[95,54]=-0.9,s[95,55]=-0.4,s[95,56]=0.5,s[95,57]=0.3,s[95,58]=-0.2,s[95,59]=0.7,s[95,60]=-0.2
s[96,1]=0.1,s[96,2]=0.7,s[96,3]=-0.9,s[96,4]=1.0,s[96,5]=0.1,s[96,6]=1.2,s[96,7]=-0.4,s[96,8]=-1.2,s[96,9]=0.7,s[96,10]=1.2,s[96,11]=1.1,s[96,12]=-0.9,s[96,13]=0.7,s[96,14]=0.4,s[96,15]=-1.1,s[96,16]=0.9,s[96,17]=0.9,s[96,18]=-1.1,s[96,19]=-0.6,s[96,20]=0.6,s[96,21]=-1.2,s[96,22]=-0.8,s[96,23]=-1.2,s[96,24]=0.2,s[96,25]=1.2,s[96,26]=1.1,s[96,27]=-0.8,s[96,28]=-0.7,s[96,29]=0.2,s[96,30]=-0.2
s[96,31]=0.6,s[96,32]=-0.7,s[96,33]=1.1,s[96,34]=0.1,s[96,35]=0.7,s[96,36]=0.7,s[96,37]=0.5,s[96,38]=0.4,s[96,39]=0.1,s[96,40]=0.3,s[96,41]=1.0,s[96,42]=0.0,s[96,43]=-0.9,s[96,44]=-0.3,s[96,45]=0.4,s[96,46]=0.7,s[96,47]=-0.2,s[96,48]=0.7,s[96,49]=-0.6,s[96,50]=-0.2,s[96,51]=0.9,s[96,52]=1.2,s[96,53]=-0.9,s[96,54]=-0.4,s[96,55]=-1.0,s[96,56]=0.0,s[96,57]=0.4,s[96,58]=-0.9,s[96,59]=0.6,s[96,60]=-0.5
s[97,1]=-0.2,s[97,2]=-0.4,s[97,3]=-0.2,s[97,4]=-0.6,s[97,5]=0.7,s[97,6]=-0.8,s[97,7]=-1.0,s[97,8]=-0.7,s[97,9]=-1.1,s[97,10]=-0.1,s[97,11]=-0.7,s[97,12]=1.2,s[97,13]=1.0,s[97,14]=-0.3,s[97,15]=0.6,s[97,16]=-0.4,s[97,17]=-0.7,s[97,18]=1.0,s[97,19]=-0.1,s[97,20]=0.9,s[97,21]=1.1,s[97,22]=0.7,s[97,23]=-0.8,s[97,24]=0.8,s[97,25]=0.9,s[97,26]=-0.3,s[97,27]=-0.6,s[97,28]=0.5,s[97,29]=0.8,s[97,30]=-1.2
s[97,31]=-0.1,s[97,32]=-0.3,s[97,33]=0.3,s[97,34]=-1.1,s[97,35]=-0.1,s[97,36]=-0.9,s[97,37]=0.5,s[97,38]=0.9,s[97,39]=-0.8,s[97,40]=0.5,s[97,41]=-0.4,s[97,42]=-0.2,s[97,43]=0.2,s[97,44]=-0.3,s[97,45]=-0.8,s[97,46]=-0.4,s[97,47]=1.2,s[97,48]=-0.3,s[97,49]=0.4,s[97,50]=-0.2,s[97,51]=0.1,s[97,52]=-0.7,s[97,53]=-0.8,s[97,54]=0.3,s[97,55]=-0.5,s[97,56]=0.5,s[97,57]=-0.4,s[97,58]=0.7,s[97,59]=-0.8,s[97,60]=-0.8
s[98,1]=-0.5,s[98,2]=-0.3,s[98,3]=-0.9,s[98,4]=-1.1,s[98,5]=-0.3,s[98,6]=0.9,s[98,7]=1.0,s[98,8]=-0.5,s[98,9]=0.2,s[98,10]=-1.2,s[98,11]=0.0,s[98,12]=-0.8,s[98,13]=-0.3,s[98,14]=0.8,s[98,15]=1.1,s[98,16]=-0.4,s[98,17]=-0.9,s[98,18]=0.0,s[98,19]=0.9,s[98,20]=0.1,s[98,21]=0.6,s[98,22]=-0.5,s[98,23]=0.6,s[98,24]=-1.0,s[98,25]=-1.1,s[98,26]=-1.1,s[98,27]=-0.5,s[98,28]=-0.6,s[98,29]=0.9,s[98,30]=0.3
s[98,31]=-1.2,s[98,32]=-0.4,s[98,33]=-0.3,s[98,34]=-0.6,s[98,35]=-1.1,s[98,36]=0.1,s[98,37]=-0.1,s[98,38]=0.8,s[98,39]=-0.7,s[98,40]=1.0,s[98,41]=-0.1,s[98,42]=0.6,s[98,43]=-1.2,s[98,44]=-0.6,s[98,45]=0.1,s[98,46]=-1.0,s[98,47]=0.7,s[98,48]=-0.6,s[98,49]=0.4,s[98,50]=-1.2,s[98,51]=-0.7,s[98,52]=-0.6,s[98,53]=-0.9,s[98,54]=0.4,s[98,55]=-0.3,s[98,56]=-0.5,s[98,57]=-0.8,s[98,58]=0.1,s[98,59]=0.8,s[98,60]=-1.2
s[99,1]=0.3,s[99,2]=1.0,s[99,3]=0.3,s[99,4]=0.0,s[99,5]=-0.7,s[99,6]=-0.9,s[99,7]=-0.8,s[99,8]=0.5,s[99,9]=0.8,s[99,10]=-0.8,s[99,11]=-0.5,s[99,12]=0.6,s[99,13]=-0.3,s[99,14]=-0.5,s[99,15]=0.4,s[99,16]=1.2,s[99,17]=-0.1,s[99,18]=0.4,s[99,19]=0.6,s[99,20]=0.5,s[99,21]=0.6,s[99,22]=0.2,s[99,23]=-0.2,s[99,24]=0.7,s[99,25]=1.0,s[99,26]=0.9,s[99,27]=0.4,s[99,28]=0.1,s[99,29]=-0.1,s[99,30]=1.0
s[99,31]=-0.2,s[99,32]=-1.0,s[99,33]=0.5,s[99,34]=-0.8,s[99,35]=-0.8,s[99,36]=0.1,s[99,37]=0.5,s[99,38]=-0.2,s[99,39]=1.2,s[99,40]=-1.0,s[99,41]=0.0,s[99,42]=-0.4,s[99,43]=-0.2,s[99,44]=-0.6,s[99,45]=1.2,s[99,46]=0.3,s[99,47]=-0.3,s[99,48]=-1.1,s[99,49]=-0.2,s[99,50]=-0.3,s[99,51]=1.1,s[99,52]=-1.0,s[99,53]=0.0,s[99,54]=0.9,s[99,55]=0.6,s[99,56]=-1.2,s[99,57]=-0.6,s[99,58]=-0.1,s[99,59]=-0.2,s[99,60]=0.3
s[100,1]=-1.1,s[100,2]=0.5,s[100,3]=0.5,s[100,4]=0.0,s[100,5]=0.9,s[100,6]=-0.8,s[100,7]=0.3,s[100,8]=-0.9,s[100,9]=0.9,s[100,10]=-0.7,s[100,11]=-1.2,s[100,12]=0.5,s[100,13]=-1.2,s[100,14]=-0.1,s[100,15]=0.0,s[100,16]=1.1,s[100,17]=-0.9,s[100,18]=-1.1,s[100,19]=-0.9,s[100,20]=0.0,s[100,21]=-0.3,s[100,22]=-0.1,s[100,23]=1.2,s[100,24]=-1.2,s[100,25]=0.8,s[100,26]=0.5,s[100,27]=0.4,s[100,28]=-0.5,s[100,29]=0.6,s[100,30]=0.3
s[100,31]=-0.3,s[100,32]=-0.3,s[100,33]=-0.5,s[100,34]=-0.9,s[100,35]=-0.9,s[100,36]=0.7,s[100,37]=0.3,s[100,38]=-0.3,s[100,39]=-0.2,s[100,40]=-1.0,s[100,41]=-0.7,s[100,42]=0.1,s[100,43]=0.2,s[100,44]=0.4,s[100,45]=0.2,s[100,46]=1.1,s[100,47]=-1.2,s[100,48]=0.3,s[100,49]=-0.3,s[100,50]=0.2,s[100,51]=0.9,s[100,52]=0.7,s[100,53]=-0.6,s[100,54]=0.9,s[100,55]=-1.2,s[100,56]=1.2,s[100,57]=0.6,s[100,58]=0.3,s[100,59]=-0.5,s[100,60]=-0.1
s[101,1]=0.8,s[101,2]=-0.3,s[101,3]=-0.4,s[101,4]=-1.1,s[101,5]=-0.2,s[101,6]=0.4,s[101,7]=0.5,s[101,8]=-0.1,s[101,9]=-0.1,s[101,10]=0.4,s[101,11]=0.6,s[101,12]=0.1,s[101,13]=-1.0,s[101,14]=0.2,s[101,15]=0.8,s[101,16]=0.8,s[101,17]=1.2,s[101,18]=-1.0,s[101,19]=0.1,s[101,20]=0.0,s[101,21]=-0.1,s[101,22]=-0.2,s[101,23]=-1.1,s[101,24]=-0.2,s[101,25]=-0.9,s[101,26]=0.0,s[101,27]=-0.7,s[101,28]=-1.1,s[101,29]=0.8,s[101,30]=0.8
s[101,31]=-0.6,s[101,32]=-1.1,s[101,33]=0.0,s[101,34]=-1.2,s[101,35]=1.2,s[101,36]=-1.2,s[101,37]=-1.0,s[101,38]=1.0,s[101,39]=-0.7,s[101,40]=0.2,s[101,41]=-0.1,s[101,42]=-0.1,s[101,43]=-0.2,s[101,44]=-0.5,s[101,45]=0.0,s[101,46]=0.9,s[101,47]=0.1,s[101,48]=1.0,s[101,49]=0.0,s[101,50]=-0.4,s[101,51]=-0.3,s[101,52]=1.2,s[101,53]=-0.3,s[101,54]=1.0,s[101,55]=1.2,s[101,56]=-0.4,s[101,57]=0.0,s[101,58]=-0.5,s[101,59]=1.1,s[101,60]=-0.6
s[102,1]=0.9,s[102,2]=-0.1,s[102,3]=-1.0,s[102,4]=-0.3,s[102,5]=-0.3,s[102,6]=-0.4,s[102,7]=0.4,s[102,8]=-0.2,s[102,9]=0.8,s[102,10]=-0.1,s[102,11]=-0.7,s[102,12]=0.3,s[102,13]=1.2,s[102,14]=0.3,s[102,15]=0.8,s[102,16]=-0.7,s[102,17]=-0.8,s[102,18]=0.3,s[102,19]=0.7,s[102,20]=-1.2,s[102,21]=-0.7,s[102,22]=-0.9,s[102,23]=-0.7,s[102,24]=-1.0,s[102,25]=0.8,s[102,26]=0.2,s[102,27]=0.4,s[102,28]=-0.9,s[102,29]=0.8,s[102,30]=0.7
s[102,31]=0.1,s[102,32]=0.2,s[102,33]=0.0,s[102,34]=-1.1,s[102,35]=-0.1,s[102,36]=1.1,s[102,37]=-0.6,s[102,38]=0.0,s[102,39]=0.9,s[102,40]=0.1,s[102,41]=-1.0,s[102,42]=1.0,s[102,43]=0.4,s[102,44]=-1.1,s[102,45]=-0.5,s[102,46]=0.7,s[102,47]=-0.9,s[102,48]=0.4,s[102,49]=0.3,s[102,50]=0.0,s[102,51]=0.1,s[102,52]=0.5,s[102,53]=-1.2,s[102,54]=-0.4,s[102,55]=-1.2,s[102,56]=1.2,s[102,57]=-0.8,s[102,58]=-1.2,s[102,59]=-1.2,s[102,60]=0.0
s[103,1]=1.1,s[103,2]=-1.0,s[103,3]=-1.1,s[103,4]=1.1,s[103,5]=0.6,s[103,6]=0.1,s[103,7]=-0.9,s[103,8]=-0.6,s[103,9]=0.4,s[103,10]=0.1,s[103,11]=-0.4,s[103,12]=0.2,s[103,13]=0.0,s[103,14]=0.6,s[103,15]=0.1,s[103,16]=0.7,s[103,17]=-0.7,s[103,18]=0.5,s[103,19]=-1.0,s[103,20]=-0.7,s[103,21]=0.7,s[103,22]=0.7,s[103,23]=0.0,s[103,24]=-0.6,s[103,25]=0.8,s[103,26]=-0.1,s[103,27]=-1.1,s[103,28]=-0.3,s[103,29]=0.6,s[103,30]=0.5
s[103,31]=1.1,s[103,32]=0.9,s[103,33]=0.7,s[103,34]=-0.2,s[103,35]=-0.8,s[103,36]=0.7,s[103,37]=-0.8,s[103,38]=-0.2,s[103,39]=1.0,s[103,40]=0.4,s[103,41]=-0.7,s[103,42]=0.8,s[103,43]=0.4,s[103,44]=0.7,s[103,45]=0.3,s[103,46]=0.1,s[103,47]=-0.4,s[103,48]=-0.2,s[103,49]=0.9,s[103,50]=-1.2,s[103,51]=-0.6,s[103,52]=-0.8,s[103,53]=-0.5,s[103,54]=0.2,s[103,55]=1.1,s[103,56]=-0.9,s[103,57]=0.1,s[103,58]=-1.0,s[103,59]=0.0,s[103,60]=-0.5
s[104,1]=0.2,s[104,2]=-0.5,s[104,3]=0.0,s[104,4]=-0.7,s[104,5]=0.6,s[104,6]=-0.3,s[104,7]=0.6,s[104,8]=-0.4,s[104,9]=0.5,s[104,10]=-0.6,s[104,11]=-1.0,s[104,12]=-0.1,s[104,13]=-1.1,s[104,14]=-0.4,s[104,15]=-1.2,s[104,16]=0.6,s[104,17]=1.0,s[104,18]=0.3,s[104,19]=0.8,s[104,20]=0.7,s[104,21]=0.3,s[104,22]=-0.3,s[104,23]=-0.3,s[104,24]=-1.2,s[104,25]=0.8,s[104,26]=-1.1,s[104,27]=0.4,s[104,28]=1.2,s[104,29]=0.4,s[104,30]=0.3
s[104,31]=-0.4,s[104,32]=0.0,s[104,33]=0.3,s[104,34]=-0.9,s[104,35]=-1.1,s[104,36]=-0.7,s[104,37]=0.7,s[104,38]=-1.1,s[104,39]=-0.8,s[104,40]=-0.6,s[104,41]=-0.1,s[104,42]=1.0,s[104,43]=0.8,s[104,44]=-0.7,s[104,45]=0.3,s[104,46]=1.1,s[104,47]=-0.9,s[104,48]=0.3,s[104,49]=0.6,s[104,50]=-0.8,s[104,51]=-0.3,s[104,52]=0.4,s[104,53]=0.3,s[104,54]=-0.2,s[104,55]=1.2,s[104,56]=0.1,s[104,57]=0.2,s[104,58]=-0.3,s[104,59]=-0.1,s[104,60]=0.0
s[105,1]=-1.1,s[105,2]=-0.4,s[105,3]=-0.9,s[105,4]=-0.6,s[105,5]=-0.3,s[105,6]=0.7,s[105,7]=0.7,s[105,8]=-0.1,s[105,9]=-1.2,s[105,10]=0.9,s[105,11]=-0.2,s[105,12]=0.8,s[105,13]=-0.9,s[105,14]=0.2,s[105,15]=1.2,s[105,16]=-0.7,s[105,17]=0.7,s[105,18]=0.2,s[105,19]=0.2,s[105,20]=-1.1,s[105,21]=0.3,s[105,22]=1.1,s[105,23]=-0.9,s[105,24]=0.5,s[105,25]=0.1,s[105,26]=-0.8,s[105,27]=0.8,s[105,28]=0.0,s[105,29]=-0.6,s[105,30]=0.1
s[105,31]=-1.0,s[105,32]=0.8,s[105,33]=-0.9,s[105,34]=-1.0,s[105,35]=-0.4,s[105,36]=0.6,s[105,37]=-0.3,s[105,38]=1.2,s[105,39]=0.0,s[105,40]=-0.3,s[105,41]=1.2,s[105,42]=1.2,s[105,43]=0.9,s[105,44]=-0.1,s[105,45]=0.0,s[105,46]=-0.8,s[105,47]=-0.7,s[105,48]=-0.9,s[105,49]=-0.4,s[105,50]=0.5,s[105,51]=-0.4,s[105,52]=-0.1,s[105,53]=-1.1,s[105,54]=1.2,s[105,55]=-0.8,s[105,56]=-1.0,s[105,57]=-0.6,s[105,58]=-1.2,s[105,59]=0.3,s[105,60]=-0.4
s[106,1]=0.0,s[106,2]=0.4,s[106,3]=0.9,s[106,4]=0.1,s[106,5]=0.7,s[106,6]=0.0,s[106,7]=1.1,s[106,8]=-1.1,s[106,9]=-0.8,s[106,10]=-1.2,s[106,11]=0.8,s[106,12]=-1.1,s[106,13]=0.6,s[106,14]=1.0,s[106,15]=0.9,s[106,16]=-0.2,s[106,17]=-0.1,s[106,18]=0.1,s[106,19]=0.9,s[106,20]=1.2,s[106,21]=0.3,s[106,22]=0.4,s[106,23]=-0.2,s[106,24]=-0.2,s[106,25]=1.2,s[106,26]=0.6,s[106,27]=-0.8,s[106,28]=-1.2,s[106,29]=0.1,s[106,30]=-1.1
s[106,31]=0.0,s[106,32]=-0.6,s[106,33]=-1.0,s[106,34]=-0.1,s[106,35]=0.8,s[106,36]=1.1,s[106,37]=0.4,s[106,38]=0.6,s[106,39]=-0.5,s[106,40]=-0.2,s[106,41]=-0.1,s[106,42]=-1.0,s[106,43]=0.4,s[106,44]=0.6,s[106,45]=-0.6,s[106,46]=0.3,s[106,47]=0.1,s[106,48]=0.9,s[106,49]=0.4,s[106,50]=1.2,s[106,51]=-1.0,s[106,52]=-0.8,s[106,53]=-0.3,s[106,54]=-0.1,s[106,55]=0.2,s[106,56]=-0.3,s[106,57]=-0.4,s[106,58]=0.0,s[106,59]=0.9,s[106,60]=0.6
s[107,1]=1.0,s[107,2]=-0.9,s[107,3]=0.8,s[107,4]=0.9,s[107,5]=0.0,s[107,6]=0.1,s[107,7]=0.9,s[107,8]=0.4,s[107,9]=-1.1,s[107,10]=-0.6,s[107,11]=-0.3,s[107,12]=1.1,s[107,13]=0.7,s[107,14]=-0.7,s[107,15]=0.8,s[107,16]=-1.2,s[107,17]=0.4,s[107,18]=-0.1,s[107,19]=-1.0,s[107,20]=0.2,s[107,21]=-0.3,s[107,22]=-1.2,s[107,23]=-1.0,s[107,24]=0.9,s[107,25]=-0.7,s[107,26]=-0.8,s[107,27]=0.7,s[107,28]=1.0,s[107,29]=0.2,s[107,30]=0.7
s[107,31]=0.6,s[107,32]=-0.3,s[107,33]=-0.2,s[107,34]=0.8,s[107,35]=0.1,s[107,36]=-0.6,s[107,37]=-0.2,s[107,38]=-0.4,s[107,39]=0.7,s[107,40]=-1.0,s[107,41]=0.4,s[107,42]=-0.7,s[107,43]=-1.2,s[107,44]=-0.4,s[107,45]=-0.2,s[107,46]=1.0,s[107,47]=-1.0,s[107,48]=-0.5,s[107,49]=-1.2,s[107,50]=0.7,s[107,51]=0.7,s[107,52]=0.1,s[107,53]=-1.2,s[107,54]=1.1,s[107,55]=-0.5,s[107,56]=1.0,s[107,57]=-0.9,s[107,58]=0.3,s[107,59]=-0.3,s[107,60]=-0.8
s[108,1]=-0.8,s[108,2]=1.2,s[108,3]=1.1,s[108,4]=-0.9,s[108,5]=1.1,s[108,6]=0.2,s[108,7]=-0.2,s[108,8]=-0.1,s[108,9]=0.5,s[108,10]=-0.7,s[108,11]=-0.3,s[108,12]=-0.3,s[108,13]=0.4,s[108,14]=0.4,s[108,15]=0.1,s[108,16]=0.1,s[108,17]=-0.1,s[108,18]=-0.2,s[108,19]=1.0,s[108,20]=-0.7,s[108,21]=0.2,s[108,22]=0.5,s[108,23]=0.2,s[108,24]=-0.6,s[108,25]=-1.0,s[108,26]=-1.1,s[108,27]=0.2,s[108,28]=-1.0,s[108,29]=-0.2,s[108,30]=-1.1
s[108,31]=0.4,s[108,32]=1.2,s[108,33]=0.0,s[108,34]=-0.9,s[108,35]=-0.6,s[108,36]=-0.7,s[108,37]=0.4,s[108,38]=1.2,s[108,39]=-0.7,s[108,40]=0.6,s[108,41]=-0.1,s[108,42]=1.0,s[108,43]=-0.5,s[108,44]=0.6,s[108,45]=-0.3,s[108,46]=1.0,s[108,47]=-0.1,s[108,48]=1.2,s[108,49]=-0.8,s[108,50]=-0.5,s[108,51]=-0.1,s[108,52]=-1.0,s[108,53]=0.0,s[108,54]=-1.2,s[108,55]=-0.2,s[108,56]=-1.1,s[108,57]=0.1,s[108,58]=0.6,s[108,59]=0.7,s[108,60]=-0.6
s[109,1]=0.3,s[109,2]=0.7,s[109,3]=-0.9,s[109,4]=-1.0,s[109,5]=-0.2,s[109,6]=0.7,s[109,7]=-0.5,s[109,8]=0.7,s[109,9]=0.8,s[109,10]=0.9,s[109,11]=-0.6,s[109,12]=-1.2,s[109,13]=1.1,s[109,14]=-0.4,s[109,15]=0.9,s[109,16]=1.0,s[109,17]=-1.1,s[109,18]=0.3,s[109,19]=0.6,s[109,20]=0.2,s[109,21]=0.9,s[109,22]=-0.1,s[109,23]=-0.7,s[109,24]=-0.4,s[109,25]=-0.8,s[109,26]=-0.4,s[109,27]=-0.1,s[109,28]=-0.6,s[109,29]=0.1,s[109,30]=1.0
s[109,31]=-0.7,s[109,32]=-1.1,s[109,33]=0.8,s[109,34]=0.0,s[109,35]=-0.7,s[109,36]=-0.2,s[109,37]=-1.2,s[109,38]=1.2,s[109,39]=-1.1,s[109,40]=0.1,s[109,41]=1.2,s[109,42]=-0.5,s[109,43]=0.7,s[109,44]=-1.1,s[109,45]=-0.6,s[109,46]=0.1,s[109,47]=-1.0,s[109,48]=-0.3,s[109,49]=0.7,s[109,50]=0.0,s[109,51]=-0.6,s[109,52]=-0.6,s[109,53]=-1.0,s[109,54]=-1.0,s[109,55]=0.5,s[109,56]=0.3,s[109,57]=-1.0,s[109,58]=-0.9,s[109,59]=-1.1,s[109,60]=-0.6
s[110,1]=-0.3,s[110,2]=-1.2,s[110,3]=0.9,s[110,4]=-1.2,s[110,5]=-0.6,s[110,6]=-0.4,s[110,7]=-1.1,s[110,8]=1.0,s[110,9]=0.9,s[110,10]=-0.6,s[110,11]=-0.5,s[110,12]=0.1,s[110,13]=-0.6,s[110,14]=0.2,s[110,15]=0.0,s[110,16]=0.7,s[110,17]=0.7,s[110,18]=0.4,s[110,19]=0.1,s[110,20]=0.0,s[110,21]=0.8,s[110,22]=1.0,s[110,23]=0.9,s[110,24]=0.0,s[110,25]=0.6,s[110,26]=-0.9,s[110,27]=-0.8,s[110,28]=0.1,s[110,29]=0.6,s[110,30]=-0.8
s[110,31]=1.0,s[110,32]=1.1,s[110,33]=-0.2,s[110,34]=-1.1,s[110,35]=0.6,s[110,36]=0.3,s[110,37]=-1.1,s[110,38]=0.7,s[110,39]=-0.8,s[110,40]=-0.8,s[110,41]=-0.3,s[110,42]=-0.1,s[110,43]=-0.3,s[110,44]=-0.4,s[110,45]=0.6,s[110,46]=0.1,s[110,47]=-0.4,s[110,48]=-1.1,s[110,49]=0.8,s[110,50]=-0.5,s[110,51]=-0.5,s[110,52]=-1.1,s[110,53]=-1.2,s[110,54]=-0.1,s[110,55]=0.4,s[110,56]=1.2,s[110,57]=1.1,s[110,58]=0.8,s[110,59]=0.0,s[110,60]=-1.0
s[111,1]=1.2,s[111,2]=0.8,s[111,3]=0.4,s[111,4]=-1.1,s[111,5]=1.0,s[111,6]=-1.2,s[111,7]=-0.4,s[111,8]=-0.9,s[111,9]=-0.3,s[111,10]=-0.4,s[111,11]=1.1,s[111,12]=1.0,s[111,13]=0.7,s[111,14]=0.9,s[111,15]=-0.7,s[111,16]=-0.5,s[111,17]=-0.6,s[111,18]=0.0,s[111,19]=1.2,s[111,20]=-0.9,s[111,21]=-0.6,s[111,22]=-1.0,s[111,23]=1.1,s[111,24]=1.1,s[111,25]=-0.2,s[111,26]=-0.4,s[111,27]=-0.8,s[111,28]=-0.3,s[111,29]=0.2,s[111,30]=0.9
s[111,31]=-0.9,s[111,32]=-1.0,s[111,33]=-0.2,s[111,34]=-0.8,s[111,35]=-0.7,s[111,36]=-0.6,s[111,37]=0.7,s[111,38]=-0.7,s[111,39]=-1.1,s[111,40]=-0.4,s[111,41]=-1.1,s[111,42]=-1.1,s[111,43]=1.2,s[111,44]=1.0,s[111,45]=0.8,s[111,46]=0.8,s[111,47]=-1.0,s[111,48]=-1.1,s[111,49]=0.9,s[111,50]=-0.4,s[111,51]=-0.9,s[111,52]=0.6,s[111,53]=-0.5,s[111,54]=-0.7,s[111,55]=-0.9,s[111,56]=0.5,s[111,57]=0.4,s[111,58]=1.1,s[111,59]=1.2,s[111,60]=-0.8
s[112,1]=1.0,s[112,2]=0.6,s[112,3]=-0.2,s[112,4]=-1.1,s[112,5]=0.3,s[112,6]=-0.8,s[112,7]=0.1,s[112,8]=-0.7,s[112,9]=0.9,s[112,10]=-0.1,s[112,11]=-1.1,s[112,12]=-1.1,s[112,13]=0.7,s[112,14]=0.4,s[112,15]=-0.2,s[112,16]=0.4,s[112,17]=0.7,s[112,18]=0.9,s[112,19]=-0.4,s[112,20]=0.6,s[112,21]=-0.9,s[112,22]=-0.1,s[112,23]=0.6,s[112,24]=-0.8,s[112,25]=0.6,s[112,26]=-0.7,s[112,27]=-1.2,s[112,28]=-0.6,s[112,29]=-0.2,s[112,30]=-0.7
s[112,31]=-0.1,s[112,32]=-0.3,s[112,33]=0.0,s[112,34]=0.3,s[112,35]=1.1,s[112,36]=1.2,s[112,37]=-0.1,s[112,38]=1.1,s[112,39]=0.4,s[112,40]=-0.3,s[112,41]=-1.0,s[112,42]=-1.2,s[112,43]=-0.6,s[112,44]=1.1,s[112,45]=-0.5,s[112,46]=-1.1,s[112,47]=-1.2,s[112,48]=0.2,s[112,49]=1.1,s[112,50]=-0.8,s[112,51]=-1.1,s[112,52]=0.0,s[112,53]=0.7,s[112,54]=0.5,s[112,55]=1.1,s[112,56]=-0.9,s[112,57]=1.0,s[112,58]=-0.7,s[112,59]=-0.6,s[112,60]=-0.2
s[113,1]=0.1,s[113,2]=-0.3,s[113,3]=-0.2,s[113,4]=-0.2,s[113,5]=0.3,s[113,6]=-0.8,s[113,7]=-0.2,s[113,8]=1.2,s[113,9]=-0.8,s[113,10]=0.9,s[113,11]=-0.9,s[113,12]=0.0,s[113,13]=-0.6,s[113,14]=0.0,s[113,15]=0.7,s[113,16]=-0.4,s[113,17]=0.3,s[113,18]=-0.8,s[113,19]=-0.8,s[113,20]=-0.2,s[113,21]=0.8,s[113,22]=0.6,s[113,23]=0.7,s[113,24]=1.1,s[113,25]=-0.2,s[113,26]=-0.4,s[113,27]=0.0,s[113,28]=-1.0,s[113,29]=0.6,s[113,30]=-0.4
s[113,31]=-0.2,s[113,32]=-0.2,s[113,33]=-0.6,s[113,34]=0.7,s[113,35]=0.3,s[113,36]=-0.2,s[113,37]=-1.2,s[113,38]=-0.7,s[113,39]=1.1,s[113,40]=0.2,s[113,41]=-0.5,s[113,42]=0.2,s[113,43]=0.2,s[113,44]=1.1,s[113,45]=0.4,s[113,46]=0.8,s[113,47]=0.4,s[113,48]=-0.5,s[113,49]=-1.0,s[113,50]=1.2,s[113,51]=1.1,s[113,52]=0.8,s[113,53]=0.6,s[113,54]=0.7,s[113,55]=-0.6,s[113,56]=-0.7,s[113,57]=-0.6,s[113,58]=-0.2,s[113,59]=0.9,s[113,60]=-1.0
s[114,1]=-1.1,s[114,2]=0.2,s[114,3]=1.1,s[114,4]=-0.8,s[114,5]=0.3,s[114,6]=0.8,s[114,7]=-1.1,s[114,8]=0.3,s[114,9]=0.2,s[114,10]=0.8,s[114,11]=-1.1,s[114,12]=0.1,s[114,13]=-0.1,s[114,14]=-0.2,s[114,15]=0.4,s[114,16]=-0.1,s[114,17]=-0.7,s[114,18]=0.6,s[114,19]=-0.7,s[114,20]=0.0,s[114,21]=-0.8,s[114,22]=0.9,s[114,23]=0.7,s[114,24]=0.4,s[114,25]=0.2,s[114,26]=-0.4,s[114,27]=0.5,s[114,28]=1.0,s[114,29]=-0.1,s[114,30]=0.4
s[114,31]=0.5,s[114,32]=-0.8,s[114,33]=-0.4,s[114,34]=-1.2,s[114,35]=-0.5,s[114,36]=0.8,s[114,37]=0.5,s[114,38]=1.1,s[114,39]=-0.9,s[114,40]=-0.5,s[114,41]=1.1,s[114,42]=-1.2,s[114,43]=-0.5,s[114,44]=-0.9,s[114,45]=-1.0,s[114,46]=-0.3,s[114,47]=1.1,s[114,48]=-0.3,s[114,49]=0.9,s[114,50]=0.0,s[114,51]=0.2,s[114,52]=0.6,s[114,53]=0.2,s[114,54]=0.9,s[114,55]=0.4,s[114,56]=-0.1,s[114,57]=1.2,s[114,58]=-0.1,s[114,59]=0.7,s[114,60]=-0.4
s[115,1]=1.2,s[115,2]=-0.5,s[115,3]=0.1,s[115,4]=0.3,s[115,5]=0.3,s[115,6]=0.4,s[115,7]=0.9,s[115,8]=1.1,s[115,9]=0.1,s[115,10]=0.0,s[115,11]=-0.2,s[115,12]=0.0,s[115,13]=-1.1,s[115,14]=-0.5,s[115,15]=0.1,s[115,16]=-0.6,s[115,17]=0.6,s[115,18]=-0.9,s[115,19]=-1.1,s[115,20]=-0.2,s[115,21]=-0.8,s[115,22]=-1.2,s[115,23]=-0.1,s[115,24]=-0.1,s[115,25]=-1.0,s[115,26]=0.5,s[115,27]=0.9,s[115,28]=-0.1,s[115,29]=1.1,s[115,30]=-0.1
s[115,31]=0.2,s[115,32]=1.2,s[115,33]=1.1,s[115,34]=0.1,s[115,35]=1.0,s[115,36]=-0.2,s[115,37]=-0.7,s[115,38]=-1.1,s[115,39]=0.2,s[115,40]=0.0,s[115,41]=-0.3,s[115,42]=0.2,s[115,43]=0.4,s[115,44]=-1.2,s[115,45]=-1.2,s[115,46]=-0.2,s[115,47]=0.5,s[115,48]=-1.1,s[115,49]=0.3,s[115,50]=0.0,s[115,51]=0.3,s[115,52]=0.7,s[115,53]=0.5,s[115,54]=-0.1,s[115,55]=-0.6,s[115,56]=0.0,s[115,57]=0.8,s[115,58]=0.1,s[115,59]=0.4,s[115,60]=-1.0
s[116,1]=-0.9,s[116,2]=-0.7,s[116,3]=-0.8,s[116,4]=0.6,s[116,5]=-1.1,s[116,6]=0.1,s[116,7]=0.9,s[116,8]=0.0,s[116,9]=0.8,s[116,10]=0.6,s[116,11]=0.2,s[116,12]=-1.0,s[116,13]=0.2,s[116,14]=-0.7,s[116,15]=-0.2,s[116,16]=1.0,s[116,17]=-0.6,s[116,18]=1.0,s[116,19]=0.1,s[116,20]=0.0,s[116,21]=-0.3,s[116,22]=1.1,s[116,23]=0.5,s[116,24]=0.5,s[116,25]=0.0,s[116,26]=-0.8,s[116,27]=-1.0,s[116,28]=-1.0,s[116,29]=0.7,s[116,30]=0.8
s[116,31]=0.0,s[116,32]=0.3,s[116,33]=0.0,s[116,34]=0.1,s[116,35]=-0.5,s[116,36]=-0.6,s[116,37]=0.2,s[116,38]=-0.1,s[116,39]=-1.0,s[116,40]=-0.7,s[116,41]=0.6,s[116,42]=0.8,s[116,43]=-0.2,s[116,44]=0.2,s[116,45]=0.3,s[116,46]=-1.1,s[116,47]=0.3,s[116,48]=-0.2,s[116,49]=-0.3,s[116,50]=-1.1,s[116,51]=-1.0,s[116,52]=0.3,s[116,53]=-0.7,s[116,54]=0.9,s[116,55]=1.2,s[116,56]=1.1,s[116,57]=-0.7,s[116,58]=0.0,s[116,59]=-0.7,s[116,60]=-0.3
s[117,1]=0.0,s[117,2]=1.2,s[117,3]=-1.0,s[117,4]=-0.6,s[117,5]=0.0,s[117,6]=0.6,s[117,7]=-0.6,s[117,8]=1.2,s[117,9]=0.3,s[117,10]=-0.4,s[117,11]=-1.0,s[117,12]=-0.7,s[117,13]=1.2,s[117,14]=-1.1,s[117,15]=0.9,s[117,16]=-0.4,s[117,17]=-0.3,s[117,18]=0.8,s[117,19]=-1.0,s[117,20]=-0.8,s[117,21]=-1.2,s[117,22]=0.3,s[117,23]=-0.8,s[117,24]=0.0,s[117,25]=-1.2,s[117,26]=-1.0,s[117,27]=1.2,s[117,28]=0.1,s[117,29]=0.2,s[117,30]=0.6
s[117,31]=-0.6,s[117,32]=-0.7,s[117,33]=0.2,s[117,34]=-0.4,s[117,35]=1.0,s[117,36]=0.4,s[117,37]=0.0,s[117,38]=0.0,s[117,39]=-0.3,s[117,40]=-0.3,s[117,41]=-1.2,s[117,42]=-1.2,s[117,43]=-1.0,s[117,44]=0.9,s[117,45]=0.1,s[117,46]=0.0,s[117,47]=0.7,s[117,48]=-0.9,s[117,49]=-0.7,s[117,50]=0.3,s[117,51]=-0.7,s[117,52]=-0.2,s[117,53]=0.0,s[117,54]=0.2,s[117,55]=1.2,s[117,56]=-0.3,s[117,57]=1.1,s[117,58]=-0.7,s[117,59]=0.5,s[117,60]=-1.2
s[118,1]=-0.7,s[118,2]=-0.5,s[118,3]=1.2,s[118,4]=0.1,s[118,5]=-1.1,s[118,6]=0.5,s[118,7]=-0.6,s[118,8]=-0.3,s[118,9]=-0.1,s[118,10]=-1.0,s[118,11]=-0.2,s[118,12]=0.0,s[118,13]=-0.2,s[118,14]=0.9,s[118,15]=-0.9,s[118,16]=-0.9,s[118,17]=-0.9,s[118,18]=1.1,s[118,19]=1.0,s[118,20]=0.1,s[118,21]=-0.3,s[118,22]=-1.2,s[118,23]=0.7,s[118,24]=1.2,s[118,25]=-0.8,s[118,26]=-0.1,s[118,27]=0.4,s[118,28]=-1.2,s[118,29]=-0.3,s[118,30]=0.9
s[118,31]=-0.4,s[118,32]=-1.2,s[118,33]=0.5,s[118,34]=-0.8,s[118,35]=1.0,s[118,36]=0.7,s[118,37]=0.0,s[118,38]=1.1,s[118,39]=-0.7,s[118,40]=0.1,s[118,41]=0.2,s[118,42]=-0.9,s[118,43]=-0.7,s[118,44]=-0.9,s[118,45]=0.3,s[118,46]=-0.3,s[118,47]=1.2,s[118,48]=0.3,s[118,49]=-1.2,s[118,50]=-0.5,s[118,51]=0.8,s[118,52]=0.3,s[118,53]=0.3,s[118,54]=0.2,s[118,55]=-0.4,s[118,56]=0.9,s[118,57]=-0.3,s[118,58]=0.3,s[118,59]=0.4,s[118,60]=-0.5
s[119,1]=0.7,s[119,2]=-1.0,s[119,3]=-0.5,s[119,4]=-1.1,s[119,5]=-0.7,s[119,6]=-0.4,s[119,7]=0.2,s[119,8]=0.1,s[119,9]=0.7,s[119,10]=-0.1,s[119,11]=-0.1,s[119,12]=1.1,s[119,13]=-0.7,s[119,14]=-0.2,s[119,15]=0.1,s[119,16]=0.6,s[119,17]=-1.2,s[119,18]=-1.1,s[119,19]=0.4,s[119,20]=1.1,s[119,21]=-0.6,s[119,22]=-1.2,s[119,23]=-0.4,s[119,24]=1.1,s[119,25]=1.1,s[119,26]=1.2,s[119,27]=0.5,s[119,28]=-0.4,s[119,29]=0.0,s[119,30]=-1.1
s[119,31]=-0.1,s[119,32]=-1.2,s[119,33]=-1.2,s[119,34]=-0.6,s[119,35]=-1.0,s[119,36]=0.5,s[119,37]=-1.1,s[119,38]=-0.2,s[119,39]=0.2,s[119,40]=-0.2,s[119,41]=-0.7,s[119,42]=-0.7,s[119,43]=0.8,s[119,44]=0.0,s[119,45]=-0.1,s[119,46]=-1.0,s[119,47]=0.6,s[119,48]=-1.1,s[119,49]=-1.1,s[119,50]=-0.5,s[119,51]=0.2,s[119,52]=-1.2,s[119,53]=1.2,s[119,54]=0.6,s[119,55]=-0.1,s[119,56]=-0.3,s[119,57]=0.2,s[119,58]=-0.6,s[119,59]=-0.5,s[119,60]=0.0
s[120,1]=-0.8,s[120,2]=-0.4,s[120,3]=0.3,s[120,4]=-1.0,s[120,5]=-1.0,s[120,6]=-1.2,s[120,7]=0.1,s[120,8]=0.4,s[120,9]=-0.2,s[120,10]=0.6,s[120,11]=0.6,s[120,12]=0.8,s[120,13]=-0.3,s[120,14]=-1.0,s[120,15]=-1.2,s[120,16]=0.1,s[120,17]=1.1,s[120,18]=-0.7,s[120,19]=0.6,s[120,20]=-0.8,s[120,21]=-0.9,s[120,22]=-0.8,s[120,23]=-0.2,s[120,24]=-0.3,s[120,25]=-1.2,s[120,26]=1.0,s[120,27]=-0.8,s[120,28]=-0.6,s[120,29]=1.2,s[120,30]=-1.1
s[120,31]=0.9,s[120,32]=1.1,s[120,33]=-0.1,s[120,34]=-0.5,s[120,35]=0.3,s[120,36]=1.2,s[120,37]=-0.4,s[120,38]=0.5,s[120,39]=0.1,s[120,40]=-0.6,s[120,41]=0.7,s[120,42]=0.6,s[120,43]=0.6,s[120,44]=1.1,s[120,45]=-1.2,s[120,46]=-0.7,s[120,47]=-0.6,s[120,48]=0.2,s[120,49]=1.1,s[120,50]=-0.8,s[120,51]=-1.0,s[120,52]=-1.0,s[120,53]=-0.7,s[120,54]=1.2,s[120,55]=-0.8,s[120,56]=0.5,s[120,57]=-0.9,s[120,58]=0.2,s[120,59]=0.7,s[120,60]=-1.1
s[121,1]=-0.6,s[121,2]=-0.1,s[121,3]=-0.4,s[121,4]=-1.0,s[121,5]=-0.2,s[121,6]=-0.9,s[121,7]=0.4,s[121,8]=-1.0,s[121,9]=0.9,s[121,10]=-0.6,s[121,11]=1.0,s[121,12]=1.2,s[121,13]=1.1,s[121,14]=0.9,s[121,15]=-0.8,s[121,16]=-0.8,s[121,17]=-1.2,s[121,18]=-0.3,s[121,19]=0.1,s[121,20]=0.7,s[121,21]=-0.1,s[121,22]=-0.3,s[121,23]=0.0,s[121,24]=0.8,s[121,25]=-1.2,s[121,26]=0.5,s[121,27]=0.9,s[121,28]=1.2,s[121,29]=-0.2,s[121,30]=-0.8
s[121,31]=0.3,s[121,32]=1.0,s[121,33]=0.4,s[121,34]=1.2,s[121,35]=-0.9,s[121,36]=-0.2,s[121,37]=-0.2,s[121,38]=-0.3,s[121,39]=1.1,s[121,40]=0.2,s[121,41]=0.2,s[121,42]=-0.4,s[121,43]=0.9,s[121,44]=-0.8,s[121,45]=0.8,s[121,46]=-1.1,s[121,47]=0.0,s[121,48]=1.0,s[121,49]=-0.6,s[121,50]=-1.0,s[121,51]=0.9,s[121,52]=-0.3,s[121,53]=0.8,s[121,54]=-0.6,s[121,55]=-0.8,s[121,56]=0.1,s[121,57]=0.5,s[121,58]=0.1,s[121,59]=1.2,s[121,60]=-0.9
s[122,1]=0.7,s[122,2]=0.9,s[122,3]=-1.0,s[122,4]=-1.2,s[122,5]=-0.1,s[122,6]=-1.2,s[122,7]=0.4,s[122,8]=0.8,s[122,9]=-1.1,s[122,10]=0.3,s[122,11]=-1.0,s[122,12]=0.6,s[122,13]=-0.1,s[122,14]=0.8,s[122,15]=0.3,s[122,16]=-1.1,s[122,17]=0.0,s[122,18]=-0.7,s[122,19]=1.1,s[122,20]=1.1,s[122,21]=0.8,s[122,22]=-1.2,s[122,23]=-0.8,s[122,24]=-0.5,s[122,25]=0.0,s[122,26]=-0.8,s[122,27]=-0.1,s[122,28]=0.2,s[122,29]=0.5,s[122,30]=-0.1
s[122,31]=0.5,s[122,32]=1.2,s[122,33]=0.7,s[122,34]=-1.0,s[122,35]=-1.1,s[122,36]=-1.1,s[122,37]=0.0,s[122,38]=-0.4,s[122,39]=-0.5,s[122,40]=0.9,s[122,41]=0.7,s[122,42]=-1.0,s[122,43]=0.1,s[122,44]=-0.6,s[122,45]=0.8,s[122,46]=0.4,s[122,47]=-0.3,s[122,48]=0.0,s[122,49]=-0.2,s[122,50]=-0.6,s[122,51]=-0.8,s[122,52]=-0.8,s[122,53]=-0.3,s[122,54]=-0.3,s[122,55]=0.7,s[122,56]=-1.0,s[122,57]=-1.1,s[122,58]=-0.6,s[122,59]=1.2,s[122,60]=-0.1
s[123,1]=0.9,s[123,2]=0.1,s[123,3]=0.1,s[123,4]=-1.2,s[123,5]=0.1,s[123,6]=0.7,s[123,7]=-1.0,s[123,8]=-0.6,s[123,9]=0.1,s[123,10]=0.6,s[123,11]=-1.1,s[123,12]=0.8,s[123,13]=-0.1,s[123,14]=0.1,s[123,15]=0.0,s[123,16]=-0.9,s[123,17]=-0.3,s[123,18]=1.1,s[123,19]=-1.0,s[123,20]=-0.9,s[123,21]=-0.9,s[123,22]=-0.7,s[123,23]=-1.0,s[123,24]=-1.1,s[123,25]=-1.2,s[123,26]=-0.8,s[123,27]=-0.1,s[123,28]=-0.2,s[123,29]=-0.7,s[123,30]=-1.2
s[123,31]=1.2,s[123,32]=-0.2,s[123,33]=-1.2,s[123,34]=-0.7,s[123,35]=-0.2,s[123,36]=-0.1,s[123,37]=0.4,s[123,38]=-0.8,s[123,39]=0.0,s[123,40]=1.1,s[123,41]=0.4,s[123,42]=1.1,s[123,43]=-0.7,s[123,44]=1.2,s[123,45]=-0.8,s[123,46]=-1.2,s[123,47]=0.7,s[123,48]=-0.7,s[123,49]=0.1,s[123,50]=1.1,s[123,51]=0.0,s[123,52]=-0.8,s[123,53]=-0.1,s[123,54]=-1.1,s[123,55]=0.9,s[123,56]=-1.2,s[123,57]=-1.2,s[123,58]=0.4,s[123,59]=-0.4,s[123,60]=-1.0
s[124,1]=-0.7,s[124,2]=0.9,s[124,3]=0.9,s[124,4]=-0.8,s[124,5]=1.0,s[124,6]=-1.1,s[124,7]=0.6,s[124,8]=-0.1,s[124,9]=-0.3,s[124,10]=-0.9,s[124,11]=0.1,s[124,12]=1.0,s[124,13]=-0.3,s[124,14]=0.5,s[124,15]=-0.5,s[124,16]=0.3,s[124,17]=1.2,s[124,18]=-0.2,s[124,19]=1.2,s[124,20]=-0.2,s[124,21]=-1.1,s[124,22]=-0.5,s[124,23]=1.0,s[124,24]=-0.9,s[124,25]=-1.0,s[124,26]=-1.1,s[124,27]=0.8,s[124,28]=0.9,s[124,29]=-0.3,s[124,30]=-1.1
s[124,31]=0.1,s[124,32]=-0.1,s[124,33]=-0.4,s[124,34]=0.6,s[124,35]=0.9,s[124,36]=0.5,s[124,37]=0.4,s[124,38]=-1.0,s[124,39]=0.8,s[124,40]=1.0,s[124,41]=-0.5,s[124,42]=-0.5,s[124,43]=1.2,s[124,44]=-1.1,s[124,45]=-0.4,s[124,46]=0.3,s[124,47]=-1.2,s[124,48]=0.6,s[124,49]=0.3,s[124,50]=-0.4,s[124,51]=-0.5,s[124,52]=1.0,s[124,53]=-0.4,s[124,54]=-0.7,s[124,55]=0.6,s[124,56]=-0.7,s[124,57]=-0.1,s[124,58]=-0.4,s[124,59]=-1.1,s[124,60]=-0.4
s[125,1]=-0.1,s[125,2]=-0.2,s[125,3]=-0.6,s[125,4]=-0.3,s[125,5]=0.7,s[125,6]=-0.2,s[125,7]=-0.5,s[125,8]=-0.1,s[125,9]=-0.5,s[125,10]=0.4,s[125,11]=0.7,s[125,12]=1.1,s[125,13]=0.6,s[125,14]=0.5,s[125,15]=1.1,s[125,16]=-0.9,s[125,17]=0.2,s[125,18]=-0.8,s[125,19]=0.7,s[125,20]=1.2,s[125,21]=-0.1,s[125,22]=0.7,s[125,23]=-1.0,s[125,24]=-1.1,s[125,25]=1.0,s[125,26]=-0.2,s[125,27]=0.4,s[125,28]=-0.9,s[125,29]=0.2,s[125,30]=0.8
s[125,31]=0.3,s[125,32]=-0.3,s[125,33]=-0.4,s[125,34]=-1.0,s[125,35]=0.6,s[125,36]=1.0,s[125,37]=0.3,s[125,38]=0.8,s[125,39]=1.1,s[125,40]=1.1,s[125,41]=-1.0,s[125,42]=0.5,s[125,43]=0.4,s[125,44]=-0.5,s[125,45]=0.3,s[125,46]=-0.4,s[125,47]=-0.3,s[125,48]=1.2,s[125,49]=0.8,s[125,50]=-0.3,s[125,51]=-0.1,s[125,52]=-1.0,s[125,53]=0.6,s[125,54]=-0.4,s[125,55]=-0.9,s[125,56]=-0.6,s[125,57]=0.0,s[125,58]=-1.1,s[125,59]=-1.0,s[125,60]=-0.6
s[126,1]=0.2,s[126,2]=1.1,s[126,3]=-0.9,s[126,4]=-0.1,s[126,5]=0.6,s[126,6]=0.2,s[126,7]=1.1,s[126,8]=-0.6,s[126,9]=-0.8,s[126,10]=0.2,s[126,11]=-1.2,s[126,12]=0.4,s[126,13]=-0.1,s[126,14]=-1.2,s[126,15]=-0.5,s[126,16]=-0.6,s[126,17]=-0.7,s[126,18]=0.0,s[126,19]=-0.5,s[126,20]=0.3,s[126,21]=0.1,s[126,22]=1.2,s[126,23]=-0.2,s[126,24]=-0.5,s[126,25]=-1.0,s[126,26]=0.6,s[126,27]=1.2,s[126,28]=1.1,s[126,29]=0.5,s[126,30]=0.1
s[126,31]=0.0,s[126,32]=-0.2,s[126,33]=-0.6,s[126,34]=1.0,s[126,35]=-1.2,s[126,36]=0.2,s[126,37]=-0.4,s[126,38]=0.4,s[126,39]=0.7,s[126,40]=0.7,s[126,41]=-0.8,s[126,42]=0.4,s[126,43]=0.6,s[126,44]=-0.1,s[126,45]=0.7,s[126,46]=-0.9,s[126,47]=1.2,s[126,48]=-0.2,s[126,49]=0.2,s[126,50]=-0.5,s[126,51]=-0.2,s[126,52]=-1.2,s[126,53]=-0.8,s[126,54]=-0.8,s[126,55]=0.7,s[126,56]=-0.9,s[126,57]=-0.1,s[126,58]=0.9,s[126,59]=-1.2,s[126,60]=-0.7
s[127,1]=-0.1,s[127,2]=-0.1,s[127,3]=-0.3,s[127,4]=-0.3,s[127,5]=-0.6,s[127,6]=1.0,s[127,7]=-0.5,s[127,8]=0.4,s[127,9]=-0.3,s[127,10]=-0.8,s[127,11]=0.3,s[127,12]=0.9,s[127,13]=0.3,s[127,14]=0.6,s[127,15]=1.1,s[127,16]=-0.7,s[127,17]=-0.9,s[127,18]=1.1,s[127,19]=1.1,s[127,20]=0.9,s[127,21]=0.1,s[127,22]=0.1,s[127,23]=0.7,s[127,24]=-1.2,s[127,25]=-0.1,s[127,26]=-0.5,s[127,27]=-0.7,s[127,28]=0.5,s[127,29]=0.0,s[127,30]=1.1
s[127,31]=-1.0,s[127,32]=-0.4,s[127,33]=-0.4,s[127,34]=-1.0,s[127,35]=0.9,s[127,36]=-0.9,s[127,37]=-0.9,s[127,38]=0.8,s[127,39]=0.0,s[127,40]=0.6,s[127,41]=-0.5,s[127,42]=0.4,s[127,43]=0.6,s[127,44]=0.7,s[127,45]=1.1,s[127,46]=-0.9,s[127,47]=0.5,s[127,48]=-0.9,s[127,49]=-0.5,s[127,50]=1.1,s[127,51]=0.3,s[127,52]=0.4,s[127,53]=-0.9,s[127,54]=-0.4,s[127,55]=-0.4,s[127,56]=0.9,s[127,57]=-0.7,s[127,58]=-1.2,s[127,59]=-0.5,s[127,60]=1.1
s[128,1]=-0.5,s[128,2]=-0.3,s[128,3]=1.1,s[128,4]=-1.0,s[128,5]=-0.6,s[128,6]=0.8,s[128,7]=0.6,s[128,8]=0.4,s[128,9]=-1.1,s[128,10]=-1.1,s[128,11]=1.1,s[128,12]=0.2,s[128,13]=-1.2,s[128,14]=0.1,s[128,15]=0.8,s[128,16]=0.3,s[128,17]=-0.4,s[128,18]=-0.1,s[128,19]=0.7,s[128,20]=1.1,s[128,21]=-0.3,s[128,22]=-0.1,s[128,23]=-1.0,s[128,24]=0.2,s[128,25]=0.4,s[128,26]=0.5,s[128,27]=1.0,s[128,28]=-0.4,s[128,29]=-0.7,s[128,30]=1.0
s[128,31]=0.4,s[128,32]=-1.1,s[128,33]=-1.2,s[128,34]=-1.2,s[128,35]=0.2,s[128,36]=-0.4,s[128,37]=-0.9,s[128,38]=0.7,s[128,39]=-0.7,s[128,40]=0.5,s[128,41]=1.1,s[128,42]=-1.0,s[128,43]=0.1,s[128,44]=-0.5,s[128,45]=-1.2,s[128,46]=-0.6,s[128,47]=0.4,s[128,48]=0.8,s[128,49]=0.8,s[128,50]=-0.1,s[128,51]=-0.7,s[128,52]=0.8,s[128,53]=0.3,s[128,54]=1.1,s[128,55]=-0.9,s[128,56]=-0.3,s[128,57]=1.1,s[128,58]=0.4,s[128,59]=1.0,s[128,60]=-0.1
s[129,1]=0.4,s[129,2]=-1.1,s[129,3]=1.2,s[129,4]=-0.5,s[129,5]=0.1,s[129,6]=0.9,s[129,7]=-1.0,s[129,8]=-0.9,s[129,9]=0.5,s[129,10]=-1.1,s[129,11]=-0.2,s[129,12]=-0.2,s[129,13]=0.9,s[129,14]=-0.5,s[129,15]=0.7,s[129,16]=-0.4,s[129,17]=-0.2,s[129,18]=0.4,s[129,19]=0.3,s[129,20]=0.8,s[129,21]=-0.7,s[129,22]=-0.5,s[129,23]=0.5,s[129,24]=-0.4,s[129,25]=0.3,s[129,26]=1.1,s[129,27]=-0.2,s[129,28]=1.0,s[129,29]=-0.7,s[129,30]=-0.5
s[129,31]=-0.2,s[129,32]=1.2,s[129,33]=-1.1,s[129,34]=-1.1,s[129,35]=-1.1,s[129,36]=-1.0,s[129,37]=-0.4,s[129,38]=1.2,s[129,39]=-0.5,s[129,40]=0.2,s[129,41]=0.1,s[129,42]=-0.2,s[129,43]=0.1,s[129,44]=0.8,s[129,45]=-1.0,s[129,46]=-1.2,s[129,47]=-0.4,s[129,48]=-0.4,s[129,49]=0.3,s[129,50]=-1.2,s[129,51]=0.7,s[129,52]=0.4,s[129,53]=-0.7,s[129,54]=-0.8,s[129,55]=-1.1,s[129,56]=-0.7,s[129,57]=-0.3,s[129,58]=-0.8,s[129,59]=0.4,s[129,60]=0.2
s[130,1]=-0.6,s[130,2]=-1.0,s[130,3]=1.2,s[130,4]=1.0,s[130,5]=0.6,s[130,6]=-0.5,s[130,7]=1.0,s[130,8]=0.8,s[130,9]=-0.9,s[130,10]=-0.2,s[130,11]=-1.0,s[130,12]=-0.3,s[130,13]=-1.2,s[130,14]=0.1,s[130,15]=-0.2,s[130,16]=-1.2,s[130,17]=-1.0,s[130,18]=-1.2,s[130,19]=0.4,s[130,20]=0.9,s[130,21]=0.7,s[130,22]=-0.6,s[130,23]=-0.5,s[130,24]=1.1,s[130,25]=0.2,s[130,26]=1.2,s[130,27]=0.1,s[130,28]=1.2,s[130,29]=0.7,s[130,30]=0.1
s[130,31]=-0.6,s[130,32]=-0.2,s[130,33]=0.6,s[130,34]=0.2,s[130,35]=-0.7,s[130,36]=1.2,s[130,37]=-1.1,s[130,38]=-0.1,s[130,39]=0.3,s[130,40]=-1.0,s[130,41]=-0.8,s[130,42]=-1.1,s[130,43]=0.9,s[130,44]=0.0,s[130,45]=-0.9,s[130,46]=-1.2,s[130,47]=0.7,s[130,48]=-0.2,s[130,49]=-0.6,s[130,50]=-0.3,s[130,51]=-0.2,s[130,52]=-1.0,s[130,53]=-0.6,s[130,54]=0.6,s[130,55]=-0.5,s[130,56]=-0.3,s[130,57]=0.4,s[130,58]=-1.0,s[130,59]=1.1,s[130,60]=-0.2
s[131,1]=0.2,s[131,2]=-1.1,s[131,3]=-0.4,s[131,4]=0.6,s[131,5]=0.8,s[131,6]=-1.1,s[131,7]=-0.4,s[131,8]=0.0,s[131,9]=0.1,s[131,10]=-0.3,s[131,11]=0.5,s[131,12]=0.6,s[131,13]=0.4,s[131,14]=-0.1,s[131,15]=-0.6,s[131,16]=0.9,s[131,17]=-1.1,s[131,18]=0.6,s[131,19]=-1.2,s[131,20]=-1.1,s[131,21]=0.2,s[131,22]=0.7,s[131,23]=0.5,s[131,24]=-0.6,s[131,25]=-1.0,s[131,26]=0.1,s[131,27]=0.1,s[131,28]=-0.5,s[131,29]=-0.7,s[131,30]=-0.6
s[131,31]=1.0,s[131,32]=-1.1,s[131,33]=-0.9,s[131,34]=1.1,s[131,35]=0.2,s[131,36]=-0.2,s[131,37]=-0.3,s[131,38]=0.9,s[131,39]=0.6,s[131,40]=0.4,s[131,41]=1.2,s[131,42]=-1.0,s[131,43]=-0.7,s[131,44]=0.6,s[131,45]=0.3,s[131,46]=0.0,s[131,47]=0.9,s[131,48]=-0.4,s[131,49]=0.5,s[131,50]=1.1,s[131,51]=1.0,s[131,52]=-0.2,s[131,53]=-0.9,s[131,54]=-0.7,s[131,55]=-1.1,s[131,56]=-0.4,s[131,57]=0.7,s[131,58]=1.2,s[131,59]=-0.9,s[131,60]=0.4
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float ppz = @ppz
float pxx = 0
float pyy = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
pyy = y
x = x + 0.1*(s[@sd,1] + s[@sd,2]*x + s[@sd,3]*x*x + s[@sd,4]*x*x*x + s[@sd,5]*x*x*y + s[@sd,6]*x*x*ppz + s[@sd,7]*x*y + \
s[@sd,8]*x*y*y + s[@sd,9]*x*y*ppz + s[@sd,10]*x*ppz + s[@sd,11]*x*ppz*ppz + s[@sd,12]*y + s[@sd,13]*y*y + s[@sd,14]*y*y*y + \
s[@sd,15]*y*y*ppz + s[@sd,16]*y*ppz + s[@sd,17]*y*ppz*ppz + s[@sd,18]*ppz +s[@sd,19]*ppz*ppz +s[@sd,20]*ppz*ppz*ppz)
y = y + 0.1*(s[@sd,21] +s[@sd,22]*pxx +s[@sd,23]*pxx*pxx +s[@sd,24]*pxx*pxx*pxx +s[@sd,25]*pxx*pxx*y +s[@sd,26]*pxx*pxx*ppz +s[@sd,27]*pxx*y +\
s[@sd,28]*pxx*y*y +s[@sd,29]*pxx*y*ppz +s[@sd,30]*pxx*ppz +s[@sd,31]*pxx*ppz*ppz +s[@sd,32]*y +s[@sd,33]*y*y +s[@sd,34]*y*y*y + \
s[@sd,35]*y*y*ppz +s[@sd,36]*y*ppz +s[@sd,37]*y*ppz*ppz +s[@sd,38]*ppz +s[@sd,39]*ppz*ppz +s[@sd,40]*ppz*ppz*ppz)
ppz = ppz + 0.1*(s[@sd,41] +s[@sd,42]*pxx +s[@sd,43]*pxx*pxx +s[@sd,44]*pxx*pxx*pxx +s[@sd,45]*pxx*pxx*pyy +s[@sd,46]*pxx*pxx*ppz +s[@sd,47]*pxx*pyy + \
s[@sd,48]*pxx*pyy*pyy +s[@sd,49]*pxx*pyy*ppz +s[@sd,50]*pxx*ppz +s[@sd,51]*pxx*ppz*ppz +s[@sd,52]*pyy +s[@sd,53]*pyy*pyy +s[@sd,54]*pyy*pyy*pyy + \
s[@sd,55]*pyy*pyy*ppz +s[@sd,56]*pyy*ppz +s[@sd,57]*pyy*ppz*ppz +s[@sd,58]*ppz +s[@sd,59]*ppz*ppz +s[@sd,60]*ppz*ppz*ppz)
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y) + ppz*@pw)
float d = @distscale*|pz-(x + sgn*flip(y) + ppz*@pw)|
return d
endfunc
private:
float s[132,61]
default:
title = "Sprott3D_Cubic_ODE"
heading
text="Sprott 3D cubic attractors"
endheading
heading
text=" x -> x + 0.1*(Cubic in x, y and z)"
endheading
heading
text=" y -> y + 0.1*(Cubic in x, y and z)"
endheading
heading
text=" z -> z + 0.1*(Cubic in x, y and z)"
endheading
int param v_trapshapesprott3d_Cubic_ODE
caption = "Version (Trap Shape Sprott3D_Cubic_ODE)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesprott3d_Cubic_ODE < 100
endparam
param sd
caption = "Sprott selector"
default = 0
enum = "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" \
"15" "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" \
"30" "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" \
"45" "46" "47" "48" "49" "50" "51" "52" "53" "54" "55" "56" "57" "58" "59" \
"60" "61" "62" "63" "64" "65" "66" "67" "69" "69" "70" "71" "72" "73" "74" \
"75" "76" "77" "78" "79" "80" "81" "82" "83" "84" "85" "86" "87" "88" "89" \
"90" "91" "92" "93" "94" "95" "96" "97" "98" "99" "100" "101" "102" "103" \
"104" "105" "106" "107" "108" "109" "110" "111" "112" "113" "114" "115" \
"116" "117" "118" "119" "120" "121" "122" "123" "124" "125" "126" "127" \
"128" "129" "130" "131"
hint = "Each Sprott selector uses a different strange attractor."
endparam
heading
text = "'Initialize Height' sets the starting z value for the attractor."
endheading
float param ppz
caption = "Initialize Height"
default = 0.0
endparam
heading
text = "'Height weight' determines the weight of the final z value which is added \
to the trap distance."
endheading
complex param pw
caption = "Height weight"
default = (0.5,0)
endparam
float param distscale
caption = "Distance scale"
default = 2
endparam
float param s
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 15
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSprott4D(common.ulb:TrapShape) {
; This shape uses a Sprott strange attractor.
; The Sprott attractors were developed by Julien C. Sprott, and are
; based upon polynomials and linear differential equations of polynomials.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSprott4D(Generic pparent)
TrapShape.TrapShape(pparent)
s[0,1]=-0.6,s[0,2]=0.5,s[0,3]=1.0,s[0,4]=-0.6,s[0,5]=0.9,s[0,6]=0.3,s[0,7]=1.0,s[0,8]=0.4,s[0,9]=-0.6,s[0,10]=1.0,s[0,11]=-0.3,s[0,12]=-1.0,s[0,13]=0.3,s[0,14]=-0.4,s[0,15]=0.5,s[0,16]=-0.3,s[0,17]=1.0,s[0,18]=0.0,s[0,19]=0.1,s[0,20]=0.7,s[0,21]=0.3,s[0,22]=0.3,s[0,23]=0.3,s[0,24]=-0.6,s[0,25]=0.7,s[0,26]=0.4,s[0,27]=-0.7,s[0,28]=-0.5,s[0,29]=0.1,s[0,30]=-0.1
s[0,31]=0.0,s[0,32]=-0.1,s[0,33]=0.8,s[0,34]=0.3,s[0,35]=0.3,s[0,36]=-0.1,s[0,37]=-0.3,s[0,38]=0.9,s[0,39]=1.0,s[0,40]=-0.8,s[0,41]=0.6,s[0,42]=-0.6,s[0,43]=-0.4,s[0,44]=0.6,s[0,45]=-0.4,s[0,46]=-0.5,s[0,47]=0.3,s[0,48]=-0.5,s[0,49]=0.5,s[0,50]=1.2,s[0,51]=-0.1,s[0,52]=1.1,s[0,53]=0.3,s[0,54]=-1.2,s[0,55]=1.0,s[0,56]=0.2,s[0,57]=-1.2,s[0,58]=0.3,s[0,59]=-0.5,s[0,60]=0.1
s[1,1]=-0.4,s[1,2]=0.1,s[1,3]=1.1,s[1,4]=0.6,s[1,5]=-1.2,s[1,6]=-0.6,s[1,7]=0.4,s[1,8]=0.4,s[1,9]=0.0,s[1,10]=0.0,s[1,11]=0.2,s[1,12]=-0.9,s[1,13]=-0.8,s[1,14]=-0.3,s[1,15]=-0.2,s[1,16]=0.3,s[1,17]=0.1,s[1,18]=0.3,s[1,19]=-0.4,s[1,20]=0.7,s[1,21]=0.2,s[1,22]=-0.5,s[1,23]=-0.5,s[1,24]=-0.6,s[1,25]=-1.2,s[1,26]=0.4,s[1,27]=0.1,s[1,28]=0.1,s[1,29]=0.3,s[1,30]=-0.3,s[1,31]=0.6,s[1,32]=0.8,s[1,33]=0.0,s[1,34]=1.0,s[1,35]=-1.0,s[1,36]=0.4,s[1,37]=1.2,s[1,38]=0.4,s[1,39]=-0.5,s[1,40]=-0.5,s[1,41]=-0.7,s[1,42]=0.3,s[1,43]=1.1,s[1,44]=-0.4,s[1,45]=-0.3,s[1,46]=0.0,s[1,47]=0.6,s[1,48]=-0.7,s[1,49]=1.0,s[1,50]=0.3,s[1,51]=1.0,s[1,52]=-0.1,s[1,53]=0.1,s[1,54]=1.0,s[1,55]=0.1,s[1,56]=0.4,s[1,57]=0.9,s[1,58]=-0.1,s[1,59]=0.5,s[1,60]=-0.5
s[2,1]=-0.2,s[2,2]=0.6,s[2,3]=0.2,s[2,4]=-0.2,s[2,5]=0.4,s[2,6]=-0.9,s[2,7]=-0.6,s[2,8]=0.9,s[2,9]=-0.6,s[2,10]=0.8,s[2,11]=-0.7,s[2,12]=-0.5,s[2,13]=1.0,s[2,14]=0.4,s[2,15]=1.2,s[2,16]=-0.1,s[2,17]=0.6,s[2,18]=-0.7,s[2,19]=0.8,s[2,20]=1.2,s[2,21]=-0.7,s[2,22]=0.4,s[2,23]=-1.1,s[2,24]=-0.9,s[2,25]=-0.5,s[2,26]=0.7,s[2,27]=-1.1,s[2,28]=0.6,s[2,29]=1.1,s[2,30]=-0.8,s[2,31]=0.0,s[2,32]=-0.5,s[2,33]=0.2,s[2,34]=0.8,s[2,35]=0.6,s[2,36]=0.1,s[2,37]=-0.9,s[2,38]=-1.0,s[2,39]=-0.3,s[2,40]=0.3,s[2,41]=-0.6,s[2,42]=-0.4,s[2,43]=-0.9,s[2,44]=0.1,s[2,45]=-0.2,s[2,46]=0.1,s[2,47]=-0.6,s[2,48]=0.3,s[2,49]=-0.2,s[2,50]=0.4,s[2,51]=-0.1,s[2,52]=0.6,s[2,53]=-0.1,s[2,54]=-0.9,s[2,55]=0.4,s[2,56]=1.0,s[2,57]=0.3,s[2,58]=-0.3,s[2,59]=0.1,s[2,60]=0.4
s[3,1]=-0.1,s[3,2]=0.4,s[3,3]=-1.2,s[3,4]=-0.1,s[3,5]=-0.7,s[3,6]=1.2,s[3,7]=-0.4,s[3,8]=-0.3,s[3,9]=0.0,s[3,10]=-0.3,s[3,11]=-0.2,s[3,12]=-0.2,s[3,13]=-1.0,s[3,14]=0.2,s[3,15]=-1.1,s[3,16]=-0.7,s[3,17]=-0.4,s[3,18]=0.9,s[3,19]=0.1,s[3,20]=1.1,s[3,21]=-0.7,s[3,22]=-0.8,s[3,23]=-0.1,s[3,24]=0.8,s[3,25]=-0.6,s[3,26]=0.6,s[3,27]=-0.6,s[3,28]=-1.1,s[3,29]=0.1,s[3,30]=1.0,s[3,31]=-0.5,s[3,32]=-1.2,s[3,33]=1.2,s[3,34]=1.0,s[3,35]=-0.9,s[3,36]=-0.4,s[3,37]=0.4,s[3,38]=1.2,s[3,39]=-0.9,s[3,40]=0.5,s[3,41]=-0.3,s[3,42]=0.2,s[3,43]=0.8,s[3,44]=1.0,s[3,45]=0.1,s[3,46]=-0.1,s[3,47]=0.0,s[3,48]=-0.1,s[3,49]=0.2,s[3,50]=0.3,s[3,51]=-1.2,s[3,52]=-0.2,s[3,53]=-0.3,s[3,54]=-0.7,s[3,55]=-1.1,s[3,56]=-0.7,s[3,57]=0.4,s[3,58]=-0.5,s[3,59]=-0.5,s[3,60]=-0.9
s[4,1]=-0.1,s[4,2]=0.5,s[4,3]=-0.1,s[4,4]=-0.9,s[4,5]=0.9,s[4,6]=-0.4,s[4,7]=0.5,s[4,8]=-0.7,s[4,9]=-0.3,s[4,10]=0.5,s[4,11]=-0.3,s[4,12]=-0.6,s[4,13]=-0.4,s[4,14]=-0.1,s[4,15]=0.8,s[4,16]=0.4,s[4,17]=1.2,s[4,18]=1.2,s[4,19]=1.2,s[4,20]=0.6,s[4,21]=-0.7,s[4,22]=-0.2,s[4,23]=-0.5,s[4,24]=0.0,s[4,25]=0.4,s[4,26]=0.4,s[4,27]=0.2,s[4,28]=1.0,s[4,29]=0.5,s[4,30]=0.0,s[4,31]=-0.4,s[4,32]=-0.4,s[4,33]=0.3,s[4,34]=0.5,s[4,35]=-0.6,s[4,36]=0.1,s[4,37]=0.4,s[4,38]=-0.3,s[4,39]=-0.5,s[4,40]=0.5,s[4,41]=-0.2,s[4,42]=-0.2,s[4,43]=-0.5,s[4,44]=1.2,s[4,45]=-0.9,s[4,46]=0.0,s[4,47]=1.1,s[4,48]=0.6,s[4,49]=-0.4,s[4,50]=1.2,s[4,51]=0.0,s[4,52]=-0.7,s[4,53]=0.3,s[4,54]=-0.1,s[4,55]=0.4,s[4,56]=0.5,s[4,57]=1.0,s[4,58]=0.6,s[4,59]=0.6,s[4,60]=-0.9
s[5,1]=0.0,s[5,2]=-0.9,s[5,3]=-0.9,s[5,4]=-0.2,s[5,5]=-1.0,s[5,6]=-1.1,s[5,7]=0.5,s[5,8]=0.2,s[5,9]=-0.2,s[5,10]=1.2,s[5,11]=-0.3,s[5,12]=0.0,s[5,13]=1.1,s[5,14]=1.1,s[5,15]=0.4,s[5,16]=-0.2,s[5,17]=0.3,s[5,18]=-1.1,s[5,19]=0.0,s[5,20]=-0.3,s[5,21]=0.6,s[5,22]=0.6,s[5,23]=0.0,s[5,24]=0.6,s[5,25]=0.8,s[5,26]=0.5,s[5,27]=0.1,s[5,28]=-0.4,s[5,29]=-0.2,s[5,30]=0.6,s[5,31]=0.2,s[5,32]=0.1,s[5,33]=-1.1,s[5,34]=0.7,s[5,35]=1.0,s[5,36]=0.8,s[5,37]=-1.0,s[5,38]=-1.0,s[5,39]=0.2,s[5,40]=0.3,s[5,41]=0.5,s[5,42]=-1.2,s[5,43]=-0.6,s[5,44]=0.0,s[5,45]=-0.7,s[5,46]=0.3,s[5,47]=0.1,s[5,48]=0.1,s[5,49]=0.7,s[5,50]=0.9,s[5,51]=-0.6,s[5,52]=0.5,s[5,53]=0.1,s[5,54]=-0.8,s[5,55]=0.4,s[5,56]=-0.9,s[5,57]=0.4,s[5,58]=1.2,s[5,59]=0.1,s[5,60]=-0.1
s[6,1]=0.0,s[6,2]=1.0,s[6,3]=1.2,s[6,4]=-0.2,s[6,5]=-1.2,s[6,6]=0.5,s[6,7]=1.1,s[6,8]=-0.3,s[6,9]=-0.6,s[6,10]=1.1,s[6,11]=0.5,s[6,12]=-0.9,s[6,13]=-0.1,s[6,14]=0.0,s[6,15]=-0.2,s[6,16]=-0.2,s[6,17]=-0.8,s[6,18]=0.6,s[6,19]=-0.5,s[6,20]=0.1,s[6,21]=0.6,s[6,22]=-0.3,s[6,23]=-0.8,s[6,24]=0.4,s[6,25]=-0.5,s[6,26]=-0.3,s[6,27]=0.5,s[6,28]=0.9,s[6,29]=-0.8,s[6,30]=-0.8,s[6,31]=0.5,s[6,32]=0.6,s[6,33]=1.0,s[6,34]=1.0,s[6,35]=-0.7,s[6,36]=1.1,s[6,37]=-0.8,s[6,38]=-0.8,s[6,39]=-0.1,s[6,40]=0.6,s[6,41]=-0.6,s[6,42]=-0.6,s[6,43]=0.0,s[6,44]=0.8,s[6,45]=-1.2,s[6,46]=0.2,s[6,47]=-0.8,s[6,48]=-0.5,s[6,49]=1.0,s[6,50]=1.2,s[6,51]=1.1,s[6,52]=-0.1,s[6,53]=0.0,s[6,54]=-0.5,s[6,55]=0.1,s[6,56]=-0.1,s[6,57]=0.0,s[6,58]=-0.1,s[6,59]=0.2,s[6,60]=0.1
s[7,1]=-0.2,s[7,2]=1.0,s[7,3]=1.0,s[7,4]=-0.7,s[7,5]=0.7,s[7,6]=0.4,s[7,7]=-0.5,s[7,8]=1.0,s[7,9]=-0.7,s[7,10]=-0.7,s[7,11]=-1.1,s[7,12]=-0.2,s[7,13]=-1.0,s[7,14]=-0.7,s[7,15]=-0.5,s[7,16]=0.0,s[7,17]=0.8,s[7,18]=0.6,s[7,19]=0.9,s[7,20]=-0.7,s[7,21]=-0.7,s[7,22]=-0.7,s[7,23]=-1.2,s[7,24]=0.1,s[7,25]=-1.0,s[7,26]=0.5,s[7,27]=0.2,s[7,28]=-0.6,s[7,29]=0.6,s[7,30]=0.6,s[7,31]=0.3,s[7,32]=0.3,s[7,33]=-0.6,s[7,34]=0.2,s[7,35]=1.2,s[7,36]=0.7,s[7,37]=0.7,s[7,38]=-1.0,s[7,39]=-1.2,s[7,40]=0.2,s[7,41]=0.1,s[7,42]=-0.4,s[7,43]=0.8,s[7,44]=-0.1,s[7,45]=0.3,s[7,46]=-0.6,s[7,47]=0.5,s[7,48]=-0.4,s[7,49]=0.7,s[7,50]=-0.8,s[7,51]=-1.2,s[7,52]=0.4,s[7,53]=0.9,s[7,54]=0.9,s[7,55]=0.4,s[7,56]=-0.4,s[7,57]=-1.0,s[7,58]=-1.1,s[7,59]=-0.2,s[7,60]=-0.2
s[8,1]=0.1,s[8,2]=-0.6,s[8,3]=-0.7,s[8,4]=0.2,s[8,5]=-0.7,s[8,6]=0.0,s[8,7]=-0.2,s[8,8]=-1.0,s[8,9]=1.2,s[8,10]=-0.4,s[8,11]=-0.7,s[8,12]=-0.6,s[8,13]=-0.3,s[8,14]=0.6,s[8,15]=0.6,s[8,16]=0.2,s[8,17]=0.9,s[8,18]=0.4,s[8,19]=-0.2,s[8,20]=0.8,s[8,21]=1.2,s[8,22]=-0.2,s[8,23]=0.8,s[8,24]=-0.5,s[8,25]=0.7,s[8,26]=-0.4,s[8,27]=0.7,s[8,28]=-0.3,s[8,29]=1.0,s[8,30]=-0.8,s[8,31]=0.0,s[8,32]=0.8,s[8,33]=-0.5,s[8,34]=0.1,s[8,35]=0.3,s[8,36]=1.1,s[8,37]=0.0,s[8,38]=-0.7,s[8,39]=-1.2,s[8,40]=-1.1,s[8,41]=0.8,s[8,42]=1.0,s[8,43]=1.1,s[8,44]=-0.6,s[8,45]=-1.2,s[8,46]=0.0,s[8,47]=0.4,s[8,48]=0.1,s[8,49]=0.4,s[8,50]=0.2,s[8,51]=1.1,s[8,52]=0.0,s[8,53]=-0.6,s[8,54]=0.4,s[8,55]=0.7,s[8,56]=0.9,s[8,57]=-0.3,s[8,58]=0.4,s[8,59]=0.2,s[8,60]=-1.2
s[9,1]=0.5,s[9,2]=-0.4,s[9,3]=-0.9,s[9,4]=-0.7,s[9,5]=0.0,s[9,6]=-0.4,s[9,7]=-0.5,s[9,8]=0.5,s[9,9]=-0.2,s[9,10]=-0.4,s[9,11]=0.5,s[9,12]=-1.2,s[9,13]=0.1,s[9,14]=-0.8,s[9,15]=0.1,s[9,16]=-0.4,s[9,17]=0.1,s[9,18]=0.9,s[9,19]=0.7,s[9,20]=-0.9,s[9,21]=0.1,s[9,22]=-0.3,s[9,23]=-0.2,s[9,24]=-1.1,s[9,25]=0.5,s[9,26]=0.9,s[9,27]=-1.2,s[9,28]=-0.7,s[9,29]=0.1,s[9,30]=1.0,s[9,31]=0.3,s[9,32]=0.4,s[9,33]=-0.3,s[9,34]=-0.9,s[9,35]=-0.9,s[9,36]=0.2,s[9,37]=-0.9,s[9,38]=-1.2,s[9,39]=0.0,s[9,40]=0.9,s[9,41]=-0.3,s[9,42]=-0.4,s[9,43]=1.0,s[9,44]=0.2,s[9,45]=-0.4,s[9,46]=0.4,s[9,47]=0.2,s[9,48]=1.0,s[9,49]=-0.7,s[9,50]=0.4,s[9,51]=-1.1,s[9,52]=-0.6,s[9,53]=-0.3,s[9,54]=-0.3,s[9,55]=-0.8,s[9,56]=-0.7,s[9,57]=-0.4,s[9,58]=0.5,s[9,59]=-0.8,s[9,60]=1.2
s[10,1]=-0.4,s[10,2]=0.9,s[10,3]=-0.4,s[10,4]=-0.3,s[10,5]=1.2,s[10,6]=-0.9,s[10,7]=1.0,s[10,8]=0.6,s[10,9]=-0.2,s[10,10]=-1.0,s[10,11]=-1.2,s[10,12]=-0.6,s[10,13]=0.7,s[10,14]=0.4,s[10,15]=-1.2,s[10,16]=0.0,s[10,17]=-0.3,s[10,18]=-0.9,s[10,19]=1.0,s[10,20]=-0.1,s[10,21]=1.2,s[10,22]=-1.0,s[10,23]=-1.1,s[10,24]=-0.2,s[10,25]=-0.3,s[10,26]=-0.6,s[10,27]=-0.9,s[10,28]=-0.3,s[10,29]=-0.2,s[10,30]=-0.1,s[10,31]=-0.6,s[10,32]=-0.8,s[10,33]=-0.8,s[10,34]=-1.2,s[10,35]=-0.1,s[10,36]=-1.0,s[10,37]=-1.1,s[10,38]=-1.0,s[10,39]=-1.0,s[10,40]=-0.7,s[10,41]=0.5,s[10,42]=0.5,s[10,43]=0.0,s[10,44]=-0.3,s[10,45]=-0.6,s[10,46]=0.1,s[10,47]=0.0,s[10,48]=0.1,s[10,49]=0.6,s[10,50]=0.7,s[10,51]=-0.1,s[10,52]=-1.1,s[10,53]=1.1,s[10,54]=0.4,s[10,55]=1.2,s[10,56]=1.2,s[10,57]=0.1,s[10,58]=1.2,s[10,59]=0.7,s[10,60]=0.8
s[11,1]=-0.2,s[11,2]=0.1,s[11,3]=-0.9,s[11,4]=0.9,s[11,5]=1.0,s[11,6]=1.1,s[11,7]=0.0,s[11,8]=0.2,s[11,9]=-0.3,s[11,10]=-1.0,s[11,11]=-0.1,s[11,12]=0.3,s[11,13]=0.3,s[11,14]=-0.7,s[11,15]=-0.9,s[11,16]=-0.9,s[11,17]=-0.6,s[11,18]=1.0,s[11,19]=-0.6,s[11,20]=-0.7,s[11,21]=-1.2,s[11,22]=-0.5,s[11,23]=0.0,s[11,24]=0.2,s[11,25]=0.3,s[11,26]=-0.2,s[11,27]=-0.2,s[11,28]=0.6,s[11,29]=-0.3,s[11,30]=1.0,s[11,31]=-0.3,s[11,32]=0.7,s[11,33]=-0.4,s[11,34]=0.5,s[11,35]=-1.0,s[11,36]=-0.7,s[11,37]=-0.9,s[11,38]=0.3,s[11,39]=-1.1,s[11,40]=1.2,s[11,41]=-0.3,s[11,42]=0.8,s[11,43]=0.1,s[11,44]=0.8,s[11,45]=-1.2,s[11,46]=-0.1,s[11,47]=-0.9,s[11,48]=-0.5,s[11,49]=1.2,s[11,50]=-0.8,s[11,51]=0.0,s[11,52]=1.0,s[11,53]=0.3,s[11,54]=0.1,s[11,55]=0.7,s[11,56]=0.8,s[11,57]=1.2,s[11,58]=0.6,s[11,59]=0.0,s[11,60]=0.1
s[12,1]=0.2,s[12,2]=-0.1,s[12,3]=0.6,s[12,4]=-0.1,s[12,5]=-1.2,s[12,6]=-0.9,s[12,7]=-0.9,s[12,8]=-0.9,s[12,9]=0.4,s[12,10]=-0.7,s[12,11]=0.3,s[12,12]=-0.4,s[12,13]=-1.2,s[12,14]=-0.4,s[12,15]=0.8,s[12,16]=-0.4,s[12,17]=1.0,s[12,18]=-0.5,s[12,19]=-1.1,s[12,20]=-0.7,s[12,21]=1.2,s[12,22]=0.4,s[12,23]=0.6,s[12,24]=0.8,s[12,25]=0.3,s[12,26]=0.6,s[12,27]=0.5,s[12,28]=0.3,s[12,29]=-0.8,s[12,30]=-0.9,s[12,31]=0.0,s[12,32]=-0.3,s[12,33]=1.1,s[12,34]=0.5,s[12,35]=-0.4,s[12,36]=-0.9,s[12,37]=0.7,s[12,38]=0.6,s[12,39]=1.1,s[12,40]=-0.6,s[12,41]=0.1,s[12,42]=-0.4,s[12,43]=0.9,s[12,44]=0.8,s[12,45]=-0.1,s[12,46]=0.0,s[12,47]=0.8,s[12,48]=0.8,s[12,49]=0.3,s[12,50]=-0.4,s[12,51]=-0.1,s[12,52]=-0.1,s[12,53]=-0.7,s[12,54]=-0.6,s[12,55]=-0.9,s[12,56]=0.4,s[12,57]=-0.5,s[12,58]=0.5,s[12,59]=0.6,s[12,60]=-0.9
s[13,1]=0.0,s[13,2]=-0.5,s[13,3]=0.5,s[13,4]=-0.5,s[13,5]=0.9,s[13,6]=-0.4,s[13,7]=0.2,s[13,8]=-0.5,s[13,9]=0.3,s[13,10]=-0.2,s[13,11]=-0.1,s[13,12]=-0.9,s[13,13]=-0.3,s[13,14]=0.1,s[13,15]=-1.0,s[13,16]=-0.2,s[13,17]=-0.8,s[13,18]=-0.1,s[13,19]=-1.2,s[13,20]=0.6,s[13,21]=-0.2,s[13,22]=-0.9,s[13,23]=0.4,s[13,24]=-0.3,s[13,25]=-0.6,s[13,26]=0.8,s[13,27]=0.0,s[13,28]=-1.2,s[13,29]=0.1,s[13,30]=1.1,s[13,31]=-0.4,s[13,32]=-0.1,s[13,33]=1.2,s[13,34]=0.1,s[13,35]=0.4,s[13,36]=-0.5,s[13,37]=-0.9,s[13,38]=0.2,s[13,39]=1.0,s[13,40]=-0.7,s[13,41]=0.7,s[13,42]=-0.6,s[13,43]=-0.6,s[13,44]=0.4,s[13,45]=1.1,s[13,46]=0.0,s[13,47]=0.1,s[13,48]=0.4,s[13,49]=-0.2,s[13,50]=0.4,s[13,51]=1.2,s[13,52]=0.7,s[13,53]=-0.4,s[13,54]=0.5,s[13,55]=1.2,s[13,56]=-0.8,s[13,57]=0.2,s[13,58]=-1.1,s[13,59]=0.2,s[13,60]=-0.9
s[14,1]=0.6,s[14,2]=-0.7,s[14,3]=-0.5,s[14,4]=-0.7,s[14,5]=1.0,s[14,6]=0.4,s[14,7]=-0.5,s[14,8]=-1.0,s[14,9]=-0.6,s[14,10]=-0.3,s[14,11]=-0.9,s[14,12]=-1.0,s[14,13]=0.0,s[14,14]=1.2,s[14,15]=-0.5,s[14,16]=0.1,s[14,17]=-0.4,s[14,18]=0.0,s[14,19]=0.5,s[14,20]=-1.0,s[14,21]=0.3,s[14,22]=0.3,s[14,23]=1.2,s[14,24]=0.0,s[14,25]=-0.4,s[14,26]=0.7,s[14,27]=0.5,s[14,28]=1.0,s[14,29]=0.3,s[14,30]=0.6,s[14,31]=0.1,s[14,32]=0.6,s[14,33]=-1.1,s[14,34]=0.2,s[14,35]=-0.8,s[14,36]=1.1,s[14,37]=-0.8,s[14,38]=0.6,s[14,39]=-1.1,s[14,40]=0.8,s[14,41]=0.0,s[14,42]=-0.3,s[14,43]=-0.5,s[14,44]=-0.5,s[14,45]=-0.8,s[14,46]=0.3,s[14,47]=-0.6,s[14,48]=0.1,s[14,49]=0.2,s[14,50]=1.0,s[14,51]=1.0,s[14,52]=-1.0,s[14,53]=1.2,s[14,54]=0.3,s[14,55]=-0.1,s[14,56]=0.3,s[14,57]=0.8,s[14,58]=0.2,s[14,59]=0.1,s[14,60]=0.5
s[15,1]=-0.1,s[15,2]=-1.0,s[15,3]=0.1,s[15,4]=0.8,s[15,5]=0.3,s[15,6]=1.1,s[15,7]=0.1,s[15,8]=-0.3,s[15,9]=0.5,s[15,10]=0.5,s[15,11]=0.7,s[15,12]=0.9,s[15,13]=0.4,s[15,14]=0.5,s[15,15]=-0.3,s[15,16]=0.2,s[15,17]=0.1,s[15,18]=0.1,s[15,19]=0.6,s[15,20]=-1.2,s[15,21]=0.5,s[15,22]=-0.7,s[15,23]=0.7,s[15,24]=-0.6,s[15,25]=0.5,s[15,26]=-0.2,s[15,27]=0.4,s[15,28]=0.1,s[15,29]=0.9,s[15,30]=0.2,s[15,31]=-0.2,s[15,32]=-1.2,s[15,33]=0.9,s[15,34]=-0.1,s[15,35]=-1.1,s[15,36]=0.6,s[15,37]=0.1,s[15,38]=-0.1,s[15,39]=-1.0,s[15,40]=0.4,s[15,41]=0.5,s[15,42]=0.7,s[15,43]=0.3,s[15,44]=0.4,s[15,45]=-0.4,s[15,46]=-0.2,s[15,47]=-0.5,s[15,48]=0.6,s[15,49]=0.1,s[15,50]=-0.8,s[15,51]=0.8,s[15,52]=-0.6,s[15,53]=0.5,s[15,54]=-1.2,s[15,55]=-1.0,s[15,56]=0.3,s[15,57]=1.1,s[15,58]=0.3,s[15,59]=-0.4,s[15,60]=-0.3
s[16,1]=0.1,s[16,2]=-0.2,s[16,3]=-0.7,s[16,4]=-1.1,s[16,5]=-0.4,s[16,6]=0.0,s[16,7]=-0.7,s[16,8]=-0.8,s[16,9]=-0.2,s[16,10]=-0.7,s[16,11]=-0.1,s[16,12]=0.1,s[16,13]=0.0,s[16,14]=0.0,s[16,15]=-1.1,s[16,16]=-0.2,s[16,17]=0.3,s[16,18]=1.2,s[16,19]=0.3,s[16,20]=0.9,s[16,21]=0.9,s[16,22]=-0.6,s[16,23]=0.0,s[16,24]=0.8,s[16,25]=1.0,s[16,26]=0.2,s[16,27]=-0.6,s[16,28]=-1.2,s[16,29]=-0.8,s[16,30]=0.5,s[16,31]=0.0,s[16,32]=-0.3,s[16,33]=-0.6,s[16,34]=-0.2,s[16,35]=-0.9,s[16,36]=0.2,s[16,37]=0.2,s[16,38]=-0.8,s[16,39]=-0.3,s[16,40]=-0.8,s[16,41]=-0.2,s[16,42]=1.0,s[16,43]=0.8,s[16,44]=1.0,s[16,45]=0.3,s[16,46]=0.3,s[16,47]=-0.6,s[16,48]=-1.1,s[16,49]=0.6,s[16,50]=-1.0,s[16,51]=0.2,s[16,52]=0.3,s[16,53]=0.1,s[16,54]=0.4,s[16,55]=1.1,s[16,56]=0.6,s[16,57]=-0.3,s[16,58]=0.1,s[16,59]=0.7,s[16,60]=0.0
s[17,1]=0.0,s[17,2]=0.1,s[17,3]=1.1,s[17,4]=1.1,s[17,5]=0.9,s[17,6]=1.2,s[17,7]=-0.8,s[17,8]=-0.3,s[17,9]=0.6,s[17,10]=0.2,s[17,11]=0.0,s[17,12]=0.0,s[17,13]=0.7,s[17,14]=-1.0,s[17,15]=-0.2,s[17,16]=-0.2,s[17,17]=0.2,s[17,18]=0.4,s[17,19]=0.0,s[17,20]=0.2,s[17,21]=0.2,s[17,22]=0.2,s[17,23]=-1.2,s[17,24]=0.0,s[17,25]=-0.8,s[17,26]=0.8,s[17,27]=1.0,s[17,28]=-1.2,s[17,29]=0.1,s[17,30]=0.0,s[17,31]=-0.2,s[17,32]=-0.8,s[17,33]=-0.3,s[17,34]=1.2,s[17,35]=-0.6,s[17,36]=1.0,s[17,37]=-0.9,s[17,38]=0.5,s[17,39]=-0.6,s[17,40]=-1.1,s[17,41]=-1.1,s[17,42]=-0.1,s[17,43]=-0.4,s[17,44]=0.6,s[17,45]=0.1,s[17,46]=-0.2,s[17,47]=0.1,s[17,48]=-1.1,s[17,49]=-1.1,s[17,50]=-0.5,s[17,51]=0.6,s[17,52]=-0.3,s[17,53]=0.8,s[17,54]=0.2,s[17,55]=0.9,s[17,56]=-0.8,s[17,57]=1.1,s[17,58]=0.7,s[17,59]=0.0,s[17,60]=-0.3
s[18,1]=0.1,s[18,2]=-0.1,s[18,3]=0.8,s[18,4]=1.1,s[18,5]=0.9,s[18,6]=-0.7,s[18,7]=0.7,s[18,8]=1.0,s[18,9]=-0.5,s[18,10]=-0.2,s[18,11]=0.0,s[18,12]=-1.1,s[18,13]=-0.7,s[18,14]=0.5,s[18,15]=0.3,s[18,16]=-0.3,s[18,17]=-0.3,s[18,18]=0.2,s[18,19]=1.2,s[18,20]=0.9,s[18,21]=-0.8,s[18,22]=-0.7,s[18,23]=0.0,s[18,24]=-1.2,s[18,25]=-0.5,s[18,26]=-0.4,s[18,27]=0.2,s[18,28]=1.0,s[18,29]=1.0,s[18,30]=-1.1,s[18,31]=0.1,s[18,32]=0.6,s[18,33]=-0.7,s[18,34]=0.0,s[18,35]=-0.1,s[18,36]=1.1,s[18,37]=0.7,s[18,38]=0.7,s[18,39]=-1.1,s[18,40]=1.2,s[18,41]=-1.2,s[18,42]=0.5,s[18,43]=-0.6,s[18,44]=-0.6,s[18,45]=1.0,s[18,46]=0.0,s[18,47]=-0.2,s[18,48]=0.2,s[18,49]=0.6,s[18,50]=-0.2,s[18,51]=0.0,s[18,52]=0.4,s[18,53]=0.2,s[18,54]=0.3,s[18,55]=1.1,s[18,56]=0.7,s[18,57]=-0.7,s[18,58]=0.2,s[18,59]=0.1,s[18,60]=0.9
s[19,1]=0.6,s[19,2]=0.3,s[19,3]=-0.3,s[19,4]=0.2,s[19,5]=-0.4,s[19,6]=0.7,s[19,7]=0.7,s[19,8]=0.8,s[19,9]=0.6,s[19,10]=1.2,s[19,11]=-0.5,s[19,12]=-1.2,s[19,13]=0.7,s[19,14]=-0.9,s[19,15]=-0.8,s[19,16]=-0.4,s[19,17]=0.7,s[19,18]=0.4,s[19,19]=-0.2,s[19,20]=-0.2,s[19,21]=-0.5,s[19,22]=-0.4,s[19,23]=-0.3,s[19,24]=-0.7,s[19,25]=-0.6,s[19,26]=0.0,s[19,27]=0.1,s[19,28]=0.2,s[19,29]=0.7,s[19,30]=0.9,s[19,31]=0.4,s[19,32]=-0.1,s[19,33]=1.1,s[19,34]=-0.4,s[19,35]=0.3,s[19,36]=0.2,s[19,37]=0.6,s[19,38]=-0.3,s[19,39]=-0.5,s[19,40]=0.3,s[19,41]=0.1,s[19,42]=-0.2,s[19,43]=-0.5,s[19,44]=-0.8,s[19,45]=-0.4,s[19,46]=-0.1,s[19,47]=-0.6,s[19,48]=-0.4,s[19,49]=0.7,s[19,50]=1.1,s[19,51]=0.0,s[19,52]=-0.8,s[19,53]=0.1,s[19,54]=0.0,s[19,55]=-0.2,s[19,56]=0.7,s[19,57]=-1.0,s[19,58]=-0.8,s[19,59]=1.0,s[19,60]=-1.1
s[20,1]=0.3,s[20,2]=0.0,s[20,3]=0.7,s[20,4]=1.0,s[20,5]=-0.8,s[20,6]=0.6,s[20,7]=0.1,s[20,8]=-0.8,s[20,9]=-0.7,s[20,10]=0.7,s[20,11]=0.0,s[20,12]=0.6,s[20,13]=-0.1,s[20,14]=0.1,s[20,15]=-0.1,s[20,16]=-1.1,s[20,17]=0.5,s[20,18]=0.9,s[20,19]=-1.1,s[20,20]=-1.2,s[20,21]=0.6,s[20,22]=1.0,s[20,23]=0.9,s[20,24]=0.7,s[20,25]=-0.2,s[20,26]=-0.3,s[20,27]=1.0,s[20,28]=-0.2,s[20,29]=-0.7,s[20,30]=0.2,s[20,31]=0.2,s[20,32]=0.9,s[20,33]=0.2,s[20,34]=0.5,s[20,35]=1.1,s[20,36]=0.4,s[20,37]=-0.8,s[20,38]=-0.7,s[20,39]=1.2,s[20,40]=0.3,s[20,41]=0.5,s[20,42]=-0.9,s[20,43]=0.9,s[20,44]=0.4,s[20,45]=-0.3,s[20,46]=-1.1,s[20,47]=0.1,s[20,48]=0.9,s[20,49]=-0.1,s[20,50]=-0.9,s[20,51]=0.5,s[20,52]=0.3,s[20,53]=0.5,s[20,54]=-0.1,s[20,55]=-0.5,s[20,56]=-1.1,s[20,57]=-0.7,s[20,58]=-0.7,s[20,59]=-0.2,s[20,60]=0.2
s[21,1]=-0.2,s[21,2]=0.0,s[21,3]=0.9,s[21,4]=0.9,s[21,5]=-0.7,s[21,6]=-0.7,s[21,7]=1.2,s[21,8]=-0.2,s[21,9]=-1.0,s[21,10]=-0.7,s[21,11]=-0.4,s[21,12]=1.1,s[21,13]=1.1,s[21,14]=-1.2,s[21,15]=0.6,s[21,16]=0.3,s[21,17]=0.4,s[21,18]=-0.4,s[21,19]=-0.9,s[21,20]=1.0,s[21,21]=1.2,s[21,22]=0.3,s[21,23]=-1.2,s[21,24]=1.1,s[21,25]=0.8,s[21,26]=0.9,s[21,27]=-1.0,s[21,28]=0.6,s[21,29]=0.4,s[21,30]=-1.0,s[21,31]=0.1,s[21,32]=-0.3,s[21,33]=-0.1,s[21,34]=1.2,s[21,35]=-1.1,s[21,36]=-0.7,s[21,37]=1.0,s[21,38]=-1.1,s[21,39]=-0.5,s[21,40]=-1.2,s[21,41]=-0.9,s[21,42]=0.9,s[21,43]=0.1,s[21,44]=-0.6,s[21,45]=-1.2,s[21,46]=-0.1,s[21,47]=0.0,s[21,48]=-0.3,s[21,49]=1.0,s[21,50]=1.2,s[21,51]=-0.7,s[21,52]=0.0,s[21,53]=-0.1,s[21,54]=-0.8,s[21,55]=-0.9,s[21,56]=0.9,s[21,57]=-0.9,s[21,58]=1.2,s[21,59]=0.1,s[21,60]=-0.6
s[22,1]=-0.1,s[22,2]=-0.2,s[22,3]=-0.1,s[22,4]=-1.0,s[22,5]=0.6,s[22,6]=1.1,s[22,7]=0.1,s[22,8]=-0.5,s[22,9]=0.2,s[22,10]=0.5,s[22,11]=-0.1,s[22,12]=-1.1,s[22,13]=-0.3,s[22,14]=0.4,s[22,15]=0.5,s[22,16]=0.2,s[22,17]=-0.1,s[22,18]=1.0,s[22,19]=0.7,s[22,20]=-1.1,s[22,21]=-0.1,s[22,22]=0.9,s[22,23]=-0.7,s[22,24]=0.1,s[22,25]=-0.6,s[22,26]=-0.7,s[22,27]=-1.1,s[22,28]=-0.7,s[22,29]=-1.0,s[22,30]=-0.8,s[22,31]=0.0,s[22,32]=0.2,s[22,33]=1.2,s[22,34]=-0.8,s[22,35]=0.1,s[22,36]=-1.2,s[22,37]=0.5,s[22,38]=-0.1,s[22,39]=0.8,s[22,40]=0.3,s[22,41]=-0.6,s[22,42]=-1.2,s[22,43]=-0.1,s[22,44]=-0.2,s[22,45]=-0.8,s[22,46]=-0.2,s[22,47]=-0.7,s[22,48]=-0.1,s[22,49]=-0.6,s[22,50]=0.7,s[22,51]=-0.3,s[22,52]=0.6,s[22,53]=0.2,s[22,54]=1.1,s[22,55]=-1.2,s[22,56]=0.4,s[22,57]=0.6,s[22,58]=-0.3,s[22,59]=-0.4,s[22,60]=1.1
s[23,1]=-0.1,s[23,2]=0.0,s[23,3]=-0.8,s[23,4]=0.6,s[23,5]=-1.1,s[23,6]=-0.6,s[23,7]=-0.9,s[23,8]=-1.0,s[23,9]=1.2,s[23,10]=0.5,s[23,11]=-1.1,s[23,12]=-1.2,s[23,13]=-0.1,s[23,14]=-0.5,s[23,15]=0.0,s[23,16]=0.4,s[23,17]=0.3,s[23,18]=0.1,s[23,19]=0.9,s[23,20]=0.0,s[23,21]=-0.9,s[23,22]=-0.4,s[23,23]=1.2,s[23,24]=-0.7,s[23,25]=0.2,s[23,26]=0.4,s[23,27]=0.9,s[23,28]=-1.1,s[23,29]=0.1,s[23,30]=0.5,s[23,31]=-0.1,s[23,32]=-0.8,s[23,33]=-1.0,s[23,34]=0.8,s[23,35]=0.4,s[23,36]=1.2,s[23,37]=0.0,s[23,38]=-0.9,s[23,39]=0.5,s[23,40]=-1.0,s[23,41]=0.6,s[23,42]=1.1,s[23,43]=0.2,s[23,44]=1.0,s[23,45]=0.6,s[23,46]=-0.4,s[23,47]=0.1,s[23,48]=0.0,s[23,49]=-0.6,s[23,50]=-1.0,s[23,51]=0.4,s[23,52]=-0.2,s[23,53]=0.0,s[23,54]=-1.0,s[23,55]=-1.2,s[23,56]=-0.3,s[23,57]=0.3,s[23,58]=1.2,s[23,59]=0.3,s[23,60]=0.2
s[24,1]=-0.3,s[24,2]=0.1,s[24,3]=-0.1,s[24,4]=0.0,s[24,5]=-0.5,s[24,6]=-0.4,s[24,7]=-1.0,s[24,8]=0.0,s[24,9]=-1.0,s[24,10]=-0.9,s[24,11]=-0.6,s[24,12]=-0.3,s[24,13]=-0.8,s[24,14]=-0.3,s[24,15]=-1.0,s[24,16]=-0.1,s[24,17]=0.8,s[24,18]=-0.3,s[24,19]=0.9,s[24,20]=-0.4,s[24,21]=-0.1,s[24,22]=-0.4,s[24,23]=-0.4,s[24,24]=0.2,s[24,25]=-0.8,s[24,26]=0.0,s[24,27]=0.6,s[24,28]=0.8,s[24,29]=-0.7,s[24,30]=0.0,s[24,31]=0.3,s[24,32]=1.1,s[24,33]=-0.3,s[24,34]=-0.1,s[24,35]=-0.6,s[24,36]=-1.0,s[24,37]=-0.9,s[24,38]=-0.3,s[24,39]=-1.1,s[24,40]=-0.9,s[24,41]=0.2,s[24,42]=0.0,s[24,43]=-0.5,s[24,44]=0.5,s[24,45]=-0.5,s[24,46]=-0.5,s[24,47]=-0.3,s[24,48]=-0.4,s[24,49]=0.9,s[24,50]=1.1,s[24,51]=0.2,s[24,52]=-0.2,s[24,53]=-0.9,s[24,54]=0.2,s[24,55]=0.7,s[24,56]=-0.2,s[24,57]=0.0,s[24,58]=0.7,s[24,59]=-0.7,s[24,60]=0.1
s[25,1]=0.3,s[25,2]=0.8,s[25,3]=-1.2,s[25,4]=1.0,s[25,5]=-0.4,s[25,6]=-0.7,s[25,7]=-0.6,s[25,8]=1.1,s[25,9]=-0.3,s[25,10]=0.9,s[25,11]=-0.5,s[25,12]=-0.2,s[25,13]=-0.2,s[25,14]=-0.1,s[25,15]=-0.7,s[25,16]=0.5,s[25,17]=-0.3,s[25,18]=-0.4,s[25,19]=0.5,s[25,20]=-0.5,s[25,21]=0.3,s[25,22]=-0.3,s[25,23]=-0.9,s[25,24]=0.7,s[25,25]=0.5,s[25,26]=0.9,s[25,27]=0.5,s[25,28]=-0.2,s[25,29]=-0.6,s[25,30]=-1.0,s[25,31]=0.2,s[25,32]=0.9,s[25,33]=-0.4,s[25,34]=-0.7,s[25,35]=-0.6,s[25,36]=-1.2,s[25,37]=-0.3,s[25,38]=0.3,s[25,39]=-1.0,s[25,40]=1.0,s[25,41]=0.7,s[25,42]=0.4,s[25,43]=-0.4,s[25,44]=-0.6,s[25,45]=0.0,s[25,46]=0.0,s[25,47]=0.1,s[25,48]=0.9,s[25,49]=0.0,s[25,50]=0.1,s[25,51]=-0.3,s[25,52]=-0.4,s[25,53]=1.1,s[25,54]=-0.3,s[25,55]=-1.2,s[25,56]=-0.8,s[25,57]=0.7,s[25,58]=0.9,s[25,59]=-0.7,s[25,60]=0.7
s[26,1]=-0.1,s[26,2]=-1.0,s[26,3]=-0.9,s[26,4]=-1.1,s[26,5]=1.2,s[26,6]=-1.1,s[26,7]=-0.5,s[26,8]=-0.2,s[26,9]=0.4,s[26,10]=-0.1,s[26,11]=0.4,s[26,12]=-0.6,s[26,13]=0.9,s[26,14]=-1.2,s[26,15]=0.0,s[26,16]=-0.1,s[26,17]=0.0,s[26,18]=0.7,s[26,19]=-1.1,s[26,20]=-0.9,s[26,21]=-1.1,s[26,22]=-0.1,s[26,23]=-0.1,s[26,24]=0.7,s[26,25]=-0.6,s[26,26]=-0.7,s[26,27]=0.8,s[26,28]=0.0,s[26,29]=0.0,s[26,30]=1.1,s[26,31]=0.5,s[26,32]=-0.1,s[26,33]=0.9,s[26,34]=-0.8,s[26,35]=-1.0,s[26,36]=-0.1,s[26,37]=1.2,s[26,38]=0.4,s[26,39]=-1.1,s[26,40]=0.1,s[26,41]=0.0,s[26,42]=0.5,s[26,43]=0.7,s[26,44]=0.3,s[26,45]=-0.8,s[26,46]=0.1,s[26,47]=-0.3,s[26,48]=0.2,s[26,49]=1.2,s[26,50]=0.4,s[26,51]=0.5,s[26,52]=1.2,s[26,53]=0.8,s[26,54]=1.1,s[26,55]=0.6,s[26,56]=0.6,s[26,57]=-1.0,s[26,58]=-0.7,s[26,59]=0.0,s[26,60]=-0.7
s[27,1]=0.2,s[27,2]=-0.8,s[27,3]=0.3,s[27,4]=-0.7,s[27,5]=0.7,s[27,6]=-0.6,s[27,7]=0.0,s[27,8]=1.0,s[27,9]=-0.1,s[27,10]=1.1,s[27,11]=1.0,s[27,12]=0.9,s[27,13]=-0.4,s[27,14]=0.6,s[27,15]=-0.1,s[27,16]=-0.2,s[27,17]=-1.0,s[27,18]=0.2,s[27,19]=0.0,s[27,20]=-0.6,s[27,21]=0.9,s[27,22]=-1.1,s[27,23]=-1.2,s[27,24]=0.8,s[27,25]=-0.6,s[27,26]=0.3,s[27,27]=-0.6,s[27,28]=0.7,s[27,29]=0.2,s[27,30]=-1.1,s[27,31]=0.2,s[27,32]=-0.4,s[27,33]=0.7,s[27,34]=-0.5,s[27,35]=-0.5,s[27,36]=0.2,s[27,37]=0.2,s[27,38]=-0.5,s[27,39]=-0.3,s[27,40]=1.1,s[27,41]=0.1,s[27,42]=-0.3,s[27,43]=-1.1,s[27,44]=-0.2,s[27,45]=-0.2,s[27,46]=0.1,s[27,47]=-1.0,s[27,48]=0.8,s[27,49]=-0.5,s[27,50]=0.8,s[27,51]=0.5,s[27,52]=-0.8,s[27,53]=-0.4,s[27,54]=0.5,s[27,55]=1.0,s[27,56]=-0.1,s[27,57]=1.1,s[27,58]=-0.8,s[27,59]=-0.3,s[27,60]=0.3
s[28,1]=0.1,s[28,2]=0.7,s[28,3]=-0.9,s[28,4]=0.0,s[28,5]=0.0,s[28,6]=1.2,s[28,7]=-0.5,s[28,8]=0.8,s[28,9]=-0.4,s[28,10]=-0.6,s[28,11]=-1.1,s[28,12]=-0.1,s[28,13]=-0.7,s[28,14]=0.4,s[28,15]=0.6,s[28,16]=0.1,s[28,17]=-0.9,s[28,18]=1.1,s[28,19]=-1.0,s[28,20]=0.5,s[28,21]=0.2,s[28,22]=0.2,s[28,23]=0.3,s[28,24]=1.0,s[28,25]=-0.8,s[28,26]=-1.1,s[28,27]=0.7,s[28,28]=-1.1,s[28,29]=-0.3,s[28,30]=-0.4,s[28,31]=-0.2,s[28,32]=0.8,s[28,33]=1.2,s[28,34]=-0.7,s[28,35]=-0.2,s[28,36]=-0.3,s[28,37]=-1.0,s[28,38]=1.2,s[28,39]=0.8,s[28,40]=0.8,s[28,41]=0.7,s[28,42]=0.7,s[28,43]=-0.7,s[28,44]=0.0,s[28,45]=0.1,s[28,46]=-0.6,s[28,47]=0.4,s[28,48]=1.1,s[28,49]=-0.9,s[28,50]=-1.1,s[28,51]=-1.0,s[28,52]=0.5,s[28,53]=-1.1,s[28,54]=1.2,s[28,55]=-0.2,s[28,56]=0.1,s[28,57]=-0.7,s[28,58]=1.0,s[28,59]=0.2,s[28,60]=-0.2
s[29,1]=-0.4,s[29,2]=-0.7,s[29,3]=-0.4,s[29,4]=0.8,s[29,5]=-0.1,s[29,6]=0.6,s[29,7]=0.4,s[29,8]=-0.3,s[29,9]=0.2,s[29,10]=-0.8,s[29,11]=-0.2,s[29,12]=-0.9,s[29,13]=-1.2,s[29,14]=-0.4,s[29,15]=-0.8,s[29,16]=0.0,s[29,17]=0.0,s[29,18]=1.1,s[29,19]=0.8,s[29,20]=1.0,s[29,21]=0.6,s[29,22]=0.8,s[29,23]=0.0,s[29,24]=-1.0,s[29,25]=0.5,s[29,26]=1.2,s[29,27]=-1.2,s[29,28]=-0.8,s[29,29]=-0.6,s[29,30]=1.0,s[29,31]=-0.5,s[29,32]=0.6,s[29,33]=1.2,s[29,34]=0.1,s[29,35]=-0.8,s[29,36]=1.0,s[29,37]=0.0,s[29,38]=0.5,s[29,39]=1.2,s[29,40]=0.3,s[29,41]=-0.2,s[29,42]=0.9,s[29,43]=-0.2,s[29,44]=0.0,s[29,45]=-0.1,s[29,46]=-0.2,s[29,47]=0.1,s[29,48]=-0.2,s[29,49]=-0.6,s[29,50]=0.0,s[29,51]=-0.9,s[29,52]=-0.6,s[29,53]=0.3,s[29,54]=-0.4,s[29,55]=-1.0,s[29,56]=-1.1,s[29,57]=-1.1,s[29,58]=0.1,s[29,59]=-0.6,s[29,60]=-0.3
s[30,1]=-0.3,s[30,2]=-0.1,s[30,3]=1.0,s[30,4]=-0.8,s[30,5]=-1.2,s[30,6]=1.0,s[30,7]=-0.6,s[30,8]=0.0,s[30,9]=0.8,s[30,10]=-0.4,s[30,11]=-0.4,s[30,12]=0.9,s[30,13]=0.8,s[30,14]=-0.2,s[30,15]=0.5,s[30,16]=-0.2,s[30,17]=-0.9,s[30,18]=-0.4,s[30,19]=-0.1,s[30,20]=-0.9,s[30,21]=0.3,s[30,22]=0.7,s[30,23]=-0.6,s[30,24]=1.2,s[30,25]=0.2,s[30,26]=0.2,s[30,27]=-0.4,s[30,28]=-1.1,s[30,29]=1.0,s[30,30]=0.9,s[30,31]=0.2,s[30,32]=-0.5,s[30,33]=-0.4,s[30,34]=0.0,s[30,35]=1.0,s[30,36]=1.1,s[30,37]=0.0,s[30,38]=-0.4,s[30,39]=-0.2,s[30,40]=1.1,s[30,41]=0.3,s[30,42]=0.8,s[30,43]=-0.6,s[30,44]=-0.7,s[30,45]=0.1,s[30,46]=0.1,s[30,47]=0.7,s[30,48]=0.4,s[30,49]=0.8,s[30,50]=0.8,s[30,51]=0.5,s[30,52]=-0.9,s[30,53]=0.8,s[30,54]=0.3,s[30,55]=-1.0,s[30,56]=-0.1,s[30,57]=0.6,s[30,58]=0.8,s[30,59]=-1.0,s[30,60]=1.2
s[31,1]=0.0,s[31,2]=0.8,s[31,3]=0.2,s[31,4]=-0.2,s[31,5]=0.4,s[31,6]=-0.1,s[31,7]=0.0,s[31,8]=-1.0,s[31,9]=1.0,s[31,10]=0.2,s[31,11]=0.3,s[31,12]=-1.0,s[31,13]=0.0,s[31,14]=1.0,s[31,15]=1.2,s[31,16]=-0.2,s[31,17]=1.2,s[31,18]=1.2,s[31,19]=-0.9,s[31,20]=-0.2,s[31,21]=0.7,s[31,22]=0.2,s[31,23]=-0.1,s[31,24]=-0.7,s[31,25]=-0.9,s[31,26]=0.6,s[31,27]=-0.3,s[31,28]=1.1,s[31,29]=1.1,s[31,30]=0.9,s[31,31]=0.8,s[31,32]=0.4,s[31,33]=0.1,s[31,34]=0.8,s[31,35]=0.8,s[31,36]=0.1,s[31,37]=-1.1,s[31,38]=0.8,s[31,39]=0.5,s[31,40]=0.2,s[31,41]=-0.9,s[31,42]=0.1,s[31,43]=0.7,s[31,44]=-1.0,s[31,45]=-0.6,s[31,46]=-0.1,s[31,47]=-0.7,s[31,48]=-0.1,s[31,49]=1.1,s[31,50]=0.2,s[31,51]=0.6,s[31,52]=0.2,s[31,53]=1.1,s[31,54]=-1.1,s[31,55]=-0.4,s[31,56]=0.0,s[31,57]=0.8,s[31,58]=1.2,s[31,59]=0.2,s[31,60]=-1.0
s[32,1]=0.1,s[32,2]=1.2,s[32,3]=0.8,s[32,4]=-0.7,s[32,5]=-0.8,s[32,6]=0.1,s[32,7]=0.1,s[32,8]=0.2,s[32,9]=0.0,s[32,10]=0.9,s[32,11]=0.3,s[32,12]=-0.4,s[32,13]=1.2,s[32,14]=0.4,s[32,15]=0.6,s[32,16]=0.2,s[32,17]=0.3,s[32,18]=-0.3,s[32,19]=-1.0,s[32,20]=-0.6,s[32,21]=-0.8,s[32,22]=-0.3,s[32,23]=1.0,s[32,24]=-0.5,s[32,25]=0.1,s[32,26]=-0.8,s[32,27]=1.0,s[32,28]=-0.6,s[32,29]=-0.9,s[32,30]=-1.2,s[32,31]=-0.1,s[32,32]=-0.1,s[32,33]=0.8,s[32,34]=1.0,s[32,35]=0.2,s[32,36]=-0.1,s[32,37]=0.2,s[32,38]=-0.1,s[32,39]=-1.2,s[32,40]=1.1,s[32,41]=-0.7,s[32,42]=-0.2,s[32,43]=0.0,s[32,44]=-0.1,s[32,45]=0.8,s[32,46]=0.0,s[32,47]=-0.3,s[32,48]=-0.5,s[32,49]=-0.9,s[32,50]=0.7,s[32,51]=0.4,s[32,52]=0.1,s[32,53]=-0.4,s[32,54]=-0.1,s[32,55]=1.0,s[32,56]=0.5,s[32,57]=-0.5,s[32,58]=-0.7,s[32,59]=-0.1,s[32,60]=-0.7
s[33,1]=-0.3,s[33,2]=-0.1,s[33,3]=0.0,s[33,4]=-0.8,s[33,5]=0.6,s[33,6]=-1.0,s[33,7]=-0.7,s[33,8]=0.3,s[33,9]=-0.5,s[33,10]=-1.1,s[33,11]=0.0,s[33,12]=0.9,s[33,13]=-1.0,s[33,14]=-0.2,s[33,15]=-0.3,s[33,16]=-0.2,s[33,17]=-0.2,s[33,18]=0.6,s[33,19]=-0.1,s[33,20]=-1.2,s[33,21]=0.4,s[33,22]=-0.7,s[33,23]=0.5,s[33,24]=0.1,s[33,25]=-0.9,s[33,26]=0.2,s[33,27]=1.0,s[33,28]=-0.5,s[33,29]=-0.5,s[33,30]=-0.7,s[33,31]=-0.5,s[33,32]=0.5,s[33,33]=-0.9,s[33,34]=0.8,s[33,35]=0.8,s[33,36]=-0.7,s[33,37]=-0.9,s[33,38]=0.8,s[33,39]=-0.2,s[33,40]=-0.3,s[33,41]=-0.2,s[33,42]=0.0,s[33,43]=-0.1,s[33,44]=0.7,s[33,45]=1.0,s[33,46]=0.0,s[33,47]=0.5,s[33,48]=0.3,s[33,49]=-0.5,s[33,50]=-0.6,s[33,51]=0.9,s[33,52]=-0.1,s[33,53]=0.7,s[33,54]=-0.7,s[33,55]=-0.2,s[33,56]=-0.6,s[33,57]=-1.1,s[33,58]=-0.4,s[33,59]=-0.5,s[33,60]=0.6
s[34,1]=-0.1,s[34,2]=1.0,s[34,3]=0.3,s[34,4]=-0.5,s[34,5]=1.1,s[34,6]=-1.1,s[34,7]=1.1,s[34,8]=1.1,s[34,9]=-0.7,s[34,10]=1.0,s[34,11]=-0.4,s[34,12]=0.6,s[34,13]=-1.1,s[34,14]=0.0,s[34,15]=0.7,s[34,16]=0.1,s[34,17]=-0.1,s[34,18]=-0.9,s[34,19]=-0.4,s[34,20]=0.4,s[34,21]=-0.3,s[34,22]=-0.8,s[34,23]=1.0,s[34,24]=0.0,s[34,25]=-0.5,s[34,26]=0.7,s[34,27]=1.0,s[34,28]=-0.5,s[34,29]=-1.2,s[34,30]=0.2,s[34,31]=0.6,s[34,32]=1.1,s[34,33]=1.2,s[34,34]=-0.8,s[34,35]=-0.4,s[34,36]=0.6,s[34,37]=-0.3,s[34,38]=0.7,s[34,39]=-1.2,s[34,40]=0.5,s[34,41]=0.2,s[34,42]=0.4,s[34,43]=-1.2,s[34,44]=-1.0,s[34,45]=-0.9,s[34,46]=0.4,s[34,47]=0.3,s[34,48]=1.2,s[34,49]=0.9,s[34,50]=0.0,s[34,51]=0.5,s[34,52]=0.4,s[34,53]=-0.1,s[34,54]=-0.8,s[34,55]=0.8,s[34,56]=0.1,s[34,57]=-0.7,s[34,58]=-0.6,s[34,59]=-0.3,s[34,60]=1.1
s[35,1]=-0.7,s[35,2]=-0.7,s[35,3]=-0.2,s[35,4]=-1.1,s[35,5]=0.1,s[35,6]=-0.4,s[35,7]=1.0,s[35,8]=-1.0,s[35,9]=1.2,s[35,10]=-0.4,s[35,11]=-1.0,s[35,12]=-0.5,s[35,13]=-0.3,s[35,14]=-0.1,s[35,15]=0.9,s[35,16]=-0.1,s[35,17]=1.0,s[35,18]=0.9,s[35,19]=-1.0,s[35,20]=0.5,s[35,21]=1.1,s[35,22]=-0.4,s[35,23]=1.2,s[35,24]=-1.0,s[35,25]=-0.6,s[35,26]=-0.4,s[35,27]=-0.2,s[35,28]=-1.2,s[35,29]=-0.1,s[35,30]=-0.5,s[35,31]=0.0,s[35,32]=-1.0,s[35,33]=-0.9,s[35,34]=1.0,s[35,35]=0.3,s[35,36]=0.3,s[35,37]=-0.5,s[35,38]=0.3,s[35,39]=-0.6,s[35,40]=-0.9,s[35,41]=0.2,s[35,42]=-0.2,s[35,43]=0.4,s[35,44]=1.0,s[35,45]=0.7,s[35,46]=-0.6,s[35,47]=0.6,s[35,48]=-0.1,s[35,49]=-0.6,s[35,50]=0.5,s[35,51]=0.1,s[35,52]=0.7,s[35,53]=1.1,s[35,54]=-1.2,s[35,55]=-1.1,s[35,56]=0.8,s[35,57]=-1.1,s[35,58]=0.1,s[35,59]=-1.0,s[35,60]=0.1
s[36,1]=0.3,s[36,2]=-0.4,s[36,3]=0.5,s[36,4]=0.4,s[36,5]=0.8,s[36,6]=0.5,s[36,7]=0.4,s[36,8]=1.0,s[36,9]=0.7,s[36,10]=0.1,s[36,11]=0.9,s[36,12]=-0.9,s[36,13]=1.0,s[36,14]=-0.2,s[36,15]=-0.9,s[36,16]=-0.6,s[36,17]=-0.1,s[36,18]=-0.2,s[36,19]=-0.7,s[36,20]=-0.9,s[36,21]=-0.3,s[36,22]=-1.0,s[36,23]=-1.0,s[36,24]=0.9,s[36,25]=-0.8,s[36,26]=0.3,s[36,27]=-1.1,s[36,28]=1.0,s[36,29]=0.3,s[36,30]=0.5,s[36,31]=0.4,s[36,32]=-0.4,s[36,33]=0.2,s[36,34]=0.3,s[36,35]=-0.3,s[36,36]=0.9,s[36,37]=-0.7,s[36,38]=-1.0,s[36,39]=-0.2,s[36,40]=-0.1,s[36,41]=0.1,s[36,42]=-0.6,s[36,43]=-0.5,s[36,44]=0.2,s[36,45]=0.0,s[36,46]=0.2,s[36,47]=0.1,s[36,48]=0.5,s[36,49]=-0.3,s[36,50]=-0.3,s[36,51]=1.2,s[36,52]=1.1,s[36,53]=0.6,s[36,54]=0.3,s[36,55]=0.6,s[36,56]=0.2,s[36,57]=-0.8,s[36,58]=-0.5,s[36,59]=-0.3,s[36,60]=1.1
s[37,1]=0.2,s[37,2]=0.2,s[37,3]=-0.6,s[37,4]=0.3,s[37,5]=0.5,s[37,6]=1.1,s[37,7]=1.2,s[37,8]=-0.2,s[37,9]=-1.1,s[37,10]=-1.2,s[37,11]=0.5,s[37,12]=0.8,s[37,13]=0.5,s[37,14]=0.6,s[37,15]=-0.7,s[37,16]=-0.3,s[37,17]=1.0,s[37,18]=0.8,s[37,19]=-0.2,s[37,20]=1.0,s[37,21]=-0.3,s[37,22]=0.8,s[37,23]=-1.1,s[37,24]=-1.0,s[37,25]=0.4,s[37,26]=0.4,s[37,27]=-0.6,s[37,28]=-0.3,s[37,29]=1.0,s[37,30]=-0.8,s[37,31]=0.1,s[37,32]=-1.1,s[37,33]=0.7,s[37,34]=0.0,s[37,35]=0.5,s[37,36]=-1.1,s[37,37]=-0.4,s[37,38]=0.4,s[37,39]=-0.6,s[37,40]=0.4,s[37,41]=-0.9,s[37,42]=-0.6,s[37,43]=-0.3,s[37,44]=0.5,s[37,45]=-1.1,s[37,46]=0.2,s[37,47]=-0.8,s[37,48]=0.9,s[37,49]=1.2,s[37,50]=0.5,s[37,51]=-0.2,s[37,52]=-1.2,s[37,53]=-0.3,s[37,54]=0.4,s[37,55]=-0.3,s[37,56]=-0.1,s[37,57]=0.4,s[37,58]=0.7,s[37,59]=0.0,s[37,60]=-0.9
s[38,1]=0.4,s[38,2]=-0.4,s[38,3]=-0.3,s[38,4]=-1.1,s[38,5]=0.7,s[38,6]=0.0,s[38,7]=-0.1,s[38,8]=-0.6,s[38,9]=0.2,s[38,10]=0.3,s[38,11]=-0.8,s[38,12]=0.6,s[38,13]=-1.1,s[38,14]=0.7,s[38,15]=0.8,s[38,16]=0.1,s[38,17]=-0.3,s[38,18]=0.4,s[38,19]=1.2,s[38,20]=-0.8,s[38,21]=-0.7,s[38,22]=0.2,s[38,23]=0.3,s[38,24]=-0.7,s[38,25]=0.6,s[38,26]=-0.3,s[38,27]=0.7,s[38,28]=0.5,s[38,29]=-1.1,s[38,30]=1.0,s[38,31]=0.4,s[38,32]=1.1,s[38,33]=-0.2,s[38,34]=-1.0,s[38,35]=-0.4,s[38,36]=-0.3,s[38,37]=0.5,s[38,38]=-0.8,s[38,39]=0.0,s[38,40]=0.6,s[38,41]=-0.5,s[38,42]=0.9,s[38,43]=0.1,s[38,44]=0.5,s[38,45]=-1.2,s[38,46]=0.5,s[38,47]=0.0,s[38,48]=1.1,s[38,49]=0.7,s[38,50]=0.6,s[38,51]=0.3,s[38,52]=-0.2,s[38,53]=-1.2,s[38,54]=0.1,s[38,55]=-0.5,s[38,56]=-0.1,s[38,57]=-0.3,s[38,58]=-0.2,s[38,59]=0.3,s[38,60]=-1.2
s[39,1]=-0.7,s[39,2]=-0.6,s[39,3]=0.9,s[39,4]=-0.5,s[39,5]=-0.2,s[39,6]=0.9,s[39,7]=0.8,s[39,8]=0.4,s[39,9]=-0.8,s[39,10]=-0.8,s[39,11]=-0.6,s[39,12]=0.9,s[39,13]=-1.2,s[39,14]=0.0,s[39,15]=1.1,s[39,16]=0.2,s[39,17]=0.9,s[39,18]=1.0,s[39,19]=-0.6,s[39,20]=-0.5,s[39,21]=-0.3,s[39,22]=-1.0,s[39,23]=1.1,s[39,24]=0.4,s[39,25]=-0.7,s[39,26]=0.4,s[39,27]=-0.9,s[39,28]=0.1,s[39,29]=0.3,s[39,30]=-0.1,s[39,31]=0.1,s[39,32]=-0.6,s[39,33]=-0.1,s[39,34]=0.9,s[39,35]=1.2,s[39,36]=-0.7,s[39,37]=0.1,s[39,38]=0.5,s[39,39]=0.0,s[39,40]=-1.0,s[39,41]=1.0,s[39,42]=-0.5,s[39,43]=-1.0,s[39,44]=0.3,s[39,45]=-0.2,s[39,46]=0.6,s[39,47]=0.4,s[39,48]=0.6,s[39,49]=-0.4,s[39,50]=1.1,s[39,51]=0.8,s[39,52]=-1.2,s[39,53]=-1.2,s[39,54]=0.2,s[39,55]=-0.8,s[39,56]=-0.1,s[39,57]=-0.5,s[39,58]=-0.3,s[39,59]=0.6,s[39,60]=-0.5
s[40,1]=-0.3,s[40,2]=0.1,s[40,3]=0.0,s[40,4]=-0.5,s[40,5]=-1.0,s[40,6]=-1.0,s[40,7]=-1.0,s[40,8]=-0.4,s[40,9]=-0.8,s[40,10]=1.1,s[40,11]=-0.8,s[40,12]=0.6,s[40,13]=0.6,s[40,14]=-0.8,s[40,15]=0.7,s[40,16]=-0.3,s[40,17]=-0.2,s[40,18]=1.2,s[40,19]=-0.5,s[40,20]=-1.2,s[40,21]=1.1,s[40,22]=0.4,s[40,23]=-0.2,s[40,24]=1.0,s[40,25]=-0.8,s[40,26]=-0.6,s[40,27]=0.3,s[40,28]=-1.0,s[40,29]=-0.5,s[40,30]=0.9,s[40,31]=0.1,s[40,32]=-1.0,s[40,33]=0.9,s[40,34]=-0.8,s[40,35]=0.7,s[40,36]=1.0,s[40,37]=0.3,s[40,38]=-1.2,s[40,39]=0.2,s[40,40]=-1.1,s[40,41]=-0.3,s[40,42]=-0.7,s[40,43]=-0.9,s[40,44]=-0.1,s[40,45]=0.2,s[40,46]=0.7,s[40,47]=0.9,s[40,48]=-0.8,s[40,49]=-1.0,s[40,50]=-0.7,s[40,51]=-0.6,s[40,52]=-0.9,s[40,53]=-0.3,s[40,54]=1.1,s[40,55]=-0.7,s[40,56]=0.8,s[40,57]=-0.6,s[40,58]=-0.1,s[40,59]=-1.1,s[40,60]=0.4
s[41,1]=0.1,s[41,2]=0.5,s[41,3]=-0.3,s[41,4]=1.1,s[41,5]=-0.4,s[41,6]=-1.0,s[41,7]=-0.1,s[41,8]=0.3,s[41,9]=1.2,s[41,10]=0.9,s[41,11]=0.1,s[41,12]=-0.2,s[41,13]=-0.4,s[41,14]=0.6,s[41,15]=-0.3,s[41,16]=-1.0,s[41,17]=0.7,s[41,18]=0.2,s[41,19]=-0.4,s[41,20]=0.5,s[41,21]=0.6,s[41,22]=0.3,s[41,23]=0.7,s[41,24]=-0.1,s[41,25]=0.6,s[41,26]=0.8,s[41,27]=0.6,s[41,28]=-1.2,s[41,29]=-0.3,s[41,30]=0.3,s[41,31]=-0.3,s[41,32]=-0.6,s[41,33]=0.8,s[41,34]=0.0,s[41,35]=0.6,s[41,36]=-0.4,s[41,37]=0.1,s[41,38]=0.3,s[41,39]=-0.2,s[41,40]=0.0,s[41,41]=0.1,s[41,42]=0.7,s[41,43]=-0.6,s[41,44]=-0.3,s[41,45]=0.2,s[41,46]=-0.5,s[41,47]=0.3,s[41,48]=0.9,s[41,49]=-0.5,s[41,50]=-1.0,s[41,51]=-0.8,s[41,52]=0.2,s[41,53]=0.0,s[41,54]=-0.4,s[41,55]=0.8,s[41,56]=0.2,s[41,57]=0.9,s[41,58]=0.8,s[41,59]=0.9,s[41,60]=-0.6
s[42,1]=0.0,s[42,2]=-0.3,s[42,3]=-0.5,s[42,4]=-0.6,s[42,5]=-1.1,s[42,6]=0.6,s[42,7]=-0.6,s[42,8]=-0.1,s[42,9]=1.0,s[42,10]=-1.2,s[42,11]=0.2,s[42,12]=0.2,s[42,13]=0.1,s[42,14]=-1.2,s[42,15]=0.0,s[42,16]=-0.1,s[42,17]=0.4,s[42,18]=-1.1,s[42,19]=0.3,s[42,20]=0.9,s[42,21]=0.7,s[42,22]=-0.5,s[42,23]=-1.0,s[42,24]=0.4,s[42,25]=-0.2,s[42,26]=0.0,s[42,27]=0.4,s[42,28]=0.2,s[42,29]=-0.1,s[42,30]=0.9,s[42,31]=-0.4,s[42,32]=-0.4,s[42,33]=-0.7,s[42,34]=0.7,s[42,35]=0.5,s[42,36]=0.3,s[42,37]=-0.2,s[42,38]=0.9,s[42,39]=0.7,s[42,40]=-0.7,s[42,41]=-0.5,s[42,42]=-1.2,s[42,43]=0.9,s[42,44]=-0.9,s[42,45]=-1.2,s[42,46]=-0.1,s[42,47]=0.1,s[42,48]=-0.1,s[42,49]=1.1,s[42,50]=0.6,s[42,51]=0.2,s[42,52]=-0.5,s[42,53]=0.6,s[42,54]=-0.5,s[42,55]=-0.9,s[42,56]=0.3,s[42,57]=-1.2,s[42,58]=1.1,s[42,59]=-0.5,s[42,60]=0.1
s[43,1]=-0.1,s[43,2]=1.0,s[43,3]=-1.2,s[43,4]=0.9,s[43,5]=0.4,s[43,6]=0.3,s[43,7]=0.8,s[43,8]=-0.6,s[43,9]=0.4,s[43,10]=0.4,s[43,11]=-0.7,s[43,12]=1.0,s[43,13]=0.9,s[43,14]=-0.1,s[43,15]=1.2,s[43,16]=-0.1,s[43,17]=0.3,s[43,18]=-0.5,s[43,19]=-0.2,s[43,20]=1.2,s[43,21]=-1.0,s[43,22]=-0.5,s[43,23]=0.4,s[43,24]=-0.4,s[43,25]=-1.2,s[43,26]=-0.4,s[43,27]=0.9,s[43,28]=-1.0,s[43,29]=-1.0,s[43,30]=-0.8,s[43,31]=-0.5,s[43,32]=0.7,s[43,33]=-0.7,s[43,34]=-0.6,s[43,35]=0.0,s[43,36]=-0.9,s[43,37]=0.1,s[43,38]=1.0,s[43,39]=-0.6,s[43,40]=0.9,s[43,41]=-0.9,s[43,42]=1.0,s[43,43]=0.9,s[43,44]=0.5,s[43,45]=0.4,s[43,46]=0.6,s[43,47]=0.1,s[43,48]=-1.0,s[43,49]=-0.9,s[43,50]=-0.2,s[43,51]=-0.7,s[43,52]=-0.4,s[43,53]=-0.8,s[43,54]=0.2,s[43,55]=0.8,s[43,56]=0.0,s[43,57]=0.3,s[43,58]=0.9,s[43,59]=-0.3,s[43,60]=-0.3
s[44,1]=0.3,s[44,2]=-0.1,s[44,3]=0.2,s[44,4]=-1.1,s[44,5]=0.2,s[44,6]=-1.0,s[44,7]=0.2,s[44,8]=0.3,s[44,9]=0.2,s[44,10]=-1.2,s[44,11]=0.1,s[44,12]=-0.2,s[44,13]=-0.1,s[44,14]=0.5,s[44,15]=0.2,s[44,16]=0.1,s[44,17]=-1.2,s[44,18]=-1.1,s[44,19]=0.9,s[44,20]=0.5,s[44,21]=0.1,s[44,22]=-0.8,s[44,23]=1.2,s[44,24]=-0.3,s[44,25]=-0.3,s[44,26]=1.0,s[44,27]=0.2,s[44,28]=-1.2,s[44,29]=0.0,s[44,30]=0.9,s[44,31]=0.5,s[44,32]=-0.1,s[44,33]=1.1,s[44,34]=-1.2,s[44,35]=-1.2,s[44,36]=0.4,s[44,37]=-0.4,s[44,38]=-0.5,s[44,39]=1.0,s[44,40]=0.8,s[44,41]=0.5,s[44,42]=-0.4,s[44,43]=0.6,s[44,44]=-1.1,s[44,45]=0.5,s[44,46]=0.1,s[44,47]=0.4,s[44,48]=1.2,s[44,49]=0.8,s[44,50]=-1.1,s[44,51]=-0.9,s[44,52]=0.1,s[44,53]=0.0,s[44,54]=-0.9,s[44,55]=-1.0,s[44,56]=-0.7,s[44,57]=0.1,s[44,58]=-1.1,s[44,59]=0.7,s[44,60]=-0.6
s[45,1]=0.3,s[45,2]=-0.8,s[45,3]=0.7,s[45,4]=-0.1,s[45,5]=1.1,s[45,6]=-0.3,s[45,7]=0.6,s[45,8]=1.0,s[45,9]=1.0,s[45,10]=0.3,s[45,11]=0.4,s[45,12]=-0.5,s[45,13]=-1.1,s[45,14]=-0.1,s[45,15]=0.4,s[45,16]=0.0,s[45,17]=-0.7,s[45,18]=-1.0,s[45,19]=-0.8,s[45,20]=1.2,s[45,21]=0.1,s[45,22]=0.0,s[45,23]=-0.6,s[45,24]=-1.0,s[45,25]=0.8,s[45,26]=0.6,s[45,27]=0.1,s[45,28]=-0.3,s[45,29]=0.5,s[45,30]=0.3,s[45,31]=-0.1,s[45,32]=0.6,s[45,33]=0.3,s[45,34]=-0.4,s[45,35]=-0.4,s[45,36]=-0.3,s[45,37]=-0.8,s[45,38]=0.4,s[45,39]=1.0,s[45,40]=-0.6,s[45,41]=-0.1,s[45,42]=0.1,s[45,43]=1.0,s[45,44]=-0.1,s[45,45]=-0.7,s[45,46]=0.6,s[45,47]=-1.2,s[45,48]=-0.3,s[45,49]=0.1,s[45,50]=-0.4,s[45,51]=-0.4,s[45,52]=1.0,s[45,53]=-0.4,s[45,54]=1.1,s[45,55]=0.4,s[45,56]=-0.1,s[45,57]=-1.1,s[45,58]=-0.5,s[45,59]=0.6,s[45,60]=-0.6
s[46,1]=-0.3,s[46,2]=0.0,s[46,3]=1.1,s[46,4]=-0.1,s[46,5]=-1.2,s[46,6]=1.2,s[46,7]=0.5,s[46,8]=-1.0,s[46,9]=-1.0,s[46,10]=-0.1,s[46,11]=-0.4,s[46,12]=-0.3,s[46,13]=0.0,s[46,14]=-0.3,s[46,15]=0.7,s[46,16]=-0.1,s[46,17]=-0.2,s[46,18]=-0.8,s[46,19]=-0.8,s[46,20]=-0.5,s[46,21]=-0.6,s[46,22]=-0.1,s[46,23]=0.7,s[46,24]=-0.4,s[46,25]=-0.7,s[46,26]=-0.3,s[46,27]=-0.1,s[46,28]=0.1,s[46,29]=-0.7,s[46,30]=-0.5,s[46,31]=0.6,s[46,32]=0.7,s[46,33]=-0.7,s[46,34]=-0.7,s[46,35]=1.2,s[46,36]=1.1,s[46,37]=0.6,s[46,38]=-0.7,s[46,39]=-1.1,s[46,40]=-0.8,s[46,41]=0.1,s[46,42]=-0.4,s[46,43]=-0.9,s[46,44]=0.5,s[46,45]=0.2,s[46,46]=0.0,s[46,47]=-1.2,s[46,48]=-0.8,s[46,49]=-0.9,s[46,50]=-0.5,s[46,51]=1.2,s[46,52]=1.2,s[46,53]=-0.4,s[46,54]=-0.5,s[46,55]=-1.0,s[46,56]=-0.6,s[46,57]=1.2,s[46,58]=0.9,s[46,59]=-0.1,s[46,60]=-0.9
s[47,1]=-0.3,s[47,2]=-1.0,s[47,3]=0.1,s[47,4]=-0.2,s[47,5]=-0.6,s[47,6]=0.0,s[47,7]=1.0,s[47,8]=0.1,s[47,9]=-0.3,s[47,10]=-0.7,s[47,11]=0.1,s[47,12]=0.1,s[47,13]=0.8,s[47,14]=0.4,s[47,15]=1.1,s[47,16]=0.0,s[47,17]=-0.4,s[47,18]=0.1,s[47,19]=0.7,s[47,20]=-0.3,s[47,21]=-1.0,s[47,22]=1.1,s[47,23]=-0.1,s[47,24]=-1.0,s[47,25]=0.4,s[47,26]=-0.5,s[47,27]=-0.9,s[47,28]=-0.3,s[47,29]=0.3,s[47,30]=0.5,s[47,31]=-1.0,s[47,32]=0.9,s[47,33]=0.9,s[47,34]=1.1,s[47,35]=1.0,s[47,36]=-0.9,s[47,37]=-0.9,s[47,38]=0.6,s[47,39]=0.6,s[47,40]=-0.8,s[47,41]=0.3,s[47,42]=1.1,s[47,43]=-0.9,s[47,44]=-0.2,s[47,45]=0.3,s[47,46]=-0.2,s[47,47]=0.3,s[47,48]=0.6,s[47,49]=0.4,s[47,50]=-0.6,s[47,51]=0.3,s[47,52]=0.4,s[47,53]=-0.6,s[47,54]=-0.5,s[47,55]=0.8,s[47,56]=0.2,s[47,57]=-0.2,s[47,58]=0.0,s[47,59]=0.0,s[47,60]=-0.4
s[48,1]=0.1,s[48,2]=-0.4,s[48,3]=-0.8,s[48,4]=0.6,s[48,5]=0.7,s[48,6]=1.2,s[48,7]=-0.4,s[48,8]=-0.7,s[48,9]=-0.1,s[48,10]=-0.6,s[48,11]=0.9,s[48,12]=-1.2,s[48,13]=-0.6,s[48,14]=0.2,s[48,15]=-0.9,s[48,16]=0.2,s[48,17]=-0.2,s[48,18]=0.0,s[48,19]=-0.1,s[48,20]=-1.1,s[48,21]=-1.1,s[48,22]=0.4,s[48,23]=-0.9,s[48,24]=-0.2,s[48,25]=0.5,s[48,26]=-0.6,s[48,27]=-1.1,s[48,28]=-0.5,s[48,29]=-0.4,s[48,30]=-1.0
s[48,31]=0.2,s[48,32]=0.0,s[48,33]=-0.2,s[48,34]=-0.6,s[48,35]=0.6,s[48,36]=0.2,s[48,37]=0.7,s[48,38]=0.0,s[48,39]=0.1,s[48,40]=-0.3,s[48,41]=-0.3,s[48,42]=-1.0,s[48,43]=-0.4,s[48,44]=0.3,s[48,45]=-0.1,s[48,46]=-0.3,s[48,47]=-0.7,s[48,48]=0.6,s[48,49]=1.1,s[48,50]=-1.2,s[48,51]=-0.7,s[48,52]=-1.2,s[48,53]=-0.6,s[48,54]=0.2,s[48,55]=0.2,s[48,56]=-0.7,s[48,57]=-0.3,s[48,58]=0.2,s[48,59]=-1.0,s[48,60]=0.2
s[49,1]=-0.4,s[49,2]=0.3,s[49,3]=0.0,s[49,4]=-0.7,s[49,5]=0.5,s[49,6]=-0.9,s[49,7]=0.2,s[49,8]=0.6,s[49,9]=1.0,s[49,10]=-1.0,s[49,11]=-0.2,s[49,12]=-0.2,s[49,13]=0.0,s[49,14]=0.5,s[49,15]=1.0,s[49,16]=0.1,s[49,17]=-0.3,s[49,18]=-0.4,s[49,19]=-0.8,s[49,20]=0.3,s[49,21]=0.5,s[49,22]=0.2,s[49,23]=0.0,s[49,24]=-0.9,s[49,25]=1.2,s[49,26]=-0.3,s[49,27]=-1.2,s[49,28]=0.9,s[49,29]=0.2,s[49,30]=-1.2
s[49,31]=-0.2,s[49,32]=1.2,s[49,33]=0.5,s[49,34]=-0.8,s[49,35]=1.0,s[49,36]=0.5,s[49,37]=0.1,s[49,38]=0.6,s[49,39]=0.4,s[49,40]=0.2,s[49,41]=0.4,s[49,42]=0.0,s[49,43]=1.1,s[49,44]=1.2,s[49,45]=-1.2,s[49,46]=0.1,s[49,47]=0.7,s[49,48]=0.9,s[49,49]=1.0,s[49,50]=-0.1,s[49,51]=-0.2,s[49,52]=-0.7,s[49,53]=-0.9,s[49,54]=-1.0,s[49,55]=0.9,s[49,56]=-0.3,s[49,57]=0.8,s[49,58]=0.9,s[49,59]=0.3,s[49,60]=0.8
s[50,1]=0.1,s[50,2]=-1.1,s[50,3]=-0.3,s[50,4]=-0.9,s[50,5]=-0.5,s[50,6]=-0.3,s[50,7]=0.5,s[50,8]=0.3,s[50,9]=-0.5,s[50,10]=-1.1,s[50,11]=-0.8,s[50,12]=-0.9,s[50,13]=0.5,s[50,14]=0.8,s[50,15]=-0.2,s[50,16]=0.1,s[50,17]=-0.7,s[50,18]=0.0,s[50,19]=1.1,s[50,20]=0.2,s[50,21]=-1.0,s[50,22]=0.9,s[50,23]=-0.8,s[50,24]=-0.2,s[50,25]=1.0,s[50,26]=-0.9,s[50,27]=-0.8,s[50,28]=0.1,s[50,29]=-0.2,s[50,30]=-0.4
s[50,31]=-0.2,s[50,32]=-0.2,s[50,33]=0.8,s[50,34]=-0.9,s[50,35]=0.3,s[50,36]=-1.0,s[50,37]=-0.1,s[50,38]=0.1,s[50,39]=0.4,s[50,40]=0.7,s[50,41]=-0.8,s[50,42]=-1.0,s[50,43]=-0.1,s[50,44]=1.0,s[50,45]=1.2,s[50,46]=-0.3,s[50,47]=-0.6,s[50,48]=0.2,s[50,49]=-0.1,s[50,50]=-1.2,s[50,51]=0.2,s[50,52]=-1.0,s[50,53]=-0.7,s[50,54]=-0.6,s[50,55]=-0.4,s[50,56]=0.5,s[50,57]=-0.7,s[50,58]=0.2,s[50,59]=0.7,s[50,60]=0.8
s[51,1]=-0.6,s[51,2]=0.4,s[51,3]=-0.1,s[51,4]=0.3,s[51,5]=1.2,s[51,6]=-0.1,s[51,7]=-0.4,s[51,8]=-0.4,s[51,9]=0.5,s[51,10]=0.8,s[51,11]=0.0,s[51,12]=-0.4,s[51,13]=-1.2,s[51,14]=-0.1,s[51,15]=-0.9,s[51,16]=-0.4,s[51,17]=-0.1,s[51,18]=-0.7,s[51,19]=-0.8,s[51,20]=-1.1,s[51,21]=-0.1,s[51,22]=-1.2,s[51,23]=0.9,s[51,24]=0.3,s[51,25]=1.0,s[51,26]=0.0,s[51,27]=1.1,s[51,28]=-0.6,s[51,29]=-0.3,s[51,30]=0.4
s[51,31]=-0.8,s[51,32]=-0.2,s[51,33]=0.7,s[51,34]=0.0,s[51,35]=-0.4,s[51,36]=0.7,s[51,37]=0.8,s[51,38]=-1.2,s[51,39]=1.0,s[51,40]=-0.9,s[51,41]=-0.1,s[51,42]=0.3,s[51,43]=-0.4,s[51,44]=0.8,s[51,45]=-0.9,s[51,46]=1.1,s[51,47]=-0.2,s[51,48]=0.3,s[51,49]=0.6,s[51,50]=0.1,s[51,51]=1.1,s[51,52]=-0.4,s[51,53]=-0.8,s[51,54]=0.0,s[51,55]=0.7,s[51,56]=1.0,s[51,57]=-0.8,s[51,58]=-1.2,s[51,59]=-0.4,s[51,60]=0.8
s[52,1]=0.1,s[52,2]=-0.5,s[52,3]=0.2,s[52,4]=-0.1,s[52,5]=0.3,s[52,6]=-0.8,s[52,7]=0.4,s[52,8]=-1.1,s[52,9]=0.1,s[52,10]=0.1,s[52,11]=0.1,s[52,12]=-0.6,s[52,13]=-1.1,s[52,14]=0.9,s[52,15]=0.4,s[52,16]=-0.1,s[52,17]=0.5,s[52,18]=1.0,s[52,19]=-1.1,s[52,20]=0.4,s[52,21]=-0.3,s[52,22]=1.2,s[52,23]=1.1,s[52,24]=-0.3,s[52,25]=0.7,s[52,26]=-0.3,s[52,27]=-0.4,s[52,28]=-1.0,s[52,29]=0.2,s[52,30]=0.9
s[52,31]=-0.2,s[52,32]=0.3,s[52,33]=0.3,s[52,34]=0.0,s[52,35]=-0.9,s[52,36]=1.2,s[52,37]=-0.4,s[52,38]=-0.2,s[52,39]=0.7,s[52,40]=-1.2,s[52,41]=-0.4,s[52,42]=-0.1,s[52,43]=0.8,s[52,44]=0.9,s[52,45]=1.2,s[52,46]=-0.2,s[52,47]=-0.5,s[52,48]=-0.2,s[52,49]=0.9,s[52,50]=0.3,s[52,51]=-0.5,s[52,52]=0.7,s[52,53]=-0.1,s[52,54]=-0.4,s[52,55]=-0.9,s[52,56]=-0.7,s[52,57]=-0.6,s[52,58]=0.5,s[52,59]=0.5,s[52,60]=0.1
s[53,1]=0.5,s[53,2]=0.6,s[53,3]=-0.2,s[53,4]=0.6,s[53,5]=0.1,s[53,6]=1.1,s[53,7]=0.7,s[53,8]=0.7,s[53,9]=-1.0,s[53,10]=0.9,s[53,11]=-0.6,s[53,12]=-0.5,s[53,13]=0.0,s[53,14]=0.4,s[53,15]=-0.8,s[53,16]=-0.1,s[53,17]=1.0,s[53,18]=-0.3,s[53,19]=1.0,s[53,20]=-0.1,s[53,21]=0.2,s[53,22]=-0.4,s[53,23]=0.5,s[53,24]=0.1,s[53,25]=1.1,s[53,26]=-0.8,s[53,27]=0.3,s[53,28]=0.7,s[53,29]=-0.4,s[53,30]=0.6
s[53,31]=0.3,s[53,32]=0.0,s[53,33]=0.9,s[53,34]=-0.3,s[53,35]=-0.6,s[53,36]=-0.3,s[53,37]=0.1,s[53,38]=-0.3,s[53,39]=0.4,s[53,40]=0.4,s[53,41]=0.9,s[53,42]=-0.6,s[53,43]=1.2,s[53,44]=1.2,s[53,45]=0.3,s[53,46]=0.0,s[53,47]=-0.6,s[53,48]=0.7,s[53,49]=0.2,s[53,50]=0.9,s[53,51]=-0.4,s[53,52]=0.3,s[53,53]=1.2,s[53,54]=0.8,s[53,55]=0.2,s[53,56]=-0.4,s[53,57]=0.7,s[53,58]=-0.6,s[53,59]=-0.8,s[53,60]=0.6
s[54,1]=0.4,s[54,2]=0.7,s[54,3]=0.5,s[54,4]=-1.2,s[54,5]=0.1,s[54,6]=0.9,s[54,7]=-1.2,s[54,8]=1.1,s[54,9]=-1.1,s[54,10]=-1.2,s[54,11]=1.1,s[54,12]=0.8,s[54,13]=-0.1,s[54,14]=-0.4,s[54,15]=-0.4,s[54,16]=0.5,s[54,17]=-0.8,s[54,18]=-0.1,s[54,19]=1.2,s[54,20]=0.3,s[54,21]=-0.6,s[54,22]=-0.2,s[54,23]=-0.9,s[54,24]=0.3,s[54,25]=0.5,s[54,26]=0.0,s[54,27]=1.1,s[54,28]=-1.2,s[54,29]=-0.5,s[54,30]=-0.2
s[54,31]=-0.8,s[54,32]=1.2,s[54,33]=0.3,s[54,34]=-0.1,s[54,35]=-0.6,s[54,36]=0.6,s[54,37]=-0.4,s[54,38]=0.4,s[54,39]=-0.5,s[54,40]=0.8,s[54,41]=-0.8,s[54,42]=-0.9,s[54,43]=-0.8,s[54,44]=-0.8,s[54,45]=-0.3,s[54,46]=-0.3,s[54,47]=-0.7,s[54,48]=-0.4,s[54,49]=1.2,s[54,50]=0.5,s[54,51]=0.5,s[54,52]=-0.4,s[54,53]=1.0,s[54,54]=-0.5,s[54,55]=-1.0,s[54,56]=0.6,s[54,57]=0.9,s[54,58]=-0.5,s[54,59]=1.0,s[54,60]=1.1
s[55,1]=-0.3,s[55,2]=0.4,s[55,3]=-0.7,s[55,4]=0.3,s[55,5]=0.7,s[55,6]=0.9,s[55,7]=-0.1,s[55,8]=1.0,s[55,9]=0.5,s[55,10]=-1.0,s[55,11]=0.6,s[55,12]=0.6,s[55,13]=-0.3,s[55,14]=0.2,s[55,15]=1.1,s[55,16]=-0.4,s[55,17]=-0.1,s[55,18]=-0.8,s[55,19]=0.6,s[55,20]=-0.9,s[55,21]=-0.5,s[55,22]=0.6,s[55,23]=0.5,s[55,24]=-0.4,s[55,25]=0.4,s[55,26]=-1.0,s[55,27]=-1.0,s[55,28]=1.0,s[55,29]=1.1,s[55,30]=0.2
s[55,31]=-0.3,s[55,32]=0.6,s[55,33]=-1.1,s[55,34]=0.4,s[55,35]=0.5,s[55,36]=-1.1,s[55,37]=-0.8,s[55,38]=-1.2,s[55,39]=1.2,s[55,40]=-0.8,s[55,41]=0.7,s[55,42]=-0.2,s[55,43]=0.7,s[55,44]=0.0,s[55,45]=0.4,s[55,46]=0.0,s[55,47]=0.0,s[55,48]=-0.3,s[55,49]=-0.1,s[55,50]=-0.4,s[55,51]=0.7,s[55,52]=-0.2,s[55,53]=-0.1,s[55,54]=-1.0,s[55,55]=0.1,s[55,56]=0.2,s[55,57]=-0.2,s[55,58]=-0.5,s[55,59]=-1.2,s[55,60]=-0.5
s[56,1]=-0.3,s[56,2]=-0.1,s[56,3]=-0.8,s[56,4]=0.2,s[56,5]=-0.4,s[56,6]=0.6,s[56,7]=-0.5,s[56,8]=-0.1,s[56,9]=-0.1,s[56,10]=1.0,s[56,11]=-0.1,s[56,12]=-0.9,s[56,13]=-0.5,s[56,14]=-0.2,s[56,15]=0.0,s[56,16]=-0.2,s[56,17]=0.6,s[56,18]=0.9,s[56,19]=-1.2,s[56,20]=-0.9,s[56,21]=0.4,s[56,22]=-0.7,s[56,23]=0.2,s[56,24]=-0.2,s[56,25]=-1.1,s[56,26]=0.2,s[56,27]=1.2,s[56,28]=-1.1,s[56,29]=0.2,s[56,30]=0.5
s[56,31]=-0.1,s[56,32]=1.0,s[56,33]=1.1,s[56,34]=-0.8,s[56,35]=0.3,s[56,36]=0.8,s[56,37]=-1.0,s[56,38]=0.2,s[56,39]=0.8,s[56,40]=1.1,s[56,41]=-0.1,s[56,42]=-0.2,s[56,43]=1.2,s[56,44]=0.4,s[56,45]=1.1,s[56,46]=-0.1,s[56,47]=-0.1,s[56,48]=1.2,s[56,49]=0.8,s[56,50]=0.8,s[56,51]=-1.2,s[56,52]=0.9,s[56,53]=-0.6,s[56,54]=1.2,s[56,55]=0.7,s[56,56]=-0.1,s[56,57]=1.1,s[56,58]=0.1,s[56,59]=-0.8,s[56,60]=1.1
s[57,1]=0.2,s[57,2]=-0.1,s[57,3]=0.7,s[57,4]=0.9,s[57,5]=-0.7,s[57,6]=-0.5,s[57,7]=-0.1,s[57,8]=-0.9,s[57,9]=0.3,s[57,10]=-0.6,s[57,11]=-0.3,s[57,12]=-1.1,s[57,13]=0.7,s[57,14]=0.0,s[57,15]=-0.3,s[57,16]=-0.2,s[57,17]=0.5,s[57,18]=0.0,s[57,19]=-1.0,s[57,20]=-0.1,s[57,21]=-0.3,s[57,22]=1.1,s[57,23]=0.0,s[57,24]=0.5,s[57,25]=0.4,s[57,26]=0.3,s[57,27]=0.6,s[57,28]=1.2,s[57,29]=0.3,s[57,30]=0.0
s[57,31]=-0.6,s[57,32]=0.8,s[57,33]=0.4,s[57,34]=0.6,s[57,35]=0.6,s[57,36]=0.0,s[57,37]=0.6,s[57,38]=0.3,s[57,39]=-0.2,s[57,40]=-0.1,s[57,41]=-1.2,s[57,42]=-0.5,s[57,43]=-0.8,s[57,44]=0.6,s[57,45]=1.0,s[57,46]=-0.7,s[57,47]=-0.7,s[57,48]=-0.4,s[57,49]=0.0,s[57,50]=0.0,s[57,51]=0.3,s[57,52]=0.0,s[57,53]=-0.8,s[57,54]=0.3,s[57,55]=-0.7,s[57,56]=0.7,s[57,57]=0.5,s[57,58]=0.8,s[57,59]=0.3,s[57,60]=0.6
s[58,1]=-0.3,s[58,2]=0.5,s[58,3]=0.4,s[58,4]=0.5,s[58,5]=-0.9,s[58,6]=-0.7,s[58,7]=1.1,s[58,8]=1.0,s[58,9]=-0.2,s[58,10]=-0.8,s[58,11]=0.5,s[58,12]=1.0,s[58,13]=1.2,s[58,14]=0.1,s[58,15]=1.0,s[58,16]=-0.1,s[58,17]=-0.4,s[58,18]=0.5,s[58,19]=0.7,s[58,20]=0.1,s[58,21]=-0.4,s[58,22]=0.1,s[58,23]=1.2,s[58,24]=0.6,s[58,25]=-0.1,s[58,26]=1.1,s[58,27]=-0.1,s[58,28]=0.8,s[58,29]=-0.8,s[58,30]=-0.5
s[58,31]=-0.4,s[58,32]=0.4,s[58,33]=0.6,s[58,34]=-0.3,s[58,35]=-0.1,s[58,36]=0.0,s[58,37]=-0.2,s[58,38]=-0.2,s[58,39]=0.8,s[58,40]=0.5,s[58,41]=-0.4,s[58,42]=-0.1,s[58,43]=-0.8,s[58,44]=-0.2,s[58,45]=0.2,s[58,46]=-0.3,s[58,47]=-0.4,s[58,48]=0.0,s[58,49]=-1.0,s[58,50]=-1.0,s[58,51]=0.8,s[58,52]=-0.8,s[58,53]=-0.5,s[58,54]=-0.1,s[58,55]=-0.9,s[58,56]=-0.4,s[58,57]=0.6,s[58,58]=0.1,s[58,59]=-0.3,s[58,60]=-0.1
s[59,1]=0.3,s[59,2]=-1.1,s[59,3]=-0.3,s[59,4]=-0.4,s[59,5]=-0.4,s[59,6]=0.3,s[59,7]=-0.5,s[59,8]=-0.1,s[59,9]=0.5,s[59,10]=0.7,s[59,11]=1.0,s[59,12]=-0.3,s[59,13]=-1.1,s[59,14]=0.8,s[59,15]=0.0,s[59,16]=0.3,s[59,17]=-0.2,s[59,18]=-0.9,s[59,19]=-0.3,s[59,20]=-1.1,s[59,21]=-0.3,s[59,22]=0.9,s[59,23]=-0.3,s[59,24]=-0.3,s[59,25]=-1.2,s[59,26]=-0.3,s[59,27]=-0.1,s[59,28]=1.0,s[59,29]=0.0,s[59,30]=-1.1
s[59,31]=0.5,s[59,32]=-1.1,s[59,33]=-1.1,s[59,34]=0.8,s[59,35]=-0.1,s[59,36]=-0.6,s[59,37]=0.0,s[59,38]=0.7,s[59,39]=0.7,s[59,40]=0.3,s[59,41]=0.3,s[59,42]=-0.4,s[59,43]=0.0,s[59,44]=-0.2,s[59,45]=1.0,s[59,46]=0.1,s[59,47]=-0.2,s[59,48]=0.3,s[59,49]=0.4,s[59,50]=1.1,s[59,51]=-1.2,s[59,52]=-1.2,s[59,53]=1.2,s[59,54]=-1.1,s[59,55]=-0.5,s[59,56]=0.8,s[59,57]=-0.7,s[59,58]=-0.8,s[59,59]=-0.1,s[59,60]=1.1
s[60,1]=0.1,s[60,2]=0.1,s[60,3]=0.4,s[60,4]=0.9,s[60,5]=-0.2,s[60,6]=0.7,s[60,7]=-0.2,s[60,8]=0.8,s[60,9]=0.6,s[60,10]=-1.1,s[60,11]=-0.7,s[60,12]=1.0,s[60,13]=-0.4,s[60,14]=0.4,s[60,15]=-0.3,s[60,16]=0.6,s[60,17]=-1.1,s[60,18]=-0.5,s[60,19]=-0.9,s[60,20]=0.3,s[60,21]=0.9,s[60,22]=-0.7,s[60,23]=0.3,s[60,24]=0.8,s[60,25]=-1.1,s[60,26]=-0.9,s[60,27]=-0.2,s[60,28]=-0.8,s[60,29]=1.1,s[60,30]=-0.5
s[60,31]=-0.1,s[60,32]=0.2,s[60,33]=0.3,s[60,34]=-0.4,s[60,35]=0.5,s[60,36]=1.1,s[60,37]=0.7,s[60,38]=0.4,s[60,39]=-1.2,s[60,40]=0.5,s[60,41]=0.3,s[60,42]=1.1,s[60,43]=0.4,s[60,44]=-1.0,s[60,45]=1.1,s[60,46]=0.4,s[60,47]=0.0,s[60,48]=-0.2,s[60,49]=0.6,s[60,50]=-0.3,s[60,51]=-0.3,s[60,52]=-0.2,s[60,53]=0.6,s[60,54]=0.1,s[60,55]=0.0,s[60,56]=-0.2,s[60,57]=-0.9,s[60,58]=0.2,s[60,59]=-0.5,s[60,60]=-0.5
s[61,1]=0.0,s[61,2]=-0.9,s[61,3]=-0.2,s[61,4]=-1.2,s[61,5]=-1.1,s[61,6]=-0.1,s[61,7]=0.6,s[61,8]=-0.3,s[61,9]=0.2,s[61,10]=0.5,s[61,11]=0.3,s[61,12]=-1.2,s[61,13]=0.0,s[61,14]=-1.1,s[61,15]=-0.4,s[61,16]=-0.1,s[61,17]=-0.2,s[61,18]=0.3,s[61,19]=0.1,s[61,20]=-1.0,s[61,21]=0.1,s[61,22]=-0.3,s[61,23]=-0.8,s[61,24]=0.3,s[61,25]=-1.0,s[61,26]=0.8,s[61,27]=0.3,s[61,28]=-0.4,s[61,29]=0.0,s[61,30]=-0.8
s[61,31]=-0.1,s[61,32]=1.0,s[61,33]=-0.2,s[61,34]=0.7,s[61,35]=-0.7,s[61,36]=-0.3,s[61,37]=-0.8,s[61,38]=0.9,s[61,39]=0.7,s[61,40]=0.3,s[61,41]=0.6,s[61,42]=1.1,s[61,43]=1.0,s[61,44]=1.1,s[61,45]=0.2,s[61,46]=0.2,s[61,47]=-0.2,s[61,48]=0.4,s[61,49]=1.0,s[61,50]=0.7,s[61,51]=0.7,s[61,52]=0.3,s[61,53]=0.6,s[61,54]=0.0,s[61,55]=0.2,s[61,56]=0.2,s[61,57]=-0.1,s[61,58]=-1.1,s[61,59]=-0.9,s[61,60]=0.3
s[62,1]=0.1,s[62,2]=1.2,s[62,3]=-0.9,s[62,4]=-0.7,s[62,5]=-0.9,s[62,6]=0.4,s[62,7]=0.3,s[62,8]=-0.9,s[62,9]=0.3,s[62,10]=0.7,s[62,11]=-1.0,s[62,12]=1.0,s[62,13]=0.0,s[62,14]=0.0,s[62,15]=-0.1,s[62,16]=0.8,s[62,17]=0.0,s[62,18]=0.6,s[62,19]=-1.1,s[62,20]=-0.2,s[62,21]=0.1,s[62,22]=-0.8,s[62,23]=1.0,s[62,24]=-0.4,s[62,25]=0.7,s[62,26]=0.9,s[62,27]=0.2,s[62,28]=0.5,s[62,29]=-0.6,s[62,30]=0.6
s[62,31]=-0.2,s[62,32]=0.0,s[62,33]=0.5,s[62,34]=0.2,s[62,35]=0.1,s[62,36]=1.1,s[62,37]=-0.2,s[62,38]=0.5,s[62,39]=0.6,s[62,40]=-0.2,s[62,41]=-0.4,s[62,42]=-1.0,s[62,43]=-1.2,s[62,44]=0.7,s[62,45]=0.7,s[62,46]=-0.1,s[62,47]=0.5,s[62,48]=-0.9,s[62,49]=-0.4,s[62,50]=-0.4,s[62,51]=-0.9,s[62,52]=-0.4,s[62,53]=-0.2,s[62,54]=-0.7,s[62,55]=-0.7,s[62,56]=-0.1,s[62,57]=1.1,s[62,58]=-0.3,s[62,59]=-0.5,s[62,60]=0.2
s[63,1]=0.0,s[63,2]=0.4,s[63,3]=0.0,s[63,4]=-0.4,s[63,5]=0.3,s[63,6]=0.1,s[63,7]=0.5,s[63,8]=-0.2,s[63,9]=0.8,s[63,10]=1.1,s[63,11]=-0.6,s[63,12]=-0.6,s[63,13]=0.0,s[63,14]=-0.1,s[63,15]=-0.4,s[63,16]=0.1,s[63,17]=0.0,s[63,18]=-1.2,s[63,19]=-0.7,s[63,20]=-1.1,s[63,21]=1.0,s[63,22]=0.0,s[63,23]=-0.8,s[63,24]=-0.7,s[63,25]=-1.2,s[63,26]=-0.4,s[63,27]=1.1,s[63,28]=0.9,s[63,29]=0.5,s[63,30]=0.2
s[63,31]=-0.1,s[63,32]=-0.5,s[63,33]=-0.8,s[63,34]=-0.1,s[63,35]=-0.8,s[63,36]=-0.5,s[63,37]=-0.6,s[63,38]=0.8,s[63,39]=1.2,s[63,40]=-1.1,s[63,41]=-0.3,s[63,42]=1.0,s[63,43]=1.2,s[63,44]=0.4,s[63,45]=1.0,s[63,46]=0.0,s[63,47]=0.2,s[63,48]=1.2,s[63,49]=-0.6,s[63,50]=-0.2,s[63,51]=-1.0,s[63,52]=-1.1,s[63,53]=-0.2,s[63,54]=1.2,s[63,55]=0.3,s[63,56]=-0.9,s[63,57]=-0.9,s[63,58]=0.4,s[63,59]=-0.4,s[63,60]=1.0
s[64,1]=0.3,s[64,2]=-1.2,s[64,3]=1.0,s[64,4]=1.1,s[64,5]=0.4,s[64,6]=-0.7,s[64,7]=-1.2,s[64,8]=0.9,s[64,9]=1.2,s[64,10]=0.5,s[64,11]=-1.2,s[64,12]=0.1,s[64,13]=-0.7,s[64,14]=0.3,s[64,15]=-0.8,s[64,16]=0.3,s[64,17]=0.3,s[64,18]=-0.1,s[64,19]=-0.3,s[64,20]=-0.4,s[64,21]=-0.7,s[64,22]=0.0,s[64,23]=-0.2,s[64,24]=-0.3,s[64,25]=1.0,s[64,26]=0.8,s[64,27]=1.0,s[64,28]=1.0,s[64,29]=-0.6,s[64,30]=-0.3
s[64,31]=0.2,s[64,32]=0.4,s[64,33]=-0.5,s[64,34]=-0.3,s[64,35]=-0.9,s[64,36]=0.8,s[64,37]=-0.6,s[64,38]=-0.2,s[64,39]=0.9,s[64,40]=0.3,s[64,41]=0.7,s[64,42]=0.0,s[64,43]=1.1,s[64,44]=-0.9,s[64,45]=1.1,s[64,46]=0.3,s[64,47]=-0.8,s[64,48]=-1.1,s[64,49]=0.7,s[64,50]=-0.4,s[64,51]=-0.9,s[64,52]=-0.3,s[64,53]=-0.8,s[64,54]=0.4,s[64,55]=-0.4,s[64,56]=-0.9,s[64,57]=-1.0,s[64,58]=-0.1,s[64,59]=0.3,s[64,60]=0.2
s[65,1]=0.3,s[65,2]=-0.1,s[65,3]=-0.4,s[65,4]=1.2,s[65,5]=-0.6,s[65,6]=-0.7,s[65,7]=0.1,s[65,8]=0.2,s[65,9]=-0.8,s[65,10]=-0.6,s[65,11]=-0.2,s[65,12]=-0.8,s[65,13]=-0.6,s[65,14]=-0.7,s[65,15]=1.1,s[65,16]=0.0,s[65,17]=1.2,s[65,18]=-0.7,s[65,19]=0.8,s[65,20]=-0.3,s[65,21]=-0.6,s[65,22]=-0.5,s[65,23]=0.9,s[65,24]=1.2,s[65,25]=-1.1,s[65,26]=1.2,s[65,27]=0.5,s[65,28]=0.0,s[65,29]=0.7,s[65,30]=1.1
s[65,31]=0.0,s[65,32]=-0.6,s[65,33]=-1.0,s[65,34]=1.1,s[65,35]=-1.0,s[65,36]=-0.6,s[65,37]=-1.1,s[65,38]=0.4,s[65,39]=-0.8,s[65,40]=-0.9,s[65,41]=0.7,s[65,42]=0.5,s[65,43]=1.1,s[65,44]=1.2,s[65,45]=0.5,s[65,46]=0.3,s[65,47]=0.8,s[65,48]=-0.7,s[65,49]=-0.2,s[65,50]=-1.0,s[65,51]=1.0,s[65,52]=-0.1,s[65,53]=-0.3,s[65,54]=0.9,s[65,55]=1.1,s[65,56]=1.1,s[65,57]=-0.4,s[65,58]=0.5,s[65,59]=0.4,s[65,60]=-1.2
s[66,1]=0.0,s[66,2]=0.1,s[66,3]=0.6,s[66,4]=-0.2,s[66,5]=-0.5,s[66,6]=0.9,s[66,7]=0.5,s[66,8]=-0.3,s[66,9]=-0.6,s[66,10]=-0.9,s[66,11]=-0.2,s[66,12]=-1.1,s[66,13]=0.9,s[66,14]=0.2,s[66,15]=0.4,s[66,16]=0.6,s[66,17]=0.1,s[66,18]=-1.2,s[66,19]=0.6,s[66,20]=0.3,s[66,21]=0.2,s[66,22]=-0.3,s[66,23]=-0.1,s[66,24]=-0.5,s[66,25]=0.3,s[66,26]=-0.6,s[66,27]=-0.2,s[66,28]=-0.3,s[66,29]=-0.4,s[66,30]=-0.9
s[66,31]=0.0,s[66,32]=1.0,s[66,33]=0.0,s[66,34]=-1.0,s[66,35]=0.7,s[66,36]=-1.0,s[66,37]=0.7,s[66,38]=-0.7,s[66,39]=-0.6,s[66,40]=1.2,s[66,41]=0.6,s[66,42]=-1.1,s[66,43]=0.6,s[66,44]=-0.8,s[66,45]=-1.2,s[66,46]=-0.4,s[66,47]=0.9,s[66,48]=0.9,s[66,49]=0.5,s[66,50]=1.0,s[66,51]=0.9,s[66,52]=0.3,s[66,53]=-0.6,s[66,54]=0.6,s[66,55]=-0.2,s[66,56]=-0.6,s[66,57]=0.1,s[66,58]=-0.9,s[66,59]=-0.2,s[66,60]=1.0
s[67,1]=-0.3,s[67,2]=-0.7,s[67,3]=-0.4,s[67,4]=0.6,s[67,5]=0.9,s[67,6]=0.6,s[67,7]=0.5,s[67,8]=-0.4,s[67,9]=0.9,s[67,10]=-0.2,s[67,11]=0.5,s[67,12]=-0.7,s[67,13]=0.2,s[67,14]=1.1,s[67,15]=-1.0,s[67,16]=0.2,s[67,17]=0.2,s[67,18]=0.6,s[67,19]=-0.2,s[67,20]=-1.1,s[67,21]=-0.9,s[67,22]=0.7,s[67,23]=0.4,s[67,24]=0.1,s[67,25]=-0.9,s[67,26]=0.1,s[67,27]=-0.4,s[67,28]=-0.7,s[67,29]=-1.0,s[67,30]=0.8
s[67,31]=0.1,s[67,32]=0.0,s[67,33]=-0.7,s[67,34]=-0.1,s[67,35]=-0.5,s[67,36]=-0.4,s[67,37]=-0.2,s[67,38]=0.4,s[67,39]=0.0,s[67,40]=0.4,s[67,41]=0.8,s[67,42]=-0.1,s[67,43]=-1.0,s[67,44]=-0.7,s[67,45]=1.2,s[67,46]=0.3,s[67,47]=0.8,s[67,48]=-1.0,s[67,49]=-0.2,s[67,50]=-1.0,s[67,51]=0.0,s[67,52]=0.7,s[67,53]=-0.3,s[67,54]=0.7,s[67,55]=1.2,s[67,56]=-0.4,s[67,57]=1.0,s[67,58]=0.8,s[67,59]=-1.2,s[67,60]=0.7
s[68,1]=0.1,s[68,2]=1.2,s[68,3]=1.2,s[68,4]=0.2,s[68,5]=0.6,s[68,6]=-1.0,s[68,7]=-1.0,s[68,8]=-0.4,s[68,9]=-1.2,s[68,10]=-0.4,s[68,11]=0.5,s[68,12]=-0.3,s[68,13]=0.3,s[68,14]=-0.1,s[68,15]=0.6,s[68,16]=0.3,s[68,17]=0.6,s[68,18]=-1.2,s[68,19]=-0.5,s[68,20]=-1.1,s[68,21]=-0.6,s[68,22]=0.8,s[68,23]=-0.6,s[68,24]=0.4,s[68,25]=0.4,s[68,26]=0.1,s[68,27]=0.6,s[68,28]=-0.1,s[68,29]=-0.9,s[68,30]=1.1
s[68,31]=0.4,s[68,32]=-0.7,s[68,33]=-0.7,s[68,34]=-0.9,s[68,35]=0.5,s[68,36]=1.0,s[68,37]=-0.4,s[68,38]=0.1,s[68,39]=0.6,s[68,40]=0.9,s[68,41]=-0.7,s[68,42]=0.6,s[68,43]=1.2,s[68,44]=-0.8,s[68,45]=-0.9,s[68,46]=0.4,s[68,47]=0.6,s[68,48]=-0.4,s[68,49]=-0.1,s[68,50]=-0.9,s[68,51]=-0.7,s[68,52]=-1.2,s[68,53]=1.2,s[68,54]=0.3,s[68,55]=0.5,s[68,56]=0.5,s[68,57]=-1.0,s[68,58]=-0.4,s[68,59]=0.1,s[68,60]=0.3
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float ppz = @ppz
float ppw = @ppw
float pxx = 0
float pyy = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
pyy = y
float pzz = ppz
x = s[@sel,1] + s[@sel,2]*x + s[@sel,3]*x*x + s[@sel,4]*x*y + s[@sel,5]*x*ppz + s[@sel,6]*x*ppw + s[@sel,7]*y + s[@sel,8]*y*y + \
s[@sel,9]*y*ppz + s[@sel,10]*y*ppw + s[@sel,11]*ppz + s[@sel,12]*ppz*ppz + s[@sel,13]*ppz*ppw + s[@sel,14]*ppw + s[@sel,15]*ppw*ppw
y = s[@sel,16] + s[@sel,17]*pxx + s[@sel,18]*pxx*pxx + s[@sel,19]*pxx*y + s[@sel,20]*pxx*ppz + s[@sel,21]*pxx*ppw + s[@sel,22]*y + s[@sel,23]*y*y + \
s[@sel,24]*y*ppz + s[@sel,25]*y*ppw + s[@sel,26]*ppz + s[@sel,27]*ppz*ppz + s[@sel,28]*ppz*ppw + s[@sel,29]*ppw + s[@sel,30]*ppw*ppw
ppz = s[@sel,31] + s[@sel,32]*pxx + s[@sel,33]*pxx*pxx + s[@sel,34]*pxx*pyy + s[@sel,35]*pxx*ppz + s[@sel,36]*pxx*ppw + s[@sel,37]*pyy + s[@sel,38]*pyy*pyy + \
s[@sel,39]*pyy*ppz + s[@sel,40]*pyy*ppw + s[@sel,41]*ppz + s[@sel,42]*ppz*ppz + s[@sel,43]*ppz*ppw + s[@sel,44]*ppw + s[@sel,45]*ppw*ppw
ppw = s[@sel,46] + s[@sel,47]*pxx + s[@sel,48]*pxx*pxx + s[@sel,49]*pxx*pyy + s[@sel,50]*pxx*pzz + s[@sel,51]*pxx*ppw + s[@sel,52]*pyy + s[@sel,53]*pyy*pyy + \
s[@sel,54]*pyy*pzz + s[@sel,55]*pyy*ppw + s[@sel,56]*pzz + s[@sel,57]*pzz*pzz + s[@sel,58]*pzz*ppw + s[@sel,59]*ppw + s[@sel,60]*ppw*ppw
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y) + ppz*@pw + ppw*@p4)
float d = @distscale*|pz-(x + sgn*flip(y) + ppz*@pw + ppw*@p4)|
return d
endfunc
private:
float s[69,61]
default:
title = "Sprott4D"
heading
text="Sprott 4D Quadratic attractors"
endheading
heading
text=" x -> Quadratic in x, y, z and w"
endheading
heading
text=" y -> Quadratic in x, y, z and w"
endheading
heading
text=" z -> Quadratic in x, y, z and w"
endheading
heading
text=" w -> Quadratic in x, y, z and w"
endheading
int param v_trapshapesprott4d
caption = "Version (Trap Shape Sprott4D)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesprott4D < 100
endparam
param sel
caption = "Sprott selector"
default = 0
enum = "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" \
"11" "12" "13" "14" "15" "16" "17" "18" "19" "20" \
"21" "22" "23" "24" "25" "26" "27" "28" "29" "30" \
"31" "32" "33" "34" "35" "36" "37" "38" "39" "40" \
"41" "42" "43" "44" "45" "46" "47" "48" "49" "50" \
"51" "52" "53" "54" "55" "56" "57" "58" "59" "60" \
"61" "62" "63" "64" "65" "66" "67" "68"
hint = "Each Sprott selector uses a different strange attractor."
endparam
heading
text = "'Initialize Height' sets the starting z value for the attractor."
endheading
float param ppz
caption = "Initialize Height"
default = 0.0
endparam
heading
text = "'Initialize 4th dim' sets the starting w value for the attractor."
endheading
float param ppw
caption = "Initialize 4th dim"
default = 0.0
endparam
heading
text = "'Height weight' determines the weight of the final z value which is added \
to the trap distance."
endheading
complex param pw
caption = "Height weight"
default = (0.5,0)
endparam
heading
text = "'4D weight' determines the weight of the final w value which is added \
to the trap distance."
endheading
complex param p4
caption = "4D weight"
default = (0,0)
endparam
float param distscale
caption = "Distance scale"
default = 2
endparam
float param s
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 20
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSprott4D_ODE(common.ulb:TrapShape) {
; This shape uses a Sprott strange attractor.
; The Sprott attractors were developed by Julien C. Sprott, and are
; based upon polynomials and linear differential equations of polynomials.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSprott4D_ODE(Generic pparent)
TrapShape.TrapShape(pparent)
s[0,1]=0.0,s[0,2]=-0.6,s[0,3]=0.0,s[0,4]=-0.8,s[0,5]=-0.8,s[0,6]=-0.6,s[0,7]=0.3,s[0,8]=0.1,s[0,9]=0.5,s[0,10]=-0.4,s[0,11]=0.0,s[0,12]=0.4,s[0,13]=0.7,s[0,14]=0.4,s[0,15]=1.2,s[0,16]=-0.6,s[0,17]=0.4,s[0,18]=-0.2,s[0,19]=-1.2,s[0,20]=0.2,s[0,21]=-1.0,s[0,22]=-0.6,s[0,23]=-0.9,s[0,24]=0.7,s[0,25]=-0.6,s[0,26]=1.2,s[0,27]=0.8,s[0,28]=-0.3,s[0,29]=0.3,s[0,30]=0.3
s[0,31]=-1.2,s[0,32]=0.6,s[0,33]=0.3,s[0,34]=0.6,s[0,35]=-0.5,s[0,36]=0.4,s[0,37]=-0.2,s[0,38]=-0.4,s[0,39]=-0.6,s[0,40]=-0.3,s[0,41]=-0.7,s[0,42]=0.0,s[0,43]=1.0,s[0,44]=0.8,s[0,45]=1.1,s[0,46]=0.7,s[0,47]=0.3,s[0,48]=-0.3,s[0,49]=-1.2,s[0,50]=-0.6,s[0,51]=-1.1,s[0,52]=-0.3,s[0,53]=-0.2,s[0,54]=-0.7,s[0,55]=-1.0,s[0,56]=1.2,s[0,57]=-1.2,s[0,58]=-0.7,s[0,59]=0.2,s[0,60]=-0.2
s[1,1]=0.7,s[1,2]=0.1,s[1,3]=0.1,s[1,4]=1.2,s[1,5]=-1.0,s[1,6]=0.4,s[1,7]=0.7,s[1,8]=-0.9,s[1,9]=-0.3,s[1,10]=-0.9,s[1,11]=-0.5,s[1,12]=-0.5,s[1,13]=-1.0,s[1,14]=0.0,s[1,15]=-0.4,s[1,16]=-0.2,s[1,17]=-0.5,s[1,18]=0.1,s[1,19]=-1.0,s[1,20]=0.3,s[1,21]=-0.4,s[1,22]=1.1,s[1,23]=1.1,s[1,24]=0.0,s[1,25]=-1.1,s[1,26]=-0.7,s[1,27]=0.0,s[1,28]=0.5,s[1,29]=0.7,s[1,30]=0.7,s[1,31]=-1.0,s[1,32]=0.7,s[1,33]=0.2,s[1,34]=-0.7,s[1,35]=-1.1,s[1,36]=0.7,s[1,37]=-0.7,s[1,38]=0.0,s[1,39]=-0.5,s[1,40]=0.2,s[1,41]=-0.1,s[1,42]=-0.6,s[1,43]=0.2,s[1,44]=-0.4,s[1,45]=-0.8,s[1,46]=0.8,s[1,47]=0.5,s[1,48]=-1.2,s[1,49]=-0.4,s[1,50]=-1.1,s[1,51]=-1.1,s[1,52]=-0.5,s[1,53]=0.2,s[1,54]=-0.8,s[1,55]=0.3,s[1,56]=0.2,s[1,57]=-0.5,s[1,58]=0.0,s[1,59]=-0.9,s[1,60]=-1.0
s[2,1]=0.0,s[2,2]=-0.9,s[2,3]=1.2,s[2,4]=0.3,s[2,5]=0.6,s[2,6]=0.6,s[2,7]=-0.7,s[2,8]=-0.1,s[2,9]=-0.1,s[2,10]=-0.9,s[2,11]=0.8,s[2,12]=0.5,s[2,13]=0.7,s[2,14]=0.8,s[2,15]=-1.2,s[2,16]=-1.0,s[2,17]=-0.2,s[2,18]=-1.1,s[2,19]=0.5,s[2,20]=-0.9,s[2,21]=0.6,s[2,22]=-0.1,s[2,23]=0.6,s[2,24]=0.2,s[2,25]=-0.3,s[2,26]=-0.5,s[2,27]=1.1,s[2,28]=-0.3,s[2,29]=-0.7,s[2,30]=-0.4,s[2,31]=-0.6,s[2,32]=0.9,s[2,33]=0.0,s[2,34]=-0.6,s[2,35]=1.2,s[2,36]=-0.4,s[2,37]=0.9,s[2,38]=0.7,s[2,39]=-0.2,s[2,40]=-0.1,s[2,41]=-0.8,s[2,42]=-0.8,s[2,43]=-1.2,s[2,44]=1.2,s[2,45]=0.2,s[2,46]=-0.7,s[2,47]=-0.9,s[2,48]=-0.4,s[2,49]=0.1,s[2,50]=0.7,s[2,51]=0.2,s[2,52]=1.1,s[2,53]=-0.1,s[2,54]=-1.2,s[2,55]=-0.5,s[2,56]=0.0,s[2,57]=1.0,s[2,58]=1.2,s[2,59]=-0.2,s[2,60]=-1.1
s[3,1]=0.0,s[3,2]=-0.7,s[3,3]=0.0,s[3,4]=-0.8,s[3,5]=-0.8,s[3,6]=-0.6,s[3,7]=0.3,s[3,8]=0.1,s[3,9]=0.5,s[3,10]=-0.4,s[3,11]=0.0,s[3,12]=0.4,s[3,13]=0.7,s[3,14]=0.4,s[3,15]=1.2,s[3,16]=-0.6,s[3,17]=0.4,s[3,18]=-0.2,s[3,19]=-1.2,s[3,20]=0.2,s[3,21]=-1.0,s[3,22]=-0.6,s[3,23]=-0.9,s[3,24]=0.7,s[3,25]=-0.6,s[3,26]=1.2,s[3,27]=0.8,s[3,28]=-0.3,s[3,29]=0.3,s[3,30]=0.3,s[3,31]=-1.2,s[3,32]=0.6,s[3,33]=0.3,s[3,34]=0.6,s[3,35]=-0.5,s[3,36]=0.4,s[3,37]=-0.2,s[3,38]=-0.4,s[3,39]=-0.6,s[3,40]=-0.3,s[3,41]=-0.7,s[3,42]=0.0,s[3,43]=1.0,s[3,44]=0.8,s[3,45]=1.1,s[3,46]=0.7,s[3,47]=0.3,s[3,48]=-0.3,s[3,49]=-1.2,s[3,50]=-0.6,s[3,51]=-1.1,s[3,52]=-0.3,s[3,53]=-0.2,s[3,54]=-0.7,s[3,55]=-1.0,s[3,56]=1.2,s[3,57]=-1.2,s[3,58]=-0.7,s[3,59]=0.2,s[3,60]=-0.2
s[4,1]=-0.7,s[4,2]=-1.1,s[4,3]=1.2,s[4,4]=-0.2,s[4,5]=-1.1,s[4,6]=0.8,s[4,7]=-1.1,s[4,8]=0.8,s[4,9]=0.3,s[4,10]=-0.9,s[4,11]=-0.5,s[4,12]=0.5,s[4,13]=-0.2,s[4,14]=-0.7,s[4,15]=0.3,s[4,16]=1.2,s[4,17]=-0.8,s[4,18]=0.0,s[4,19]=-1.0,s[4,20]=-1.0,s[4,21]=-1.0,s[4,22]=0.8,s[4,23]=-0.4,s[4,24]=0.6,s[4,25]=-1.1,s[4,26]=0.7,s[4,27]=-0.5,s[4,28]=-0.4,s[4,29]=-1.2,s[4,30]=0.7,s[4,31]=-0.9,s[4,32]=0.5,s[4,33]=0.9,s[4,34]=-0.6,s[4,35]=-1.1,s[4,36]=-0.5,s[4,37]=0.0,s[4,38]=-1.0,s[4,39]=0.1,s[4,40]=1.0,s[4,41]=-1.0,s[4,42]=-0.3,s[4,43]=-0.8,s[4,44]=1.2,s[4,45]=-0.3,s[4,46]=0.8,s[4,47]=0.8,s[4,48]=-1.2,s[4,49]=-0.3,s[4,50]=0.7,s[4,51]=1.1,s[4,52]=0.8,s[4,53]=0.1,s[4,54]=0.8,s[4,55]=0.3,s[4,56]=1.2,s[4,57]=1.0,s[4,58]=0.2,s[4,59]=0.6,s[4,60]=-0.6
s[5,1]=-0.2,s[5,2]=0.0,s[5,3]=-1.0,s[5,4]=1.0,s[5,5]=-0.3,s[5,6]=-0.7,s[5,7]=-1.2,s[5,8]=-0.6,s[5,9]=0.4,s[5,10]=0.5,s[5,11]=0.9,s[5,12]=1.1,s[5,13]=0.8,s[5,14]=1.2,s[5,15]=0.1,s[5,16]=1.1,s[5,17]=-0.5,s[5,18]=-0.4,s[5,19]=-0.4,s[5,20]=0.4,s[5,21]=-0.9,s[5,22]=-0.2,s[5,23]=0.0,s[5,24]=-0.9,s[5,25]=-0.8,s[5,26]=1.2,s[5,27]=-1.2,s[5,28]=0.2,s[5,29]=0.4,s[5,30]=-0.1,s[5,31]=0.3,s[5,32]=-0.6,s[5,33]=-0.1,s[5,34]=-1.1,s[5,35]=-0.5,s[5,36]=-1.0,s[5,37]=0.7,s[5,38]=0.0,s[5,39]=-1.0,s[5,40]=0.0,s[5,41]=0.3,s[5,42]=0.3,s[5,43]=1.0,s[5,44]=0.1,s[5,45]=1.0,s[5,46]=1.2,s[5,47]=-0.1,s[5,48]=-0.4,s[5,49]=-0.5,s[5,50]=0.1,s[5,51]=-0.4,s[5,52]=0.4,s[5,53]=-0.6,s[5,54]=-1.1,s[5,55]=-0.1,s[5,56]=0.0,s[5,57]=0.2,s[5,58]=0.0,s[5,59]=-0.1,s[5,60]=-0.9
s[6,1]=-0.3,s[6,2]=0.6,s[6,3]=0.0,s[6,4]=-0.7,s[6,5]=0.6,s[6,6]=1.2,s[6,7]=-0.1,s[6,8]=0.7,s[6,9]=-0.9,s[6,10]=-1.1,s[6,11]=1.2,s[6,12]=1.1,s[6,13]=-1.1,s[6,14]=-0.1,s[6,15]=0.3,s[6,16]=-0.1,s[6,17]=-0.9,s[6,18]=-0.4,s[6,19]=0.3,s[6,20]=0.1,s[6,21]=-1.2,s[6,22]=-0.6,s[6,23]=-0.3,s[6,24]=0.2,s[6,25]=-0.2,s[6,26]=-0.2,s[6,27]=0.3,s[6,28]=1.1,s[6,29]=-1.1,s[6,30]=-1.0,s[6,31]=-1.0,s[6,32]=0.3,s[6,33]=-0.3,s[6,34]=0.6,s[6,35]=-1.2,s[6,36]=0.1,s[6,37]=-0.2,s[6,38]=0.5,s[6,39]=1.2,s[6,40]=0.9,s[6,41]=-0.5,s[6,42]=1.1,s[6,43]=-0.3,s[6,44]=0.9,s[6,45]=-0.3,s[6,46]=1.0,s[6,47]=-0.5,s[6,48]=-0.2,s[6,49]=0.2,s[6,50]=0.9,s[6,51]=1.1,s[6,52]=0.5,s[6,53]=-1.0,s[6,54]=-0.5,s[6,55]=0.9,s[6,56]=-0.6,s[6,57]=-1.1,s[6,58]=-0.2,s[6,59]=-0.3,s[6,60]=0.5
s[7,1]=-0.8,s[7,2]=0.7,s[7,3]=-0.5,s[7,4]=-1.1,s[7,5]=-0.7,s[7,6]=0.7,s[7,7]=-1.1,s[7,8]=-0.3,s[7,9]=0.6,s[7,10]=-0.1,s[7,11]=-0.8,s[7,12]=0.6,s[7,13]=1.2,s[7,14]=-1.1,s[7,15]=0.6,s[7,16]=-0.1,s[7,17]=-0.3,s[7,18]=0.5,s[7,19]=0.1,s[7,20]=0.9,s[7,21]=0.8,s[7,22]=-0.6,s[7,23]=0.8,s[7,24]=1.2,s[7,25]=0.3,s[7,26]=-0.5,s[7,27]=0.7,s[7,28]=0.1,s[7,29]=1.2,s[7,30]=-1.1,s[7,31]=0.9,s[7,32]=-0.9,s[7,33]=0.6,s[7,34]=-0.4,s[7,35]=0.2,s[7,36]=-0.7,s[7,37]=-0.8,s[7,38]=-0.6,s[7,39]=-0.7,s[7,40]=-0.5,s[7,41]=0.8,s[7,42]=-1.2,s[7,43]=1.0,s[7,44]=-1.2,s[7,45]=0.1,s[7,46]=-0.4,s[7,47]=0.1,s[7,48]=-0.6,s[7,49]=-0.6,s[7,50]=0.2,s[7,51]=-0.4,s[7,52]=0.5,s[7,53]=-0.2,s[7,54]=-0.5,s[7,55]=0.9,s[7,56]=-0.1,s[7,57]=-1.1,s[7,58]=0.4,s[7,59]=-1.0,s[7,60]=-0.3
s[8,1]=1.1,s[8,2]=-1.0,s[8,3]=0.7,s[8,4]=0.9,s[8,5]=1.1,s[8,6]=-0.1,s[8,7]=0.3,s[8,8]=0.4,s[8,9]=-1.1,s[8,10]=-1.0,s[8,11]=-0.9,s[8,12]=-1.1,s[8,13]=-0.4,s[8,14]=-1.1,s[8,15]=-0.2,s[8,16]=-1.2,s[8,17]=-0.2,s[8,18]=0.1,s[8,19]=0.7,s[8,20]=0.7,s[8,21]=0.5,s[8,22]=-0.3,s[8,23]=-1.0,s[8,24]=0.1,s[8,25]=-0.7,s[8,26]=0.8,s[8,27]=-1.2,s[8,28]=-0.7,s[8,29]=0.5,s[8,30]=0.9,s[8,31]=-0.6,s[8,32]=-0.8,s[8,33]=-0.5,s[8,34]=0.3,s[8,35]=0.2,s[8,36]=0.8,s[8,37]=-0.6,s[8,38]=1.0,s[8,39]=-0.8,s[8,40]=-1.2,s[8,41]=0.5,s[8,42]=-0.2,s[8,43]=-1.1,s[8,44]=-0.4,s[8,45]=0.4,s[8,46]=0.9,s[8,47]=0.6,s[8,48]=0.6,s[8,49]=0.1,s[8,50]=1.0,s[8,51]=0.6,s[8,52]=-0.8,s[8,53]=0.6,s[8,54]=0.2,s[8,55]=0.7,s[8,56]=1.1,s[8,57]=0.8,s[8,58]=0.2,s[8,59]=-0.6,s[8,60]=-0.5
s[9,1]=0.8,s[9,2]=-0.1,s[9,3]=-0.2,s[9,4]=-0.4,s[9,5]=1.2,s[9,6]=-0.6,s[9,7]=-0.2,s[9,8]=0.7,s[9,9]=-0.9,s[9,10]=0.0,s[9,11]=-0.2,s[9,12]=-1.0,s[9,13]=0.9,s[9,14]=-1.1,s[9,15]=0.5,s[9,16]=0.0,s[9,17]=1.0,s[9,18]=-0.9,s[9,19]=-0.2,s[9,20]=-1.0,s[9,21]=1.0,s[9,22]=0.0,s[9,23]=0.8,s[9,24]=1.2,s[9,25]=1.2,s[9,26]=0.7,s[9,27]=0.0,s[9,28]=-0.5,s[9,29]=0.7,s[9,30]=-0.7,s[9,31]=0.1,s[9,32]=-0.9,s[9,33]=-0.9,s[9,34]=0.6,s[9,35]=-0.5,s[9,36]=0.0,s[9,37]=0.9,s[9,38]=-0.2,s[9,39]=0.6,s[9,40]=-1.1,s[9,41]=0.0,s[9,42]=1.2,s[9,43]=0.6,s[9,44]=-0.3,s[9,45]=-1.1,s[9,46]=-1.0,s[9,47]=-0.5,s[9,48]=-1.0,s[9,49]=0.5,s[9,50]=0.7,s[9,51]=-0.5,s[9,52]=-1.1,s[9,53]=0.7,s[9,54]=-0.8,s[9,55]=-0.7,s[9,56]=0.9,s[9,57]=1.1,s[9,58]=-0.6,s[9,59]=1.1,s[9,60]=1.2
s[10,1]=0.1,s[10,2]=0.3,s[10,3]=-1.0,s[10,4]=-0.3,s[10,5]=-0.7,s[10,6]=0.8,s[10,7]=0.5,s[10,8]=-0.5,s[10,9]=0.5,s[10,10]=-1.1,s[10,11]=-0.7,s[10,12]=0.9,s[10,13]=0.1,s[10,14]=-0.8,s[10,15]=0.0,s[10,16]=-0.6,s[10,17]=-0.8,s[10,18]=1.2,s[10,19]=-1.2,s[10,20]=0.9,s[10,21]=1.1,s[10,22]=-1.1,s[10,23]=-0.3,s[10,24]=0.8,s[10,25]=0.9,s[10,26]=1.2,s[10,27]=1.0,s[10,28]=0.6,s[10,29]=0.5,s[10,30]=-0.9,s[10,31]=-1.0,s[10,32]=1.2,s[10,33]=-0.2,s[10,34]=-0.3,s[10,35]=-1.2,s[10,36]=0.7,s[10,37]=-0.3,s[10,38]=-0.2,s[10,39]=-0.8,s[10,40]=-1.1,s[10,41]=-0.4,s[10,42]=1.2,s[10,43]=1.1,s[10,44]=0.3,s[10,45]=-1.1,s[10,46]=1.0,s[10,47]=-1.0,s[10,48]=-0.3,s[10,49]=0.3,s[10,50]=-0.7,s[10,51]=-0.9,s[10,52]=0.2,s[10,53]=0.2,s[10,54]=0.1,s[10,55]=-0.4,s[10,56]=0.6,s[10,57]=-1.1,s[10,58]=0.6,s[10,59]=-0.1,s[10,60]=-0.9
s[11,1]=0.0,s[11,2]=0.8,s[11,3]=-0.3,s[11,4]=-0.5,s[11,5]=-0.4,s[11,6]=0.3,s[11,7]=0.8,s[11,8]=-0.3,s[11,9]=-0.5,s[11,10]=-0.6,s[11,11]=0.6,s[11,12]=1.1,s[11,13]=-0.6,s[11,14]=-0.1,s[11,15]=0.0,s[11,16]=-0.1,s[11,17]=0.5,s[11,18]=0.0,s[11,19]=0.8,s[11,20]=0.7,s[11,21]=0.4,s[11,22]=-0.9,s[11,23]=-0.1,s[11,24]=0.3,s[11,25]=-0.6,s[11,26]=0.7,s[11,27]=-0.7,s[11,28]=1.1,s[11,29]=0.3,s[11,30]=-0.9,s[11,31]=0.6,s[11,32]=-0.9,s[11,33]=0.7,s[11,34]=-0.5,s[11,35]=0.7,s[11,36]=1.1,s[11,37]=-1.2,s[11,38]=1.2,s[11,39]=-0.9,s[11,40]=-1.0,s[11,41]=-1.2,s[11,42]=1.0,s[11,43]=-0.6,s[11,44]=0.2,s[11,45]=-0.6,s[11,46]=1.2,s[11,47]=0.3,s[11,48]=-0.3,s[11,49]=-0.6,s[11,50]=0.8,s[11,51]=-0.4,s[11,52]=0.7,s[11,53]=-0.4,s[11,54]=0.0,s[11,55]=0.2,s[11,56]=-0.1,s[11,57]=0.1,s[11,58]=0.3,s[11,59]=-0.6,s[11,60]=-0.7
s[12,1]=-0.7,s[12,2]=-1.1,s[12,3]=-0.1,s[12,4]=-0.8,s[12,5]=1.2,s[12,6]=-0.6,s[12,7]=0.6,s[12,8]=-0.7,s[12,9]=0.5,s[12,10]=1.2,s[12,11]=0.1,s[12,12]=0.5,s[12,13]=0.9,s[12,14]=1.1,s[12,15]=-1.0,s[12,16]=0.8,s[12,17]=0.4,s[12,18]=-1.0,s[12,19]=-0.4,s[12,20]=0.0,s[12,21]=-0.2,s[12,22]=0.3,s[12,23]=0.0,s[12,24]=-1.1,s[12,25]=-0.1,s[12,26]=-0.7,s[12,27]=-1.2,s[12,28]=0.1,s[12,29]=0.9,s[12,30]=1.0,s[12,31]=-0.6,s[12,32]=-1.0,s[12,33]=0.7,s[12,34]=-1.0,s[12,35]=0.3,s[12,36]=-1.1,s[12,37]=-1.1,s[12,38]=1.0,s[12,39]=0.1,s[12,40]=0.8,s[12,41]=0.4,s[12,42]=-0.4,s[12,43]=-0.3,s[12,44]=-0.1,s[12,45]=0.2,s[12,46]=-0.3,s[12,47]=-0.4,s[12,48]=0.5,s[12,49]=-1.0,s[12,50]=-0.9,s[12,51]=1.1,s[12,52]=1.2,s[12,53]=0.5,s[12,54]=0.0,s[12,55]=-0.1,s[12,56]=-0.9,s[12,57]=0.4,s[12,58]=1.0,s[12,59]=-0.4,s[12,60]=-1.2
s[13,1]=0.7,s[13,2]=1.1,s[13,3]=-0.1,s[13,4]=-0.3,s[13,5]=0.6,s[13,6]=0.8,s[13,7]=0.3,s[13,8]=-0.3,s[13,9]=-1.2,s[13,10]=0.7,s[13,11]=-0.2,s[13,12]=1.0,s[13,13]=0.4,s[13,14]=0.2,s[13,15]=-0.3,s[13,16]=0.6,s[13,17]=0.9,s[13,18]=0.3,s[13,19]=-1.0,s[13,20]=0.8,s[13,21]=-0.6,s[13,22]=-0.8,s[13,23]=-0.7,s[13,24]=-0.3,s[13,25]=-0.1,s[13,26]=-0.4,s[13,27]=0.1,s[13,28]=1.1,s[13,29]=0.6,s[13,30]=0.9,s[13,31]=-0.7,s[13,32]=0.7,s[13,33]=0.0,s[13,34]=0.6,s[13,35]=0.8,s[13,36]=-0.9,s[13,37]=0.8,s[13,38]=0.7,s[13,39]=-0.6,s[13,40]=0.9,s[13,41]=-1.1,s[13,42]=-0.7,s[13,43]=0.5,s[13,44]=0.0,s[13,45]=0.8,s[13,46]=1.0,s[13,47]=0.3,s[13,48]=-0.9,s[13,49]=-0.7,s[13,50]=-0.1,s[13,51]=0.4,s[13,52]=0.2,s[13,53]=-0.9,s[13,54]=-1.2,s[13,55]=-0.4,s[13,56]=0.3,s[13,57]=-0.8,s[13,58]=-0.5,s[13,59]=-0.5,s[13,60]=1.1
s[14,1]=-0.2,s[14,2]=1.1,s[14,3]=-1.1,s[14,4]=1.2,s[14,5]=1.2,s[14,6]=1.0,s[14,7]=0.2,s[14,8]=1.0,s[14,9]=-0.3,s[14,10]=0.6,s[14,11]=0.5,s[14,12]=0.8,s[14,13]=-0.6,s[14,14]=-0.6,s[14,15]=-0.3,s[14,16]=-1.0,s[14,17]=-0.6,s[14,18]=0.8,s[14,19]=0.6,s[14,20]=0.5,s[14,21]=1.0,s[14,22]=-0.3,s[14,23]=1.1,s[14,24]=-0.7,s[14,25]=-0.7,s[14,26]=1.0,s[14,27]=-0.8,s[14,28]=0.5,s[14,29]=0.5,s[14,30]=1.2,s[14,31]=0.1,s[14,32]=-0.3,s[14,33]=-1.2,s[14,34]=-0.4,s[14,35]=0.7,s[14,36]=0.3,s[14,37]=0.3,s[14,38]=0.9,s[14,39]=-0.9,s[14,40]=0.8,s[14,41]=0.9,s[14,42]=0.0,s[14,43]=0.8,s[14,44]=-0.3,s[14,45]=-0.4,s[14,46]=-1.2,s[14,47]=1.1,s[14,48]=1.0,s[14,49]=1.0,s[14,50]=-1.2,s[14,51]=-1.2,s[14,52]=0.8,s[14,53]=-0.3,s[14,54]=0.5,s[14,55]=-0.5,s[14,56]=0.9,s[14,57]=0.0,s[14,58]=0.6,s[14,59]=-1.0,s[14,60]=-0.1
s[15,1]=0.3,s[15,2]=0.1,s[15,3]=0.2,s[15,4]=0.7,s[15,5]=0.6,s[15,6]=-0.6,s[15,7]=-0.1,s[15,8]=-0.7,s[15,9]=0.3,s[15,10]=-0.5,s[15,11]=0.3,s[15,12]=-0.2,s[15,13]=0.0,s[15,14]=0.6,s[15,15]=-0.3,s[15,16]=-0.1,s[15,17]=0.4,s[15,18]=0.1,s[15,19]=0.7,s[15,20]=-1.0,s[15,21]=0.9,s[15,22]=0.4,s[15,23]=-0.5,s[15,24]=1.1,s[15,25]=1.1,s[15,26]=-0.6,s[15,27]=0.6,s[15,28]=0.6,s[15,29]=-0.3,s[15,30]=-0.9,s[15,31]=0.8,s[15,32]=0.1,s[15,33]=0.0,s[15,34]=0.4,s[15,35]=1.2,s[15,36]=1.0,s[15,37]=1.2,s[15,38]=-1.1,s[15,39]=-0.3,s[15,40]=-0.3,s[15,41]=-0.3,s[15,42]=0.2,s[15,43]=0.6,s[15,44]=-0.8,s[15,45]=0.3,s[15,46]=1.2,s[15,47]=0.8,s[15,48]=0.6,s[15,49]=1.0,s[15,50]=0.0,s[15,51]=0.0,s[15,52]=1.1,s[15,53]=-1.0,s[15,54]=1.1,s[15,55]=0.6,s[15,56]=0.1,s[15,57]=-1.2,s[15,58]=1.2,s[15,59]=-0.9,s[15,60]=0.3
s[16,1]=-0.5,s[16,2]=0.5,s[16,3]=0.8,s[16,4]=0.4,s[16,5]=0.1,s[16,6]=-0.3,s[16,7]=-0.3,s[16,8]=0.9,s[16,9]=-0.9,s[16,10]=-0.6,s[16,11]=1.2,s[16,12]=-0.9,s[16,13]=-0.3,s[16,14]=0.4,s[16,15]=0.2,s[16,16]=-0.3,s[16,17]=-0.1,s[16,18]=0.7,s[16,19]=1.2,s[16,20]=0.3,s[16,21]=-0.5,s[16,22]=-0.2,s[16,23]=0.7,s[16,24]=-0.8,s[16,25]=0.9,s[16,26]=0.9,s[16,27]=0.2,s[16,28]=-0.4,s[16,29]=1.2,s[16,30]=0.5,s[16,31]=-0.3,s[16,32]=-0.2,s[16,33]=0.5,s[16,34]=-0.2,s[16,35]=-0.6,s[16,36]=0.9,s[16,37]=-0.5,s[16,38]=1.2,s[16,39]=0.7,s[16,40]=0.9,s[16,41]=0.4,s[16,42]=-0.9,s[16,43]=0.4,s[16,44]=0.6,s[16,45]=-0.6,s[16,46]=0.9,s[16,47]=-0.4,s[16,48]=-0.6,s[16,49]=-0.5,s[16,50]=-0.6,s[16,51]=-0.1,s[16,52]=-0.8,s[16,53]=-1.2,s[16,54]=-0.8,s[16,55]=1.2,s[16,56]=0.1,s[16,57]=-0.8,s[16,58]=0.8,s[16,59]=-1.1,s[16,60]=0.4
s[17,1]=0.5,s[17,2]=0.0,s[17,3]=-1.2,s[17,4]=0.7,s[17,5]=0.3,s[17,6]=0.8,s[17,7]=0.5,s[17,8]=1.1,s[17,9]=-0.5,s[17,10]=-1.0,s[17,11]=-1.2,s[17,12]=-0.3,s[17,13]=0.0,s[17,14]=1.2,s[17,15]=0.5,s[17,16]=1.2,s[17,17]=-0.6,s[17,18]=0.7,s[17,19]=0.2,s[17,20]=0.7,s[17,21]=1.2,s[17,22]=-0.3,s[17,23]=-0.8,s[17,24]=0.7,s[17,25]=-1.0,s[17,26]=0.6,s[17,27]=0.3,s[17,28]=-0.5,s[17,29]=1.2,s[17,30]=-0.7,s[17,31]=1.0,s[17,32]=0.0,s[17,33]=-0.7,s[17,34]=0.7,s[17,35]=0.3,s[17,36]=-0.5,s[17,37]=-0.3,s[17,38]=-0.7,s[17,39]=0.0,s[17,40]=-0.6,s[17,41]=0.7,s[17,42]=0.9,s[17,43]=-1.2,s[17,44]=0.3,s[17,45]=0.2,s[17,46]=-0.1,s[17,47]=-1.1,s[17,48]=-1.1,s[17,49]=1.0,s[17,50]=-0.5,s[17,51]=-0.3,s[17,52]=0.3,s[17,53]=-0.5,s[17,54]=0.7,s[17,55]=-1.2,s[17,56]=0.9,s[17,57]=1.1,s[17,58]=0.9,s[17,59]=1.0,s[17,60]=0.4
s[18,1]=-1.0,s[18,2]=-0.3,s[18,3]=1.2,s[18,4]=-0.9,s[18,5]=-0.6,s[18,6]=1.0,s[18,7]=0.5,s[18,8]=-1.2,s[18,9]=-1.0,s[18,10]=-0.9,s[18,11]=0.8,s[18,12]=-1.1,s[18,13]=0.2,s[18,14]=-0.6,s[18,15]=-0.2,s[18,16]=-0.7,s[18,17]=0.6,s[18,18]=0.4,s[18,19]=0.6,s[18,20]=0.3,s[18,21]=-0.4,s[18,22]=-0.1,s[18,23]=0.5,s[18,24]=0.1,s[18,25]=-0.3,s[18,26]=-0.7,s[18,27]=-0.4,s[18,28]=-0.2,s[18,29]=0.5,s[18,30]=0.7,s[18,31]=-0.9,s[18,32]=0.2,s[18,33]=0.4,s[18,34]=0.0,s[18,35]=-0.4,s[18,36]=0.2,s[18,37]=-0.4,s[18,38]=0.0,s[18,39]=1.2,s[18,40]=-1.2,s[18,41]=-1.1,s[18,42]=-0.1,s[18,43]=-1.1,s[18,44]=0.6,s[18,45]=1.1,s[18,46]=0.3,s[18,47]=1.0,s[18,48]=-1.1,s[18,49]=-0.8,s[18,50]=-0.8,s[18,51]=0.2,s[18,52]=0.2,s[18,53]=-1.2,s[18,54]=-1.0,s[18,55]=-1.1,s[18,56]=-0.5,s[18,57]=0.8,s[18,58]=-1.2,s[18,59]=-1.1,s[18,60]=0.0
s[19,1]=-0.2,s[19,2]=-1.0,s[19,3]=0.9,s[19,4]=0.3,s[19,5]=-0.6,s[19,6]=1.2,s[19,7]=0.1,s[19,8]=-1.2,s[19,9]=0.9,s[19,10]=0.1,s[19,11]=0.6,s[19,12]=-1.1,s[19,13]=-1.0,s[19,14]=0.1,s[19,15]=0.6,s[19,16]=0.6,s[19,17]=-1.1,s[19,18]=-0.5,s[19,19]=1.2,s[19,20]=-0.2,s[19,21]=0.5,s[19,22]=-0.8,s[19,23]=0.5,s[19,24]=-0.7,s[19,25]=-1.1,s[19,26]=0.9,s[19,27]=-0.3,s[19,28]=0.4,s[19,29]=0.0,s[19,30]=-1.0,s[19,31]=1.0,s[19,32]=-1.1,s[19,33]=-0.9,s[19,34]=0.7,s[19,35]=0.8,s[19,36]=-0.4,s[19,37]=-0.5,s[19,38]=0.3,s[19,39]=0.2,s[19,40]=-0.8,s[19,41]=-0.6,s[19,42]=0.4,s[19,43]=0.5,s[19,44]=-0.4,s[19,45]=-0.9,s[19,46]=-0.9,s[19,47]=-0.5,s[19,48]=1.0,s[19,49]=0.9,s[19,50]=-0.8,s[19,51]=-0.6,s[19,52]=-1.2,s[19,53]=-0.2,s[19,54]=-0.6,s[19,55]=-0.6,s[19,56]=-0.1,s[19,57]=-1.2,s[19,58]=1.0,s[19,59]=-1.0,s[19,60]=-0.2
s[20,1]=0.9,s[20,2]=0.5,s[20,3]=-0.6,s[20,4]=0.8,s[20,5]=-0.4,s[20,6]=0.9,s[20,7]=-1.0,s[20,8]=0.0,s[20,9]=-0.1,s[20,10]=0.5,s[20,11]=0.8,s[20,12]=-0.6,s[20,13]=0.8,s[20,14]=-0.8,s[20,15]=0.2,s[20,16]=-0.2,s[20,17]=-1.0,s[20,18]=0.0,s[20,19]=-1.2,s[20,20]=0.8,s[20,21]=0.8,s[20,22]=1.2,s[20,23]=-0.9,s[20,24]=1.1,s[20,25]=1.0,s[20,26]=-0.4,s[20,27]=0.9,s[20,28]=0.8,s[20,29]=-1.2,s[20,30]=-0.2,s[20,31]=-0.6,s[20,32]=1.2,s[20,33]=-0.5,s[20,34]=-0.3,s[20,35]=-1.0,s[20,36]=-0.1,s[20,37]=-0.7,s[20,38]=-0.1,s[20,39]=0.8,s[20,40]=0.1,s[20,41]=-0.1,s[20,42]=1.0,s[20,43]=1.2,s[20,44]=0.6,s[20,45]=-0.8,s[20,46]=-1.1,s[20,47]=0.2,s[20,48]=-0.1,s[20,49]=-1.2,s[20,50]=-1.2,s[20,51]=-0.8,s[20,52]=-1.2,s[20,53]=-1.1,s[20,54]=1.0,s[20,55]=0.9,s[20,56]=0.3,s[20,57]=-0.6,s[20,58]=-0.4,s[20,59]=-1.1,s[20,60]=-0.9
s[21,1]=-0.1,s[21,2]=-0.6,s[21,3]=-0.7,s[21,4]=0.3,s[21,5]=0.3,s[21,6]=-0.7,s[21,7]=-0.7,s[21,8]=-0.6,s[21,9]=1.2,s[21,10]=-0.1,s[21,11]=0.1,s[21,12]=0.5,s[21,13]=-0.3,s[21,14]=1.2,s[21,15]=1.1,s[21,16]=0.7,s[21,17]=-0.8,s[21,18]=-1.1,s[21,19]=0.0,s[21,20]=-0.6,s[21,21]=-1.2,s[21,22]=-0.8,s[21,23]=0.7,s[21,24]=0.9,s[21,25]=0.5,s[21,26]=-0.9,s[21,27]=-0.6,s[21,28]=0.1,s[21,29]=0.5,s[21,30]=-0.9,s[21,31]=0.0,s[21,32]=0.5,s[21,33]=-1.2,s[21,34]=1.0,s[21,35]=-0.4,s[21,36]=0.1,s[21,37]=1.1,s[21,38]=-0.1,s[21,39]=-0.3,s[21,40]=-0.9,s[21,41]=-0.6,s[21,42]=-0.2,s[21,43]=0.7,s[21,44]=-1.0,s[21,45]=-0.1,s[21,46]=-1.2,s[21,47]=-0.1,s[21,48]=1.2,s[21,49]=-1.0,s[21,50]=-0.7,s[21,51]=-0.1,s[21,52]=-0.7,s[21,53]=1.2,s[21,54]=-1.2,s[21,55]=-0.1,s[21,56]=-1.1,s[21,57]=-0.4,s[21,58]=1.2,s[21,59]=-0.4,s[21,60]=-0.3
s[22,1]=1.2,s[22,2]=0.5,s[22,3]=-0.7,s[22,4]=0.4,s[22,5]=-1.0,s[22,6]=0.7,s[22,7]=-0.3,s[22,8]=1.1,s[22,9]=-0.6,s[22,10]=-0.5,s[22,11]=1.2,s[22,12]=-1.1,s[22,13]=-0.8,s[22,14]=0.3,s[22,15]=0.5,s[22,16]=0.8,s[22,17]=-1.2,s[22,18]=-0.4,s[22,19]=0.1,s[22,20]=-0.4,s[22,21]=-1.2,s[22,22]=0.6,s[22,23]=0.8,s[22,24]=0.9,s[22,25]=0.1,s[22,26]=-0.2,s[22,27]=-0.1,s[22,28]=0.5,s[22,29]=0.5,s[22,30]=0.9,s[22,31]=0.8,s[22,32]=0.0,s[22,33]=0.3,s[22,34]=1.0,s[22,35]=-0.6,s[22,36]=-0.3,s[22,37]=0.0,s[22,38]=0.9,s[22,39]=1.1,s[22,40]=0.8,s[22,41]=0.6,s[22,42]=-0.8,s[22,43]=0.1,s[22,44]=-0.9,s[22,45]=0.9,s[22,46]=0.5,s[22,47]=-1.0,s[22,48]=-0.4,s[22,49]=0.7,s[22,50]=0.6,s[22,51]=0.4,s[22,52]=1.1,s[22,53]=-1.2,s[22,54]=-0.9,s[22,55]=1.2,s[22,56]=-0.8,s[22,57]=0.8,s[22,58]=-1.0,s[22,59]=0.0,s[22,60]=0.9
s[23,1]=-1.1,s[23,2]=-0.5,s[23,3]=-0.9,s[23,4]=0.8,s[23,5]=-0.3,s[23,6]=-0.2,s[23,7]=1.2,s[23,8]=0.2,s[23,9]=-1.0,s[23,10]=0.1,s[23,11]=0.2,s[23,12]=0.8,s[23,13]=-1.0,s[23,14]=-1.1,s[23,15]=0.6,s[23,16]=0.7,s[23,17]=-0.3,s[23,18]=-0.6,s[23,19]=0.8,s[23,20]=0.1,s[23,21]=0.2,s[23,22]=-0.3,s[23,23]=-0.8,s[23,24]=-0.9,s[23,25]=-0.9,s[23,26]=0.9,s[23,27]=-1.1,s[23,28]=1.1,s[23,29]=-0.6,s[23,30]=0.6,s[23,31]=-0.2,s[23,32]=-0.4,s[23,33]=0.6,s[23,34]=-0.5,s[23,35]=-0.4,s[23,36]=-0.4,s[23,37]=-0.3,s[23,38]=0.8,s[23,39]=0.9,s[23,40]=0.9,s[23,41]=-0.1,s[23,42]=-0.7,s[23,43]=0.6,s[23,44]=0.9,s[23,45]=-0.6,s[23,46]=1.1,s[23,47]=-0.5,s[23,48]=0.9,s[23,49]=-1.0,s[23,50]=1.1,s[23,51]=0.8,s[23,52]=1.2,s[23,53]=1.2,s[23,54]=0.0,s[23,55]=-0.7,s[23,56]=-0.9,s[23,57]=-0.2,s[23,58]=-0.7,s[23,59]=-0.6,s[23,60]=-0.3
s[24,1]=1.1,s[24,2]=0.4,s[24,3]=-0.4,s[24,4]=-1.0,s[24,5]=0.3,s[24,6]=0.4,s[24,7]=0.5,s[24,8]=-0.6,s[24,9]=0.9,s[24,10]=-0.5,s[24,11]=-0.8,s[24,12]=-0.7,s[24,13]=0.5,s[24,14]=0.3,s[24,15]=-1.2,s[24,16]=0.8,s[24,17]=-0.4,s[24,18]=-0.9,s[24,19]=-0.4,s[24,20]=-0.9,s[24,21]=1.1,s[24,22]=-0.6,s[24,23]=0.2,s[24,24]=-0.7,s[24,25]=-1.1,s[24,26]=-0.5,s[24,27]=1.1,s[24,28]=-1.1,s[24,29]=0.6,s[24,30]=0.2,s[24,31]=1.2,s[24,32]=-0.5,s[24,33]=1.2,s[24,34]=0.7,s[24,35]=0.9,s[24,36]=1.0,s[24,37]=0.3,s[24,38]=-1.0,s[24,39]=-0.5,s[24,40]=-0.9,s[24,41]=-0.5,s[24,42]=0.4,s[24,43]=-1.1,s[24,44]=0.7,s[24,45]=0.2,s[24,46]=-0.5,s[24,47]=0.5,s[24,48]=-0.8,s[24,49]=0.4,s[24,50]=-0.2,s[24,51]=1.1,s[24,52]=0.9,s[24,53]=1.0,s[24,54]=0.2,s[24,55]=-0.8,s[24,56]=0.9,s[24,57]=0.2,s[24,58]=-1.2,s[24,59]=0.3,s[24,60]=0.6
s[25,1]=-0.2,s[25,2]=0.9,s[25,3]=-0.5,s[25,4]=-0.8,s[25,5]=-0.5,s[25,6]=0.3,s[25,7]=0.2,s[25,8]=0.7,s[25,9]=0.7,s[25,10]=0.2,s[25,11]=-0.3,s[25,12]=-0.4,s[25,13]=-0.9,s[25,14]=-1.2,s[25,15]=0.9,s[25,16]=0.5,s[25,17]=0.5,s[25,18]=0.1,s[25,19]=-0.1,s[25,20]=0.6,s[25,21]=-0.4,s[25,22]=0.0,s[25,23]=0.0,s[25,24]=0.6,s[25,25]=0.0,s[25,26]=-1.1,s[25,27]=-0.7,s[25,28]=-1.2,s[25,29]=0.8,s[25,30]=0.9,s[25,31]=-0.3,s[25,32]=1.0,s[25,33]=1.0,s[25,34]=0.2,s[25,35]=0.1,s[25,36]=0.3,s[25,37]=-0.8,s[25,38]=-0.9,s[25,39]=0.3,s[25,40]=1.1,s[25,41]=-0.1,s[25,42]=0.1,s[25,43]=-0.1,s[25,44]=-0.5,s[25,45]=-0.7,s[25,46]=-1.2,s[25,47]=-0.1,s[25,48]=0.9,s[25,49]=-0.6,s[25,50]=0.5,s[25,51]=-0.9,s[25,52]=1.1,s[25,53]=-0.2,s[25,54]=-0.3,s[25,55]=-0.7,s[25,56]=0.1,s[25,57]=0.2,s[25,58]=1.0,s[25,59]=1.2,s[25,60]=0.9
s[26,1]=-1.2,s[26,2]=0.2,s[26,3]=-0.4,s[26,4]=1.0,s[26,5]=0.8,s[26,6]=0.0,s[26,7]=1.1,s[26,8]=-0.4,s[26,9]=1.1,s[26,10]=0.5,s[26,11]=0.7,s[26,12]=0.3,s[26,13]=0.8,s[26,14]=-0.7,s[26,15]=1.2,s[26,16]=-0.8,s[26,17]=-1.0,s[26,18]=-0.9,s[26,19]=0.6,s[26,20]=-0.9,s[26,21]=-0.6,s[26,22]=-0.7,s[26,23]=-0.4,s[26,24]=0.7,s[26,25]=0.6,s[26,26]=-1.1,s[26,27]=0.4,s[26,28]=0.7,s[26,29]=1.1,s[26,30]=-0.4,s[26,31]=-0.4,s[26,32]=0.8,s[26,33]=-0.6,s[26,34]=-0.7,s[26,35]=-0.2,s[26,36]=-1.1,s[26,37]=0.6,s[26,38]=0.2,s[26,39]=0.3,s[26,40]=-0.9,s[26,41]=0.7,s[26,42]=0.3,s[26,43]=1.0,s[26,44]=-0.6,s[26,45]=0.4,s[26,46]=0.2,s[26,47]=-0.6,s[26,48]=-0.9,s[26,49]=-0.4,s[26,50]=0.4,s[26,51]=0.5,s[26,52]=0.8,s[26,53]=0.1,s[26,54]=-0.1,s[26,55]=0.9,s[26,56]=-1.1,s[26,57]=-0.7,s[26,58]=-0.1,s[26,59]=-0.9,s[26,60]=0.0
s[27,1]=0.7,s[27,2]=-0.8,s[27,3]=0.3,s[27,4]=-0.5,s[27,5]=-0.1,s[27,6]=-0.2,s[27,7]=-0.9,s[27,8]=0.6,s[27,9]=-0.8,s[27,10]=-0.6,s[27,11]=-1.1,s[27,12]=1.0,s[27,13]=-0.4,s[27,14]=-0.6,s[27,15]=0.6,s[27,16]=-1.0,s[27,17]=0.1,s[27,18]=1.2,s[27,19]=0.6,s[27,20]=0.7,s[27,21]=-1.2,s[27,22]=-1.0,s[27,23]=-0.6,s[27,24]=0.9,s[27,25]=0.8,s[27,26]=-0.6,s[27,27]=-1.2,s[27,28]=0.0,s[27,29]=0.0,s[27,30]=0.3,s[27,31]=-0.2,s[27,32]=0.7,s[27,33]=0.0,s[27,34]=0.5,s[27,35]=0.5,s[27,36]=1.2,s[27,37]=-0.3,s[27,38]=-1.1,s[27,39]=-0.7,s[27,40]=0.2,s[27,41]=-0.5,s[27,42]=0.0,s[27,43]=-0.7,s[27,44]=-0.7,s[27,45]=1.1,s[27,46]=0.5,s[27,47]=0.6,s[27,48]=-1.0,s[27,49]=1.1,s[27,50]=-0.4,s[27,51]=0.2,s[27,52]=-0.7,s[27,53]=1.1,s[27,54]=-0.3,s[27,55]=-0.7,s[27,56]=-0.4,s[27,57]=0.7,s[27,58]=-0.8,s[27,59]=-1.2,s[27,60]=-0.9
s[28,1]=0.5,s[28,2]=-0.8,s[28,3]=-0.1,s[28,4]=-0.3,s[28,5]=0.1,s[28,6]=0.6,s[28,7]=0.2,s[28,8]=0.7,s[28,9]=-1.0,s[28,10]=0.8,s[28,11]=-1.1,s[28,12]=-1.0,s[28,13]=0.9,s[28,14]=0.1,s[28,15]=1.2,s[28,16]=-1.2,s[28,17]=1.2,s[28,18]=-0.9,s[28,19]=-1.0,s[28,20]=0.5,s[28,21]=-1.2,s[28,22]=-0.4,s[28,23]=-0.9,s[28,24]=0.4,s[28,25]=-0.5,s[28,26]=-1.1,s[28,27]=0.4,s[28,28]=0.9,s[28,29]=-1.0,s[28,30]=0.1,s[28,31]=0.3,s[28,32]=-0.4,s[28,33]=0.1,s[28,34]=0.2,s[28,35]=-1.1,s[28,36]=-0.1,s[28,37]=-0.9,s[28,38]=-0.4,s[28,39]=-1.0,s[28,40]=-0.9,s[28,41]=-0.3,s[28,42]=0.5,s[28,43]=0.4,s[28,44]=-1.0,s[28,45]=-0.8,s[28,46]=0.0,s[28,47]=0.9,s[28,48]=-0.2,s[28,49]=0.8,s[28,50]=0.0,s[28,51]=0.4,s[28,52]=0.3,s[28,53]=-0.6,s[28,54]=-0.7,s[28,55]=-0.7,s[28,56]=0.3,s[28,57]=0.7,s[28,58]=-0.1,s[28,59]=-0.8,s[28,60]=1.0
s[29,1]=1.1,s[29,2]=0.0,s[29,3]=-0.8,s[29,4]=0.7,s[29,5]=0.8,s[29,6]=1.2,s[29,7]=0.8,s[29,8]=0.8,s[29,9]=-0.7,s[29,10]=0.9,s[29,11]=0.3,s[29,12]=0.9,s[29,13]=1.0,s[29,14]=0.7,s[29,15]=-0.3,s[29,16]=-0.7,s[29,17]=0.7,s[29,18]=-0.9,s[29,19]=0.0,s[29,20]=-1.1,s[29,21]=0.0,s[29,22]=0.0,s[29,23]=0.8,s[29,24]=-1.2,s[29,25]=0.0,s[29,26]=-0.8,s[29,27]=0.3,s[29,28]=1.1,s[29,29]=-0.7,s[29,30]=0.8,s[29,31]=0.3,s[29,32]=-0.9,s[29,33]=-0.6,s[29,34]=-0.7,s[29,35]=0.7,s[29,36]=-0.9,s[29,37]=-0.9,s[29,38]=0.3,s[29,39]=1.0,s[29,40]=-1.0,s[29,41]=1.2,s[29,42]=0.1,s[29,43]=0.3,s[29,44]=0.3,s[29,45]=-0.4,s[29,46]=1.0,s[29,47]=-0.2,s[29,48]=-1.1,s[29,49]=0.1,s[29,50]=0.4,s[29,51]=-0.8,s[29,52]=-0.1,s[29,53]=-0.9,s[29,54]=-0.7,s[29,55]=0.1,s[29,56]=-0.3,s[29,57]=-0.9,s[29,58]=-0.9,s[29,59]=-0.6,s[29,60]=-0.4
s[30,1]=0.8,s[30,2]=0.6,s[30,3]=-0.2,s[30,4]=-1.2,s[30,5]=-0.7,s[30,6]=0.9,s[30,7]=0.6,s[30,8]=-1.2,s[30,9]=-0.1,s[30,10]=0.3,s[30,11]=-0.8,s[30,12]=0.0,s[30,13]=1.0,s[30,14]=0.8,s[30,15]=-1.0,s[30,16]=-0.3,s[30,17]=0.9,s[30,18]=0.6,s[30,19]=-0.2,s[30,20]=1.1,s[30,21]=-1.2,s[30,22]=0.0,s[30,23]=0.5,s[30,24]=0.5,s[30,25]=0.1,s[30,26]=0.8,s[30,27]=0.0,s[30,28]=0.0,s[30,29]=-0.4,s[30,30]=-0.9,s[30,31]=-1.1,s[30,32]=0.5,s[30,33]=-0.4,s[30,34]=0.6,s[30,35]=-0.2,s[30,36]=0.4,s[30,37]=0.4,s[30,38]=-0.9,s[30,39]=0.8,s[30,40]=-0.8,s[30,41]=-1.1,s[30,42]=1.2,s[30,43]=0.5,s[30,44]=0.2,s[30,45]=-0.7,s[30,46]=-1.0,s[30,47]=1.0,s[30,48]=0.3,s[30,49]=1.0,s[30,50]=1.2,s[30,51]=-0.3,s[30,52]=0.7,s[30,53]=-1.2,s[30,54]=-1.0,s[30,55]=0.9,s[30,56]=-0.2,s[30,57]=-0.9,s[30,58]=0.6,s[30,59]=-1.0,s[30,60]=-0.2
s[31,1]=-0.3,s[31,2]=-0.7,s[31,3]=1.1,s[31,4]=0.1,s[31,5]=0.2,s[31,6]=1.1,s[31,7]=0.6,s[31,8]=-1.1,s[31,9]=0.6,s[31,10]=0.7,s[31,11]=-0.4,s[31,12]=-0.9,s[31,13]=0.2,s[31,14]=-1.2,s[31,15]=-1.0,s[31,16]=0.8,s[31,17]=-0.2,s[31,18]=-1.2,s[31,19]=0.8,s[31,20]=0.9,s[31,21]=-1.1,s[31,22]=-0.5,s[31,23]=1.2,s[31,24]=-1.0,s[31,25]=0.2,s[31,26]=-0.7,s[31,27]=-0.7,s[31,28]=0.4,s[31,29]=0.0,s[31,30]=-0.6,s[31,31]=-0.8,s[31,32]=-0.4,s[31,33]=-0.3,s[31,34]=0.0,s[31,35]=0.4,s[31,36]=-1.1,s[31,37]=0.0,s[31,38]=0.7,s[31,39]=0.5,s[31,40]=0.7,s[31,41]=-0.5,s[31,42]=1.2,s[31,43]=0.3,s[31,44]=0.2,s[31,45]=-1.2,s[31,46]=-0.6,s[31,47]=0.3,s[31,48]=0.7,s[31,49]=0.2,s[31,50]=-0.6,s[31,51]=0.5,s[31,52]=-0.9,s[31,53]=-0.8,s[31,54]=-1.1,s[31,55]=-0.1,s[31,56]=-0.5,s[31,57]=0.7,s[31,58]=0.8,s[31,59]=1.0,s[31,60]=-1.1
s[32,1]=0.6,s[32,2]=0.0,s[32,3]=-1.1,s[32,4]=0.9,s[32,5]=0.7,s[32,6]=-0.7,s[32,7]=-1.2,s[32,8]=0.9,s[32,9]=-0.5,s[32,10]=-0.6,s[32,11]=-0.4,s[32,12]=1.0,s[32,13]=0.8,s[32,14]=0.8,s[32,15]=-1.0,s[32,16]=1.2,s[32,17]=0.2,s[32,18]=0.9,s[32,19]=0.6,s[32,20]=1.2,s[32,21]=-0.9,s[32,22]=0.8,s[32,23]=-0.1,s[32,24]=-0.9,s[32,25]=-0.9,s[32,26]=-1.0,s[32,27]=-1.1,s[32,28]=0.4,s[32,29]=0.2,s[32,30]=0.0,s[32,31]=-0.9,s[32,32]=0.2,s[32,33]=-0.5,s[32,34]=-0.6,s[32,35]=-0.7,s[32,36]=0.1,s[32,37]=-0.3,s[32,38]=0.4,s[32,39]=-0.8,s[32,40]=0.0,s[32,41]=-0.3,s[32,42]=0.1,s[32,43]=-0.2,s[32,44]=-0.5,s[32,45]=0.0,s[32,46]=0.6,s[32,47]=-0.7,s[32,48]=1.2,s[32,49]=1.0,s[32,50]=-0.7,s[32,51]=-0.7,s[32,52]=-1.2,s[32,53]=-0.3,s[32,54]=1.0,s[32,55]=-1.1,s[32,56]=-0.4,s[32,57]=0.5,s[32,58]=1.2,s[32,59]=0.7,s[32,60]=0.5
s[33,1]=-0.8,s[33,2]=-1.0,s[33,3]=0.8,s[33,4]=0.9,s[33,5]=0.1,s[33,6]=-0.1,s[33,7]=0.5,s[33,8]=-0.2,s[33,9]=-0.5,s[33,10]=-1.1,s[33,11]=-0.1,s[33,12]=1.1,s[33,13]=0.7,s[33,14]=-0.9,s[33,15]=-0.5,s[33,16]=-0.6,s[33,17]=0.1,s[33,18]=0.6,s[33,19]=-0.1,s[33,20]=-0.8,s[33,21]=1.0,s[33,22]=-1.2,s[33,23]=-0.1,s[33,24]=-0.1,s[33,25]=0.1,s[33,26]=-0.9,s[33,27]=1.1,s[33,28]=-1.0,s[33,29]=-0.5,s[33,30]=-0.9,s[33,31]=1.1,s[33,32]=-0.1,s[33,33]=-1.0,s[33,34]=0.4,s[33,35]=0.0,s[33,36]=0.0,s[33,37]=-0.5,s[33,38]=-1.2,s[33,39]=0.8,s[33,40]=-1.2,s[33,41]=0.0,s[33,42]=0.0,s[33,43]=0.7,s[33,44]=-0.9,s[33,45]=0.0,s[33,46]=-1.1,s[33,47]=0.3,s[33,48]=0.6,s[33,49]=-0.2,s[33,50]=-0.7,s[33,51]=0.3,s[33,52]=-0.2,s[33,53]=-0.2,s[33,54]=-0.2,s[33,55]=0.4,s[33,56]=0.7,s[33,57]=-1.1,s[33,58]=1.1,s[33,59]=1.0,s[33,60]=0.3
s[34,1]=-0.7,s[34,2]=-0.8,s[34,3]=-0.4,s[34,4]=-0.1,s[34,5]=1.2,s[34,6]=-0.4,s[34,7]=0.5,s[34,8]=0.1,s[34,9]=0.5,s[34,10]=0.3,s[34,11]=-1.0,s[34,12]=1.0,s[34,13]=0.5,s[34,14]=0.6,s[34,15]=0.9,s[34,16]=-0.6,s[34,17]=1.1,s[34,18]=0.1,s[34,19]=0.0,s[34,20]=-0.6,s[34,21]=-0.8,s[34,22]=-0.1,s[34,23]=0.1,s[34,24]=-0.1,s[34,25]=0.1,s[34,26]=-1.2,s[34,27]=-1.2,s[34,28]=-0.4,s[34,29]=0.6,s[34,30]=0.7,s[34,31]=-0.8,s[34,32]=-0.6,s[34,33]=0.6,s[34,34]=-0.1,s[34,35]=-1.2,s[34,36]=-1.2,s[34,37]=0.8,s[34,38]=0.7,s[34,39]=1.0,s[34,40]=0.8,s[34,41]=0.0,s[34,42]=0.0,s[34,43]=0.5,s[34,44]=0.4,s[34,45]=-0.5,s[34,46]=-0.8,s[34,47]=0.2,s[34,48]=0.6,s[34,49]=-0.7,s[34,50]=0.8,s[34,51]=-0.9,s[34,52]=-1.1,s[34,53]=1.0,s[34,54]=0.3,s[34,55]=-0.8,s[34,56]=1.1,s[34,57]=0.5,s[34,58]=0.0,s[34,59]=-0.4,s[34,60]=-0.2
s[35,1]=-0.9,s[35,2]=-1.0,s[35,3]=0.9,s[35,4]=0.1,s[35,5]=-0.1,s[35,6]=0.3,s[35,7]=-0.9,s[35,8]=-1.1,s[35,9]=0.5,s[35,10]=0.7,s[35,11]=-0.9,s[35,12]=-0.5,s[35,13]=-0.4,s[35,14]=0.1,s[35,15]=-0.9,s[35,16]=0.0,s[35,17]=-0.1,s[35,18]=0.2,s[35,19]=-0.1,s[35,20]=-0.1,s[35,21]=1.2,s[35,22]=1.0,s[35,23]=0.1,s[35,24]=0.9,s[35,25]=-0.3,s[35,26]=-0.5,s[35,27]=1.2,s[35,28]=0.5,s[35,29]=-0.8,s[35,30]=0.2,s[35,31]=-0.2,s[35,32]=0.7,s[35,33]=-0.6,s[35,34]=-0.4,s[35,35]=1.1,s[35,36]=-0.8,s[35,37]=0.6,s[35,38]=-0.2,s[35,39]=0.1,s[35,40]=0.8,s[35,41]=-0.5,s[35,42]=-0.7,s[35,43]=0.5,s[35,44]=-0.3,s[35,45]=0.9,s[35,46]=-0.3,s[35,47]=0.1,s[35,48]=-0.6,s[35,49]=-0.9,s[35,50]=0.9,s[35,51]=1.2,s[35,52]=1.2,s[35,53]=-0.1,s[35,54]=-1.2,s[35,55]=-0.9,s[35,56]=-1.2,s[35,57]=-0.2,s[35,58]=-0.7,s[35,59]=1.1,s[35,60]=-1.0
s[36,1]=-0.6,s[36,2]=0.2,s[36,3]=0.8,s[36,4]=0.3,s[36,5]=-0.7,s[36,6]=0.5,s[36,7]=0.2,s[36,8]=-1.0,s[36,9]=-0.4,s[36,10]=-0.6,s[36,11]=-0.2,s[36,12]=0.6,s[36,13]=1.1,s[36,14]=-0.9,s[36,15]=0.2,s[36,16]=0.1,s[36,17]=0.0,s[36,18]=-0.6,s[36,19]=0.4,s[36,20]=-0.2,s[36,21]=-0.7,s[36,22]=-0.7,s[36,23]=0.6,s[36,24]=0.0,s[36,25]=-0.2,s[36,26]=1.2,s[36,27]=-0.8,s[36,28]=-0.8,s[36,29]=-0.6,s[36,30]=0.4,s[36,31]=0.7,s[36,32]=-0.9,s[36,33]=1.1,s[36,34]=0.4,s[36,35]=0.3,s[36,36]=-0.1,s[36,37]=-0.9,s[36,38]=-0.5,s[36,39]=1.1,s[36,40]=0.1,s[36,41]=0.8,s[36,42]=0.4,s[36,43]=0.2,s[36,44]=1.0,s[36,45]=-0.7,s[36,46]=0.7,s[36,47]=0.6,s[36,48]=1.0,s[36,49]=0.9,s[36,50]=0.2,s[36,51]=0.0,s[36,52]=-0.2,s[36,53]=-1.0,s[36,54]=-1.0,s[36,55]=-0.7,s[36,56]=-0.3,s[36,57]=-0.6,s[36,58]=-1.2,s[36,59]=0.8,s[36,60]=1.0
s[37,1]=-1.2,s[37,2]=-0.7,s[37,3]=0.2,s[37,4]=-1.2,s[37,5]=0.7,s[37,6]=0.7,s[37,7]=0.1,s[37,8]=-0.4,s[37,9]=0.1,s[37,10]=0.6,s[37,11]=0.2,s[37,12]=0.9,s[37,13]=0.8,s[37,14]=-1.2,s[37,15]=1.1,s[37,16]=0.2,s[37,17]=-0.2,s[37,18]=-1.1,s[37,19]=-1.2,s[37,20]=-0.1,s[37,21]=0.4,s[37,22]=0.7,s[37,23]=-0.2,s[37,24]=-0.3,s[37,25]=0.1,s[37,26]=1.2,s[37,27]=0.5,s[37,28]=-0.1,s[37,29]=0.1,s[37,30]=0.7,s[37,31]=1.2,s[37,32]=-1.1,s[37,33]=0.5,s[37,34]=-1.0,s[37,35]=0.5,s[37,36]=0.0,s[37,37]=-0.8,s[37,38]=0.2,s[37,39]=0.1,s[37,40]=0.1,s[37,41]=-1.0,s[37,42]=-1.0,s[37,43]=-1.0,s[37,44]=0.6,s[37,45]=1.1,s[37,46]=-0.8,s[37,47]=1.2,s[37,48]=0.8,s[37,49]=0.0,s[37,50]=0.8,s[37,51]=-1.0,s[37,52]=-0.3,s[37,53]=-0.4,s[37,54]=0.7,s[37,55]=0.0,s[37,56]=-0.7,s[37,57]=0.3,s[37,58]=0.1,s[37,59]=-0.8,s[37,60]=0.2
s[38,1]=-0.8,s[38,2]=1.0,s[38,3]=-0.2,s[38,4]=0.9,s[38,5]=-0.9,s[38,6]=1.0,s[38,7]=-0.2,s[38,8]=0.9,s[38,9]=-0.3,s[38,10]=-1.1,s[38,11]=0.7,s[38,12]=-0.8,s[38,13]=0.9,s[38,14]=0.8,s[38,15]=-0.8,s[38,16]=-0.4,s[38,17]=0.6,s[38,18]=-0.1,s[38,19]=-0.1,s[38,20]=0.4,s[38,21]=0.7,s[38,22]=-1.2,s[38,23]=-0.7,s[38,24]=0.0,s[38,25]=-0.9,s[38,26]=-0.9,s[38,27]=-0.9,s[38,28]=0.8,s[38,29]=1.0,s[38,30]=1.2,s[38,31]=0.7,s[38,32]=-1.2,s[38,33]=0.8,s[38,34]=-0.7,s[38,35]=-0.6,s[38,36]=-0.2,s[38,37]=0.0,s[38,38]=-0.9,s[38,39]=1.1,s[38,40]=0.2,s[38,41]=-0.7,s[38,42]=-0.9,s[38,43]=1.2,s[38,44]=-1.2,s[38,45]=-0.5,s[38,46]=0.6,s[38,47]=0.1,s[38,48]=1.0,s[38,49]=-0.2,s[38,50]=0.3,s[38,51]=0.7,s[38,52]=-0.7,s[38,53]=0.6,s[38,54]=-0.5,s[38,55]=1.1,s[38,56]=0.7,s[38,57]=-1.0,s[38,58]=1.2,s[38,59]=-1.2,s[38,60]=-0.6
s[39,1]=-0.3,s[39,2]=-0.9,s[39,3]=-0.8,s[39,4]=1.2,s[39,5]=-0.6,s[39,6]=-0.6,s[39,7]=0.4,s[39,8]=0.3,s[39,9]=-0.5,s[39,10]=-0.7,s[39,11]=0.2,s[39,12]=-1.1,s[39,13]=1.2,s[39,14]=0.3,s[39,15]=-1.0,s[39,16]=-0.9,s[39,17]=0.8,s[39,18]=-1.2,s[39,19]=-1.0,s[39,20]=-0.8,s[39,21]=0.9,s[39,22]=-0.2,s[39,23]=0.3,s[39,24]=0.4,s[39,25]=0.4,s[39,26]=-0.7,s[39,27]=-1.2,s[39,28]=1.2,s[39,29]=-0.1,s[39,30]=0.4,s[39,31]=0.3,s[39,32]=0.4,s[39,33]=0.2,s[39,34]=-0.4,s[39,35]=-0.9,s[39,36]=-0.7,s[39,37]=-1.0,s[39,38]=-0.4,s[39,39]=0.0,s[39,40]=1.1,s[39,41]=1.2,s[39,42]=0.3,s[39,43]=-0.6,s[39,44]=-0.6,s[39,45]=0.0,s[39,46]=-1.2,s[39,47]=-0.7,s[39,48]=0.2,s[39,49]=0.4,s[39,50]=-0.9,s[39,51]=-0.3,s[39,52]=0.9,s[39,53]=0.2,s[39,54]=0.1,s[39,55]=1.0,s[39,56]=-0.7,s[39,57]=-0.2,s[39,58]=-0.4,s[39,59]=0.8,s[39,60]=0.0
s[40,1]=1.0,s[40,2]=0.9,s[40,3]=-1.2,s[40,4]=0.8,s[40,5]=-0.2,s[40,6]=-0.2,s[40,7]=-0.9,s[40,8]=-0.9,s[40,9]=-0.3,s[40,10]=-0.9,s[40,11]=-1.0,s[40,12]=1.0,s[40,13]=0.3,s[40,14]=0.6,s[40,15]=0.4,s[40,16]=-0.7,s[40,17]=-0.3,s[40,18]=-0.9,s[40,19]=1.2,s[40,20]=1.0,s[40,21]=0.2,s[40,22]=0.0,s[40,23]=1.0,s[40,24]=-0.7,s[40,25]=-0.8,s[40,26]=-1.2,s[40,27]=-0.2,s[40,28]=0.8,s[40,29]=-0.9,s[40,30]=0.8,s[40,31]=0.3,s[40,32]=0.0,s[40,33]=0.2,s[40,34]=-0.1,s[40,35]=-1.1,s[40,36]=0.6,s[40,37]=-1.0,s[40,38]=-0.3,s[40,39]=1.2,s[40,40]=-1.2,s[40,41]=-1.0,s[40,42]=0.9,s[40,43]=0.0,s[40,44]=1.2,s[40,45]=0.9,s[40,46]=-0.3,s[40,47]=0.5,s[40,48]=-1.0,s[40,49]=-0.5,s[40,50]=-1.0,s[40,51]=1.0,s[40,52]=0.8,s[40,53]=1.0,s[40,54]=-0.7,s[40,55]=-0.5,s[40,56]=0.0,s[40,57]=-1.1,s[40,58]=0.8,s[40,59]=-1.0,s[40,60]=0.8
s[41,1]=0.1,s[41,2]=0.5,s[41,3]=-0.3,s[41,4]=-1.1,s[41,5]=-1.2,s[41,6]=0.7,s[41,7]=-1.2,s[41,8]=0.6,s[41,9]=-1.1,s[41,10]=0.3,s[41,11]=0.2,s[41,12]=-1.0,s[41,13]=-1.2,s[41,14]=-0.7,s[41,15]=0.9,s[41,16]=0.9,s[41,17]=0.4,s[41,18]=0.2,s[41,19]=-0.8,s[41,20]=0.1,s[41,21]=1.1,s[41,22]=0.6,s[41,23]=-0.4,s[41,24]=-0.4,s[41,25]=1.0,s[41,26]=0.5,s[41,27]=-0.8,s[41,28]=0.7,s[41,29]=-0.7,s[41,30]=1.1,s[41,31]=-0.8,s[41,32]=0.7,s[41,33]=-0.2,s[41,34]=-0.1,s[41,35]=-0.8,s[41,36]=-0.6,s[41,37]=0.3,s[41,38]=-0.2,s[41,39]=-0.7,s[41,40]=-1.1,s[41,41]=-1.2,s[41,42]=0.1,s[41,43]=-0.3,s[41,44]=0.7,s[41,45]=0.9,s[41,46]=-0.3,s[41,47]=-0.6,s[41,48]=0.1,s[41,49]=-0.2,s[41,50]=-1.2,s[41,51]=-1.2,s[41,52]=0.7,s[41,53]=-1.1,s[41,54]=1.0,s[41,55]=0.2,s[41,56]=-0.9,s[41,57]=0.8,s[41,58]=-0.3,s[41,59]=-0.4,s[41,60]=0.0
s[42,1]=-1.2,s[42,2]=0.5,s[42,3]=-0.6,s[42,4]=0.3,s[42,5]=0.1,s[42,6]=-1.1,s[42,7]=0.6,s[42,8]=-0.3,s[42,9]=0.7,s[42,10]=-0.6,s[42,11]=1.1,s[42,12]=-0.4,s[42,13]=0.2,s[42,14]=0.1,s[42,15]=0.3,s[42,16]=1.0,s[42,17]=0.0,s[42,18]=-1.0,s[42,19]=1.2,s[42,20]=-0.6,s[42,21]=-0.3,s[42,22]=-1.1,s[42,23]=-0.1,s[42,24]=0.2,s[42,25]=0.1,s[42,26]=-0.2,s[42,27]=0.9,s[42,28]=-0.7,s[42,29]=0.6,s[42,30]=-1.1,s[42,31]=-1.2,s[42,32]=0.6,s[42,33]=0.2,s[42,34]=0.2,s[42,35]=0.5,s[42,36]=0.1,s[42,37]=-0.3,s[42,38]=-0.1,s[42,39]=-0.8,s[42,40]=0.0,s[42,41]=-1.2,s[42,42]=0.5,s[42,43]=-0.6,s[42,44]=0.2,s[42,45]=-0.9,s[42,46]=-0.7,s[42,47]=-0.5,s[42,48]=0.5,s[42,49]=1.2,s[42,50]=-0.7,s[42,51]=1.0,s[42,52]=-0.4,s[42,53]=-0.9,s[42,54]=0.7,s[42,55]=0.0,s[42,56]=1.2,s[42,57]=1.2,s[42,58]=1.2,s[42,59]=-0.7,s[42,60]=0.6
s[43,1]=0.7,s[43,2]=0.1,s[43,3]=0.3,s[43,4]=1.1,s[43,5]=-0.3,s[43,6]=0.9,s[43,7]=0.9,s[43,8]=0.5,s[43,9]=-0.2,s[43,10]=0.1,s[43,11]=-1.2,s[43,12]=1.0,s[43,13]=-0.3,s[43,14]=-0.3,s[43,15]=-0.8,s[43,16]=-1.0,s[43,17]=0.4,s[43,18]=0.2,s[43,19]=-0.5,s[43,20]=-0.1,s[43,21]=1.0,s[43,22]=0.9,s[43,23]=0.6,s[43,24]=-1.1,s[43,25]=0.5,s[43,26]=0.5,s[43,27]=0.1,s[43,28]=0.7,s[43,29]=0.5,s[43,30]=-1.2,s[43,31]=0.8,s[43,32]=0.6,s[43,33]=-0.2,s[43,34]=-1.2,s[43,35]=0.3,s[43,36]=-0.9,s[43,37]=1.1,s[43,38]=0.2,s[43,39]=0.4,s[43,40]=-0.2,s[43,41]=-0.4,s[43,42]=-0.7,s[43,43]=0.5,s[43,44]=-0.7,s[43,45]=-0.1,s[43,46]=1.2,s[43,47]=-0.7,s[43,48]=-1.2,s[43,49]=-0.2,s[43,50]=-1.0,s[43,51]=0.5,s[43,52]=0.5,s[43,53]=1.1,s[43,54]=-0.4,s[43,55]=1.0,s[43,56]=0.4,s[43,57]=-1.2,s[43,58]=-0.7,s[43,59]=0.8,s[43,60]=-0.8
s[44,1]=0.8,s[44,2]=0.8,s[44,3]=-0.6,s[44,4]=-0.8,s[44,5]=0.0,s[44,6]=0.0,s[44,7]=-0.6,s[44,8]=0.4,s[44,9]=0.7,s[44,10]=-0.6,s[44,11]=1.1,s[44,12]=0.3,s[44,13]=0.6,s[44,14]=0.4,s[44,15]=-1.0,s[44,16]=0.6,s[44,17]=-0.6,s[44,18]=-0.4,s[44,19]=-0.7,s[44,20]=0.5,s[44,21]=-0.4,s[44,22]=-1.1,s[44,23]=0.5,s[44,24]=-0.4,s[44,25]=-0.5,s[44,26]=0.7,s[44,27]=-0.2,s[44,28]=0.2,s[44,29]=0.4,s[44,30]=-0.9,s[44,31]=0.5,s[44,32]=-1.2,s[44,33]=-0.1,s[44,34]=-0.6,s[44,35]=1.0,s[44,36]=-0.2,s[44,37]=-1.0,s[44,38]=0.6,s[44,39]=0.2,s[44,40]=1.1,s[44,41]=0.6,s[44,42]=-1.1,s[44,43]=-0.7,s[44,44]=0.4,s[44,45]=0.7,s[44,46]=-0.4,s[44,47]=0.3,s[44,48]=-1.2,s[44,49]=-0.6,s[44,50]=-0.1,s[44,51]=0.7,s[44,52]=-0.4,s[44,53]=0.1,s[44,54]=0.9,s[44,55]=1.1,s[44,56]=0.3,s[44,57]=1.0,s[44,58]=0.0,s[44,59]=0.2,s[44,60]=0.2
s[45,1]=-0.5,s[45,2]=0.2,s[45,3]=1.0,s[45,4]=-0.6,s[45,5]=1.0,s[45,6]=1.2,s[45,7]=0.7,s[45,8]=-0.1,s[45,9]=-0.7,s[45,10]=-0.6,s[45,11]=-0.1,s[45,12]=-0.8,s[45,13]=-0.9,s[45,14]=1.1,s[45,15]=-1.1,s[45,16]=-0.1,s[45,17]=0.0,s[45,18]=0.3,s[45,19]=0.9,s[45,20]=1.2,s[45,21]=-0.5,s[45,22]=-0.7,s[45,23]=-0.9,s[45,24]=-0.6,s[45,25]=0.2,s[45,26]=1.2,s[45,27]=0.7,s[45,28]=0.9,s[45,29]=-0.1,s[45,30]=-0.1,s[45,31]=1.2,s[45,32]=0.3,s[45,33]=-0.3,s[45,34]=-0.5,s[45,35]=-0.1,s[45,36]=0.0,s[45,37]=-0.7,s[45,38]=0.0,s[45,39]=-0.1,s[45,40]=-1.2,s[45,41]=-1.0,s[45,42]=0.1,s[45,43]=-0.3,s[45,44]=1.1,s[45,45]=-1.2,s[45,46]=0.4,s[45,47]=0.9,s[45,48]=-1.1,s[45,49]=0.6,s[45,50]=-0.6,s[45,51]=0.5,s[45,52]=0.0,s[45,53]=1.1,s[45,54]=-0.9,s[45,55]=0.1,s[45,56]=0.6,s[45,57]=-1.1,s[45,58]=0.4,s[45,59]=0.2,s[45,60]=0.8
s[46,1]=-0.7,s[46,2]=0.0,s[46,3]=0.6,s[46,4]=0.3,s[46,5]=-0.3,s[46,6]=-1.0,s[46,7]=1.2,s[46,8]=-0.9,s[46,9]=-0.9,s[46,10]=-0.5,s[46,11]=-0.4,s[46,12]=-0.1,s[46,13]=-0.9,s[46,14]=-0.7,s[46,15]=-0.9,s[46,16]=0.9,s[46,17]=0.4,s[46,18]=-0.1,s[46,19]=1.1,s[46,20]=1.1,s[46,21]=-0.3,s[46,22]=0.0,s[46,23]=-0.3,s[46,24]=-0.6,s[46,25]=0.0,s[46,26]=-0.2,s[46,27]=-0.5,s[46,28]=0.4,s[46,29]=0.6,s[46,30]=-1.1,s[46,31]=-0.3,s[46,32]=-0.8,s[46,33]=0.4,s[46,34]=0.5,s[46,35]=0.1,s[46,36]=1.1,s[46,37]=1.2,s[46,38]=-0.9,s[46,39]=0.2,s[46,40]=1.2,s[46,41]=-1.2,s[46,42]=0.5,s[46,43]=1.0,s[46,44]=-0.7,s[46,45]=-1.2,s[46,46]=0.9,s[46,47]=1.2,s[46,48]=0.7,s[46,49]=0.0,s[46,50]=-0.6,s[46,51]=0.6,s[46,52]=-0.7,s[46,53]=1.1,s[46,54]=0.2,s[46,55]=-0.3,s[46,56]=-1.2,s[46,57]=-1.1,s[46,58]=0.9,s[46,59]=0.7,s[46,60]=0.7
s[47,1]=-0.3,s[47,2]=-0.7,s[47,3]=-0.7,s[47,4]=0.5,s[47,5]=-1.1,s[47,6]=-0.5,s[47,7]=0.0,s[47,8]=1.0,s[47,9]=0.6,s[47,10]=1.1,s[47,11]=0.5,s[47,12]=0.0,s[47,13]=-0.7,s[47,14]=-0.3,s[47,15]=1.0,s[47,16]=-1.1,s[47,17]=0.3,s[47,18]=-0.2,s[47,19]=1.1,s[47,20]=-1.0,s[47,21]=1.2,s[47,22]=-0.5,s[47,23]=-0.7,s[47,24]=-1.0,s[47,25]=-0.4,s[47,26]=1.2,s[47,27]=1.1,s[47,28]=0.6,s[47,29]=-0.1,s[47,30]=1.1,s[47,31]=0.5,s[47,32]=-1.1,s[47,33]=-0.4,s[47,34]=1.2,s[47,35]=-0.9,s[47,36]=0.7,s[47,37]=0.1,s[47,38]=0.9,s[47,39]=-0.7,s[47,40]=-0.4,s[47,41]=-1.1,s[47,42]=0.7,s[47,43]=-0.1,s[47,44]=-0.8,s[47,45]=-0.1,s[47,46]=0.0,s[47,47]=-0.2,s[47,48]=-0.2,s[47,49]=0.1,s[47,50]=-0.2,s[47,51]=0.3,s[47,52]=0.6,s[47,53]=-0.8,s[47,54]=-0.1,s[47,55]=0.4,s[47,56]=1.0,s[47,57]=-0.7,s[47,58]=0.5,s[47,59]=-0.9,s[47,60]=0.7
s[48,1]=0.1,s[48,2]=-0.6,s[48,3]=1.2,s[48,4]=-0.8,s[48,5]=0.2,s[48,6]=-0.8,s[48,7]=-1.0,s[48,8]=0.8,s[48,9]=0.4,s[48,10]=-0.2,s[48,11]=1.0,s[48,12]=-0.4,s[48,13]=0.3,s[48,14]=-0.1,s[48,15]=0.0,s[48,16]=-0.3,s[48,17]=0.5,s[48,18]=-0.9,s[48,19]=0.7,s[48,20]=0.8,s[48,21]=0.5,s[48,22]=0.3,s[48,23]=0.3,s[48,24]=0.4,s[48,25]=0.2,s[48,26]=-0.1,s[48,27]=1.2,s[48,28]=-0.5,s[48,29]=-0.2,s[48,30]=-0.9,s[48,31]=-1.1,s[48,32]=-1.1,s[48,33]=0.8,s[48,34]=-1.1,s[48,35]=1.1,s[48,36]=-0.2,s[48,37]=-0.7,s[48,38]=-0.4,s[48,39]=-0.7,s[48,40]=0.0,s[48,41]=-1.1,s[48,42]=0.4,s[48,43]=-0.8,s[48,44]=-0.6,s[48,45]=-0.8,s[48,46]=-1.1,s[48,47]=-0.7,s[48,48]=-1.1,s[48,49]=0.9,s[48,50]=-0.6,s[48,51]=0.3,s[48,52]=0.8,s[48,53]=-0.5,s[48,54]=-1.0,s[48,55]=0.3,s[48,56]=-0.1,s[48,57]=0.7,s[48,58]=-0.1,s[48,59]=0.1,s[48,60]=0.4
s[49,1]=-1.0,s[49,2]=0.2,s[49,3]=0.4,s[49,4]=-0.6,s[49,5]=0.2,s[49,6]=-0.7,s[49,7]=-0.8,s[49,8]=0.4,s[49,9]=0.9,s[49,10]=0.5,s[49,11]=0.4,s[49,12]=0.6,s[49,13]=0.1,s[49,14]=-0.6,s[49,15]=-0.8,s[49,16]=-0.6,s[49,17]=0.1,s[49,18]=0.2,s[49,19]=-0.8,s[49,20]=-1.1,s[49,21]=0.4,s[49,22]=0.1,s[49,23]=-0.6,s[49,24]=-0.8,s[49,25]=-1.2,s[49,26]=0.7,s[49,27]=0.4,s[49,28]=0.3,s[49,29]=0.7,s[49,30]=0.7,s[49,31]=0.5,s[49,32]=0.7,s[49,33]=0.0,s[49,34]=1.2,s[49,35]=0.8,s[49,36]=0.8,s[49,37]=-0.9,s[49,38]=-1.0,s[49,39]=0.8,s[49,40]=-0.7,s[49,41]=0.0,s[49,42]=-1.2,s[49,43]=-1.2,s[49,44]=0.2,s[49,45]=0.7,s[49,46]=-0.2,s[49,47]=-1.1,s[49,48]=0.5,s[49,49]=0.9,s[49,50]=-1.1,s[49,51]=-1.1,s[49,52]=-1.2,s[49,53]=-0.7,s[49,54]=1.0,s[49,55]=-0.3,s[49,56]=-0.2,s[49,57]=1.2,s[49,58]=0.1,s[49,59]=-0.3,s[49,60]=-1.2
s[50,1]=-1.0,s[50,2]=-0.1,s[50,3]=0.8,s[50,4]=-0.1,s[50,5]=0.2,s[50,6]=1.0,s[50,7]=1.0,s[50,8]=0.1,s[50,9]=0.4,s[50,10]=0.6,s[50,11]=0.2,s[50,12]=0.5,s[50,13]=-1.1,s[50,14]=0.9,s[50,15]=0.9,s[50,16]=-1.0,s[50,17]=0.3,s[50,18]=-0.4,s[50,19]=0.9,s[50,20]=1.0,s[50,21]=0.3,s[50,22]=0.5,s[50,23]=0.6,s[50,24]=-0.5,s[50,25]=1.1,s[50,26]=0.9,s[50,27]=-0.2,s[50,28]=-0.3,s[50,29]=0.3,s[50,30]=-1.1,s[50,31]=1.1,s[50,32]=-0.4,s[50,33]=0.9,s[50,34]=-0.2,s[50,35]=1.1,s[50,36]=0.9,s[50,37]=-0.9,s[50,38]=0.5,s[50,39]=0.6,s[50,40]=1.0,s[50,41]=-0.3,s[50,42]=-0.7,s[50,43]=-0.2,s[50,44]=-0.1,s[50,45]=0.3,s[50,46]=0.7,s[50,47]=0.4,s[50,48]=-0.5,s[50,49]=0.0,s[50,50]=1.2,s[50,51]=-0.5,s[50,52]=-1.1,s[50,53]=-1.2,s[50,54]=-0.5,s[50,55]=1.0,s[50,56]=0.1,s[50,57]=0.9,s[50,58]=0.5,s[50,59]=0.4,s[50,60]=-0.7
s[51,1]=-1.1,s[51,2]=0.9,s[51,3]=0.9,s[51,4]=0.6,s[51,5]=-1.2,s[51,6]=-1.1,s[51,7]=0.1,s[51,8]=1.2,s[51,9]=-0.1,s[51,10]=0.9,s[51,11]=-0.4,s[51,12]=-0.2,s[51,13]=0.1,s[51,14]=-0.6,s[51,15]=-0.2,s[51,16]=-0.5,s[51,17]=1.2,s[51,18]=0.0,s[51,19]=0.9,s[51,20]=0.8,s[51,21]=0.7,s[51,22]=0.8,s[51,23]=0.3,s[51,24]=0.4,s[51,25]=0.1,s[51,26]=0.6,s[51,27]=0.4,s[51,28]=-0.3,s[51,29]=0.1,s[51,30]=-0.6,s[51,31]=0.9,s[51,32]=0.4,s[51,33]=0.3,s[51,34]=0.3,s[51,35]=-0.5,s[51,36]=-0.1,s[51,37]=0.2,s[51,38]=-0.3,s[51,39]=-1.1,s[51,40]=-0.5,s[51,41]=0.3,s[51,42]=-0.9,s[51,43]=-0.7,s[51,44]=0.8,s[51,45]=-0.7,s[51,46]=0.9,s[51,47]=0.3,s[51,48]=0.9,s[51,49]=-0.9,s[51,50]=0.2,s[51,51]=0.5,s[51,52]=-1.2,s[51,53]=-0.7,s[51,54]=0.3,s[51,55]=0.3,s[51,56]=-0.9,s[51,57]=-1.2,s[51,58]=-0.6,s[51,59]=-0.8,s[51,60]=0.6
s[52,1]=0.2,s[52,2]=-0.9,s[52,3]=0.9,s[52,4]=-1.0,s[52,5]=0.3,s[52,6]=-0.4,s[52,7]=1.0,s[52,8]=1.2,s[52,9]=-0.4,s[52,10]=-0.5,s[52,11]=0.0,s[52,12]=-0.4,s[52,13]=-0.1,s[52,14]=0.4,s[52,15]=1.0,s[52,16]=-0.5,s[52,17]=-0.8,s[52,18]=0.8,s[52,19]=-0.3,s[52,20]=0.9,s[52,21]=0.8,s[52,22]=-0.8,s[52,23]=-0.9,s[52,24]=1.1,s[52,25]=0.3,s[52,26]=-0.2,s[52,27]=0.0,s[52,28]=-0.3,s[52,29]=0.9,s[52,30]=-0.4,s[52,31]=-0.8,s[52,32]=-0.6,s[52,33]=1.1,s[52,34]=-0.3,s[52,35]=-0.7,s[52,36]=1.1,s[52,37]=0.8,s[52,38]=-0.5,s[52,39]=0.3,s[52,40]=1.2,s[52,41]=1.1,s[52,42]=0.8,s[52,43]=0.8,s[52,44]=0.3,s[52,45]=-0.4,s[52,46]=-1.2,s[52,47]=0.1,s[52,48]=-0.8,s[52,49]=-0.1,s[52,50]=0.7,s[52,51]=-0.3,s[52,52]=-0.7,s[52,53]=1.1,s[52,54]=1.1,s[52,55]=1.2,s[52,56]=-0.3,s[52,57]=0.2,s[52,58]=0.1,s[52,59]=0.7,s[52,60]=-0.3
s[53,1]=-0.1,s[53,2]=0.3,s[53,3]=0.0,s[53,4]=0.1,s[53,5]=0.1,s[53,6]=0.5,s[53,7]=1.1,s[53,8]=0.2,s[53,9]=-1.1,s[53,10]=-0.8,s[53,11]=0.0,s[53,12]=0.4,s[53,13]=-1.0,s[53,14]=-0.7,s[53,15]=0.7,s[53,16]=0.3,s[53,17]=-0.1,s[53,18]=-0.3,s[53,19]=0.5,s[53,20]=0.3,s[53,21]=1.1,s[53,22]=1.1,s[53,23]=0.0,s[53,24]=-0.4,s[53,25]=0.5,s[53,26]=1.2,s[53,27]=0.4,s[53,28]=-0.7,s[53,29]=-0.8,s[53,30]=-0.8,s[53,31]=-0.4,s[53,32]=-0.9,s[53,33]=0.2,s[53,34]=-1.2,s[53,35]=0.8,s[53,36]=0.0,s[53,37]=1.1,s[53,38]=0.5,s[53,39]=-0.3,s[53,40]=1.0,s[53,41]=-1.1,s[53,42]=0.5,s[53,43]=0.4,s[53,44]=0.6,s[53,45]=-0.1,s[53,46]=-1.0,s[53,47]=-1.1,s[53,48]=-0.9,s[53,49]=-0.5,s[53,50]=0.8,s[53,51]=-0.5,s[53,52]=1.1,s[53,53]=0.0,s[53,54]=1.1,s[53,55]=0.9,s[53,56]=-1.1,s[53,57]=1.1,s[53,58]=-0.8,s[53,59]=-0.8,s[53,60]=1.0
s[54,1]=-1.1,s[54,2]=0.1,s[54,3]=0.8,s[54,4]=0.5,s[54,5]=-0.4,s[54,6]=1.0,s[54,7]=0.1,s[54,8]=-0.5,s[54,9]=1.1,s[54,10]=1.1,s[54,11]=0.5,s[54,12]=0.2,s[54,13]=-1.1,s[54,14]=-0.9,s[54,15]=-0.2,s[54,16]=0.4,s[54,17]=1.1,s[54,18]=0.5,s[54,19]=0.0,s[54,20]=0.9,s[54,21]=-0.5,s[54,22]=-1.2,s[54,23]=-0.5,s[54,24]=-0.2,s[54,25]=-0.6,s[54,26]=-1.1,s[54,27]=0.5,s[54,28]=0.2,s[54,29]=-0.6,s[54,30]=0.8,s[54,31]=-1.2,s[54,32]=-0.9,s[54,33]=-0.1,s[54,34]=-1.2,s[54,35]=-0.8,s[54,36]=0.0,s[54,37]=1.1,s[54,38]=1.0,s[54,39]=-1.1,s[54,40]=0.3,s[54,41]=0.4,s[54,42]=-1.1,s[54,43]=1.2,s[54,44]=-1.0,s[54,45]=-0.7,s[54,46]=0.6,s[54,47]=0.1,s[54,48]=-0.4,s[54,49]=1.0,s[54,50]=1.2,s[54,51]=0.6,s[54,52]=0.7,s[54,53]=0.7,s[54,54]=0.3,s[54,55]=-0.4,s[54,56]=0.2,s[54,57]=-0.5,s[54,58]=0.9,s[54,59]=-0.4,s[54,60]=-0.1
s[55,1]=0.6,s[55,2]=-0.6,s[55,3]=-0.4,s[55,4]=1.0,s[55,5]=1.2,s[55,6]=0.4,s[55,7]=0.2,s[55,8]=0.9,s[55,9]=-0.1,s[55,10]=0.3,s[55,11]=1.2,s[55,12]=0.6,s[55,13]=0.0,s[55,14]=-1.1,s[55,15]=0.2,s[55,16]=0.8,s[55,17]=0.0,s[55,18]=-1.1,s[55,19]=-0.4,s[55,20]=-1.1,s[55,21]=-0.6,s[55,22]=-0.1,s[55,23]=-0.3,s[55,24]=0.5,s[55,25]=0.7,s[55,26]=1.2,s[55,27]=0.3,s[55,28]=0.3,s[55,29]=0.5,s[55,30]=0.7,s[55,31]=-0.1,s[55,32]=0.0,s[55,33]=-1.1,s[55,34]=0.1,s[55,35]=0.3,s[55,36]=-0.2,s[55,37]=0.7,s[55,38]=0.1,s[55,39]=-0.1,s[55,40]=0.9,s[55,41]=0.1,s[55,42]=0.8,s[55,43]=-0.4,s[55,44]=0.6,s[55,45]=0.0,s[55,46]=1.0,s[55,47]=-0.2,s[55,48]=0.8,s[55,49]=0.7,s[55,50]=0.3,s[55,51]=0.6,s[55,52]=0.1,s[55,53]=-1.2,s[55,54]=-1.0,s[55,55]=-0.8,s[55,56]=0.5,s[55,57]=0.3,s[55,58]=0.4,s[55,59]=-0.4,s[55,60]=-0.8
s[56,1]=-0.1,s[56,2]=0.0,s[56,3]=0.2,s[56,4]=0.9,s[56,5]=-0.5,s[56,6]=-0.4,s[56,7]=0.3,s[56,8]=0.6,s[56,9]=-0.7,s[56,10]=-0.5,s[56,11]=-1.2,s[56,12]=-0.9,s[56,13]=0.5,s[56,14]=0.0,s[56,15]=0.6,s[56,16]=0.5,s[56,17]=0.3,s[56,18]=-0.4,s[56,19]=-0.4,s[56,20]=-1.2,s[56,21]=1.2,s[56,22]=-1.1,s[56,23]=0.2,s[56,24]=0.1,s[56,25]=0.2,s[56,26]=-0.3,s[56,27]=0.6,s[56,28]=-0.2,s[56,29]=0.5,s[56,30]=0.3,s[56,31]=0.6,s[56,32]=0.7,s[56,33]=-0.2,s[56,34]=1.2,s[56,35]=1.2,s[56,36]=-1.1,s[56,37]=-0.1,s[56,38]=-1.2,s[56,39]=-0.9,s[56,40]=1.1,s[56,41]=1.2,s[56,42]=0.7,s[56,43]=-0.9,s[56,44]=0.1,s[56,45]=0.8,s[56,46]=1.2,s[56,47]=0.9,s[56,48]=-0.6,s[56,49]=0.3,s[56,50]=0.5,s[56,51]=0.3,s[56,52]=1.2,s[56,53]=0.9,s[56,54]=0.8,s[56,55]=-0.8,s[56,56]=-0.3,s[56,57]=1.2,s[56,58]=0.3,s[56,59]=-0.9,s[56,60]=-0.8
s[57,1]=0.4,s[57,2]=1.1,s[57,3]=-0.5,s[57,4]=-1.1,s[57,5]=-0.4,s[57,6]=0.7,s[57,7]=0.4,s[57,8]=0.7,s[57,9]=1.1,s[57,10]=-0.4,s[57,11]=-0.9,s[57,12]=-0.7,s[57,13]=-0.2,s[57,14]=-0.4,s[57,15]=-0.5,s[57,16]=0.9,s[57,17]=0.1,s[57,18]=0.9,s[57,19]=-0.3,s[57,20]=-1.0,s[57,21]=0.9,s[57,22]=-1.1,s[57,23]=-0.5,s[57,24]=-0.1,s[57,25]=-0.2,s[57,26]=0.2,s[57,27]=-0.7,s[57,28]=0.0,s[57,29]=-1.1,s[57,30]=-0.3,s[57,31]=0.7,s[57,32]=0.8,s[57,33]=0.4,s[57,34]=1.0,s[57,35]=1.2,s[57,36]=-0.4,s[57,37]=-0.9,s[57,38]=-0.7,s[57,39]=-0.9,s[57,40]=0.4,s[57,41]=-0.8,s[57,42]=1.0,s[57,43]=0.5,s[57,44]=-0.3,s[57,45]=0.4,s[57,46]=0.0,s[57,47]=-0.8,s[57,48]=-1.0,s[57,49]=0.2,s[57,50]=-0.6,s[57,51]=0.4,s[57,52]=0.9,s[57,53]=0.0,s[57,54]=0.1,s[57,55]=-0.9,s[57,56]=0.5,s[57,57]=-0.4,s[57,58]=0.7,s[57,59]=0.1,s[57,60]=1.1
s[58,1]=0.1,s[58,2]=-0.9,s[58,3]=-0.7,s[58,4]=0.8,s[58,5]=1.0,s[58,6]=0.6,s[58,7]=0.0,s[58,8]=1.1,s[58,9]=-1.1,s[58,10]=-0.9,s[58,11]=-0.6,s[58,12]=0.4,s[58,13]=1.0,s[58,14]=-0.5,s[58,15]=-0.6,s[58,16]=0.0,s[58,17]=-0.3,s[58,18]=-0.4,s[58,19]=-0.4,s[58,20]=-0.1,s[58,21]=0.1,s[58,22]=-0.6,s[58,23]=-0.6,s[58,24]=-0.4,s[58,25]=0.1,s[58,26]=0.0,s[58,27]=1.2,s[58,28]=0.3,s[58,29]=0.9,s[58,30]=-1.2,s[58,31]=-0.7,s[58,32]=0.9,s[58,33]=-0.8,s[58,34]=-1.1,s[58,35]=1.1,s[58,36]=-0.3,s[58,37]=-0.5,s[58,38]=0.0,s[58,39]=1.0,s[58,40]=-1.1,s[58,41]=0.2,s[58,42]=-0.5,s[58,43]=0.7,s[58,44]=-0.8,s[58,45]=0.0,s[58,46]=-0.9,s[58,47]=0.7,s[58,48]=-0.3,s[58,49]=-0.9,s[58,50]=-0.6,s[58,51]=-0.5,s[58,52]=-0.4,s[58,53]=0.2,s[58,54]=1.0,s[58,55]=0.2,s[58,56]=1.1,s[58,57]=-1.2,s[58,58]=-0.8,s[58,59]=-0.2,s[58,60]=1.1
s[59,1]=-0.6,s[59,2]=-1.0,s[59,3]=0.8,s[59,4]=-1.1,s[59,5]=-0.5,s[59,6]=-0.2,s[59,7]=-0.5,s[59,8]=-0.7,s[59,9]=0.9,s[59,10]=-0.8,s[59,11]=-0.7,s[59,12]=1.1,s[59,13]=-1.0,s[59,14]=0.5,s[59,15]=0.3,s[59,16]=0.7,s[59,17]=-1.1,s[59,18]=0.9,s[59,19]=0.8,s[59,20]=0.2,s[59,21]=-1.1,s[59,22]=1.0,s[59,23]=0.0,s[59,24]=1.0,s[59,25]=0.2,s[59,26]=1.0,s[59,27]=1.1,s[59,28]=-0.4,s[59,29]=0.8,s[59,30]=0.3,s[59,31]=-0.8,s[59,32]=-0.7,s[59,33]=0.0,s[59,34]=1.1,s[59,35]=-1.1,s[59,36]=0.4,s[59,37]=-0.9,s[59,38]=-0.4,s[59,39]=-1.1,s[59,40]=0.3,s[59,41]=0.0,s[59,42]=0.0,s[59,43]=-0.5,s[59,44]=0.6,s[59,45]=0.9,s[59,46]=-1.1,s[59,47]=-0.6,s[59,48]=0.5,s[59,49]=0.1,s[59,50]=1.2,s[59,51]=-0.2,s[59,52]=-0.9,s[59,53]=-0.5,s[59,54]=-0.3,s[59,55]=-0.3,s[59,56]=-1.1,s[59,57]=-0.5,s[59,58]=-0.9,s[59,59]=1.2,s[59,60]=1.1
s[60,1]=-0.3,s[60,2]=0.3,s[60,3]=0.1,s[60,4]=0.7,s[60,5]=1.2,s[60,6]=-0.4,s[60,7]=0.2,s[60,8]=1.1,s[60,9]=-0.4,s[60,10]=-1.2,s[60,11]=0.0,s[60,12]=1.2,s[60,13]=0.8,s[60,14]=-0.9,s[60,15]=-0.9,s[60,16]=-0.8,s[60,17]=0.2,s[60,18]=-0.8,s[60,19]=0.6,s[60,20]=-0.7,s[60,21]=-1.1,s[60,22]=-0.9,s[60,23]=0.2,s[60,24]=1.1,s[60,25]=0.3,s[60,26]=-1.1,s[60,27]=0.6,s[60,28]=-0.4,s[60,29]=0.1,s[60,30]=0.0,s[60,31]=-0.7,s[60,32]=-0.2,s[60,33]=1.1,s[60,34]=0.9,s[60,35]=-0.2,s[60,36]=-0.6,s[60,37]=0.9,s[60,38]=-0.2,s[60,39]=-0.7,s[60,40]=0.1,s[60,41]=-0.9,s[60,42]=0.6,s[60,43]=0.4,s[60,44]=-1.1,s[60,45]=1.0,s[60,46]=-0.5,s[60,47]=0.7,s[60,48]=0.0,s[60,49]=0.6,s[60,50]=-0.2,s[60,51]=0.7,s[60,52]=0.0,s[60,53]=1.2,s[60,54]=-1.1,s[60,55]=0.9,s[60,56]=0.3,s[60,57]=1.2,s[60,58]=-1.1,s[60,59]=-0.1,s[60,60]=-0.4
s[61,1]=0.2,s[61,2]=-0.7,s[61,3]=0.4,s[61,4]=-1.0,s[61,5]=0.0,s[61,6]=-0.9,s[61,7]=1.2,s[61,8]=0.6,s[61,9]=-0.3,s[61,10]=-0.8,s[61,11]=1.2,s[61,12]=0.2,s[61,13]=-0.9,s[61,14]=-0.5,s[61,15]=0.9,s[61,16]=0.8,s[61,17]=-1.1,s[61,18]=-0.8,s[61,19]=0.6,s[61,20]=0.9,s[61,21]=-0.6,s[61,22]=-1.0,s[61,23]=0.6,s[61,24]=0.3,s[61,25]=0.6,s[61,26]=0.2,s[61,27]=-0.9,s[61,28]=1.0,s[61,29]=-0.7,s[61,30]=0.7,s[61,31]=0.3,s[61,32]=-1.2,s[61,33]=0.2,s[61,34]=0.1,s[61,35]=1.0,s[61,36]=-0.3,s[61,37]=1.2,s[61,38]=-0.7,s[61,39]=1.0,s[61,40]=0.3,s[61,41]=-1.2,s[61,42]=-0.9,s[61,43]=0.2,s[61,44]=0.7,s[61,45]=1.2,s[61,46]=0.0,s[61,47]=0.8,s[61,48]=-1.1,s[61,49]=0.8,s[61,50]=-1.1,s[61,51]=-0.7,s[61,52]=0.6,s[61,53]=0.8,s[61,54]=-0.6,s[61,55]=0.0,s[61,56]=0.3,s[61,57]=-0.8,s[61,58]=0.3,s[61,59]=-0.9,s[61,60]=0.5
s[62,1]=-0.7,s[62,2]=1.2,s[62,3]=0.6,s[62,4]=0.9,s[62,5]=-1.0,s[62,6]=0.4,s[62,7]=-1.0,s[62,8]=-0.3,s[62,9]=-0.9,s[62,10]=-1.2,s[62,11]=0.6,s[62,12]=-1.1,s[62,13]=1.0,s[62,14]=-0.9,s[62,15]=0.6,s[62,16]=0.9,s[62,17]=0.0,s[62,18]=0.0,s[62,19]=0.8,s[62,20]=-0.4,s[62,21]=-0.4,s[62,22]=-0.3,s[62,23]=0.4,s[62,24]=1.1,s[62,25]=-0.9,s[62,26]=1.2,s[62,27]=0.8,s[62,28]=0.0,s[62,29]=-0.3,s[62,30]=-0.6,s[62,31]=0.3,s[62,32]=-0.1,s[62,33]=0.3,s[62,34]=0.5,s[62,35]=0.2,s[62,36]=0.9,s[62,37]=-0.3,s[62,38]=-0.4,s[62,39]=1.2,s[62,40]=0.5,s[62,41]=0.0,s[62,42]=-1.0,s[62,43]=-0.7,s[62,44]=1.2,s[62,45]=-0.7,s[62,46]=-0.3,s[62,47]=-0.5,s[62,48]=-0.2,s[62,49]=0.5,s[62,50]=-1.2,s[62,51]=0.2,s[62,52]=-0.7,s[62,53]=1.2,s[62,54]=0.7,s[62,55]=-0.8,s[62,56]=-0.4,s[62,57]=0.0,s[62,58]=-0.9,s[62,59]=0.9,s[62,60]=0.2
s[63,1]=1.2,s[63,2]=-0.2,s[63,3]=-1.2,s[63,4]=-0.4,s[63,5]=-0.5,s[63,6]=-0.7,s[63,7]=0.1,s[63,8]=0.9,s[63,9]=0.5,s[63,10]=-1.2,s[63,11]=-1.1,s[63,12]=-0.8,s[63,13]=0.0,s[63,14]=0.5,s[63,15]=1.1,s[63,16]=-1.2,s[63,17]=-0.5,s[63,18]=-0.1,s[63,19]=0.4,s[63,20]=0.9,s[63,21]=-0.1,s[63,22]=-1.2,s[63,23]=0.1,s[63,24]=-1.2,s[63,25]=0.0,s[63,26]=-0.4,s[63,27]=0.1,s[63,28]=0.4,s[63,29]=-0.2,s[63,30]=-0.6,s[63,31]=-1.2,s[63,32]=0.1,s[63,33]=1.1,s[63,34]=-0.7,s[63,35]=0.6,s[63,36]=-0.3,s[63,37]=-0.8,s[63,38]=0.5,s[63,39]=-1.0,s[63,40]=0.6,s[63,41]=-0.7,s[63,42]=-0.9,s[63,43]=-0.1,s[63,44]=-0.9,s[63,45]=0.6,s[63,46]=0.1,s[63,47]=-0.7,s[63,48]=1.1,s[63,49]=-0.8,s[63,50]=-1.2,s[63,51]=1.2,s[63,52]=1.2,s[63,53]=-0.6,s[63,54]=1.2,s[63,55]=0.6,s[63,56]=-0.6,s[63,57]=0.7,s[63,58]=-0.9,s[63,59]=-0.1,s[63,60]=1.0
s[64,1]=1.1,s[64,2]=0.8,s[64,3]=0.4,s[64,4]=0.8,s[64,5]=1.2,s[64,6]=0.5,s[64,7]=0.5,s[64,8]=-0.4,s[64,9]=0.0,s[64,10]=-0.2,s[64,11]=0.9,s[64,12]=-0.3,s[64,13]=-0.5,s[64,14]=0.0,s[64,15]=0.9,s[64,16]=-0.9,s[64,17]=-1.2,s[64,18]=-0.6,s[64,19]=-0.1,s[64,20]=0.9,s[64,21]=0.0,s[64,22]=-0.6,s[64,23]=-0.1,s[64,24]=0.3,s[64,25]=-0.6,s[64,26]=-0.9,s[64,27]=0.6,s[64,28]=1.2,s[64,29]=-1.1,s[64,30]=0.5,s[64,31]=0.8,s[64,32]=-0.8,s[64,33]=-0.7,s[64,34]=0.7,s[64,35]=0.1,s[64,36]=-0.6,s[64,37]=0.0,s[64,38]=-0.7,s[64,39]=-1.0,s[64,40]=0.3,s[64,41]=0.1,s[64,42]=1.0,s[64,43]=0.2,s[64,44]=1.0,s[64,45]=-1.0,s[64,46]=0.5,s[64,47]=-1.2,s[64,48]=0.3,s[64,49]=0.1,s[64,50]=1.2,s[64,51]=-0.9,s[64,52]=-0.3,s[64,53]=0.5,s[64,54]=0.1,s[64,55]=-0.8,s[64,56]=-0.6,s[64,57]=-1.1,s[64,58]=0.8,s[64,59]=-0.1,s[64,60]=-1.0
s[65,1]=0.9,s[65,2]=-1.1,s[65,3]=0.9,s[65,4]=0.8,s[65,5]=-0.7,s[65,6]=-0.1,s[65,7]=0.2,s[65,8]=0.5,s[65,9]=-0.6,s[65,10]=-1.0,s[65,11]=0.9,s[65,12]=-0.8,s[65,13]=0.5,s[65,14]=0.7,s[65,15]=-0.4,s[65,16]=0.0,s[65,17]=-1.0,s[65,18]=-1.1,s[65,19]=-0.5,s[65,20]=0.4,s[65,21]=-1.2,s[65,22]=-1.1,s[65,23]=1.2,s[65,24]=-0.9,s[65,25]=-0.7,s[65,26]=-0.5,s[65,27]=0.1,s[65,28]=-0.6,s[65,29]=0.1,s[65,30]=-0.7,s[65,31]=0.3,s[65,32]=-1.0,s[65,33]=0.6,s[65,34]=1.0,s[65,35]=0.7,s[65,36]=-0.1,s[65,37]=1.1,s[65,38]=-0.9,s[65,39]=0.5,s[65,40]=1.2,s[65,41]=0.0,s[65,42]=-0.1,s[65,43]=0.4,s[65,44]=0.3,s[65,45]=0.6,s[65,46]=0.5,s[65,47]=1.2,s[65,48]=-0.2,s[65,49]=-0.2,s[65,50]=-0.3,s[65,51]=0.9,s[65,52]=-0.6,s[65,53]=0.5,s[65,54]=-0.8,s[65,55]=0.4,s[65,56]=1.2,s[65,57]=0.6,s[65,58]=0.9,s[65,59]=0.7,s[65,60]=-1.0
s[66,1]=-0.8,s[66,2]=-0.9,s[66,3]=0.2,s[66,4]=0.8,s[66,5]=-1.2,s[66,6]=-0.8,s[66,7]=0.2,s[66,8]=-0.9,s[66,9]=-1.1,s[66,10]=-0.5,s[66,11]=-0.7,s[66,12]=1.0,s[66,13]=0.0,s[66,14]=0.8,s[66,15]=-1.0,s[66,16]=-1.2,s[66,17]=-0.4,s[66,18]=0.0,s[66,19]=0.7,s[66,20]=-1.2,s[66,21]=-0.4,s[66,22]=-1.1,s[66,23]=1.0,s[66,24]=0.2,s[66,25]=0.4,s[66,26]=0.0,s[66,27]=0.4,s[66,28]=0.0,s[66,29]=-0.3,s[66,30]=-0.2,s[66,31]=1.0,s[66,32]=0.9,s[66,33]=-0.8,s[66,34]=0.8,s[66,35]=0.8,s[66,36]=-0.8,s[66,37]=-0.6,s[66,38]=-0.5,s[66,39]=0.0,s[66,40]=0.0,s[66,41]=0.4,s[66,42]=0.3,s[66,43]=-0.2,s[66,44]=0.0,s[66,45]=-0.5,s[66,46]=0.0,s[66,47]=-0.5,s[66,48]=0.2,s[66,49]=1.2,s[66,50]=-0.3,s[66,51]=0.1,s[66,52]=0.4,s[66,53]=-0.8,s[66,54]=0.5,s[66,55]=1.1,s[66,56]=-0.6,s[66,57]=-0.8,s[66,58]=0.8,s[66,59]=-0.2,s[66,60]=0.0
s[67,1]=-1.0,s[67,2]=0.2,s[67,3]=0.5,s[67,4]=-0.5,s[67,5]=1.1,s[67,6]=-0.7,s[67,7]=0.2,s[67,8]=-0.3,s[67,9]=0.2,s[67,10]=0.7,s[67,11]=-0.8,s[67,12]=0.5,s[67,13]=1.2,s[67,14]=0.4,s[67,15]=-1.0,s[67,16]=0.9,s[67,17]=-0.8,s[67,18]=0.9,s[67,19]=0.5,s[67,20]=0.7,s[67,21]=0.1,s[67,22]=-1.1,s[67,23]=-0.9,s[67,24]=0.7,s[67,25]=0.2,s[67,26]=0.2,s[67,27]=0.8,s[67,28]=1.1,s[67,29]=-0.7,s[67,30]=0.6,s[67,31]=1.0,s[67,32]=-0.7,s[67,33]=-1.2,s[67,34]=0.6,s[67,35]=0.4,s[67,36]=-0.2,s[67,37]=-1.1,s[67,38]=-1.2,s[67,39]=0.2,s[67,40]=1.1,s[67,41]=1.1,s[67,42]=0.9,s[67,43]=0.1,s[67,44]=0.2,s[67,45]=0.7,s[67,46]=-0.7,s[67,47]=0.5,s[67,48]=0.5,s[67,49]=1.0,s[67,50]=0.0,s[67,51]=0.1,s[67,52]=-1.1,s[67,53]=1.0,s[67,54]=0.5,s[67,55]=-0.4,s[67,56]=0.8,s[67,57]=1.1,s[67,58]=-1.2,s[67,59]=-1.1,s[67,60]=-0.8
s[68,1]=0.4,s[68,2]=-0.4,s[68,3]=0.7,s[68,4]=0.4,s[68,5]=-0.6,s[68,6]=0.6,s[68,7]=-0.2,s[68,8]=-0.3,s[68,9]=0.3,s[68,10]=1.1,s[68,11]=0.0,s[68,12]=0.5,s[68,13]=-1.2,s[68,14]=-0.9,s[68,15]=-0.7,s[68,16]=-0.4,s[68,17]=-1.0,s[68,18]=-0.3,s[68,19]=0.7,s[68,20]=-0.9,s[68,21]=0.3,s[68,22]=1.2,s[68,23]=0.0,s[68,24]=1.2,s[68,25]=0.3,s[68,26]=-0.4,s[68,27]=0.5,s[68,28]=0.7,s[68,29]=-0.9,s[68,30]=0.1,s[68,31]=0.4,s[68,32]=0.3,s[68,33]=-1.0,s[68,34]=-1.2,s[68,35]=-0.9,s[68,36]=0.6,s[68,37]=1.0,s[68,38]=-1.1,s[68,39]=0.4,s[68,40]=-0.6,s[68,41]=-1.1,s[68,42]=0.8,s[68,43]=-0.5,s[68,44]=0.3,s[68,45]=-1.0,s[68,46]=0.7,s[68,47]=-0.7,s[68,48]=-1.1,s[68,49]=-0.4,s[68,50]=1.0,s[68,51]=-0.7,s[68,52]=1.1,s[68,53]=-1.0,s[68,54]=-0.6,s[68,55]=-1.2,s[68,56]=-0.4,s[68,57]=-0.6,s[68,58]=1.1,s[68,59]=1.1,s[68,60]=-0.7
s[69,1]=0.4,s[69,2]=0.7,s[69,3]=-0.5,s[69,4]=1.1,s[69,5]=-0.6,s[69,6]=-0.8,s[69,7]=-1.1,s[69,8]=0.4,s[69,9]=0.8,s[69,10]=-0.9,s[69,11]=-0.3,s[69,12]=0.2,s[69,13]=0.4,s[69,14]=-0.7,s[69,15]=0.7,s[69,16]=1.1,s[69,17]=-0.5,s[69,18]=0.4,s[69,19]=0.0,s[69,20]=-0.5,s[69,21]=1.2,s[69,22]=0.0,s[69,23]=0.7,s[69,24]=-0.6,s[69,25]=-0.7,s[69,26]=-0.6,s[69,27]=-0.2,s[69,28]=0.5,s[69,29]=-1.2,s[69,30]=0.3,s[69,31]=-0.8,s[69,32]=0.5,s[69,33]=-0.1,s[69,34]=-0.5,s[69,35]=1.1,s[69,36]=-0.7,s[69,37]=-0.4,s[69,38]=0.6,s[69,39]=-0.9,s[69,40]=0.1,s[69,41]=-1.1,s[69,42]=-0.5,s[69,43]=-1.2,s[69,44]=-0.2,s[69,45]=0.3,s[69,46]=-0.1,s[69,47]=0.8,s[69,48]=0.4,s[69,49]=-0.1,s[69,50]=0.5,s[69,51]=-0.9,s[69,52]=1.1,s[69,53]=1.0,s[69,54]=0.9,s[69,55]=1.2,s[69,56]=0.9,s[69,57]=-0.4,s[69,58]=-1.2,s[69,59]=-0.3,s[69,60]=-1.0
s[70,1]=0.7,s[70,2]=0.8,s[70,3]=-0.2,s[70,4]=0.3,s[70,5]=1.0,s[70,6]=-0.8,s[70,7]=0.8,s[70,8]=-0.9,s[70,9]=-0.6,s[70,10]=-0.8,s[70,11]=0.8,s[70,12]=-0.9,s[70,13]=-0.5,s[70,14]=0.9,s[70,15]=0.6,s[70,16]=-0.2,s[70,17]=0.5,s[70,18]=-0.6,s[70,19]=0.3,s[70,20]=0.5,s[70,21]=-1.0,s[70,22]=0.0,s[70,23]=0.6,s[70,24]=0.9,s[70,25]=-1.1,s[70,26]=0.9,s[70,27]=-0.9,s[70,28]=0.8,s[70,29]=-0.8,s[70,30]=-0.3,s[70,31]=0.4,s[70,32]=-1.1,s[70,33]=-0.8,s[70,34]=-0.4,s[70,35]=0.7,s[70,36]=-1.2,s[70,37]=-0.6,s[70,38]=-0.9,s[70,39]=0.3,s[70,40]=-1.0,s[70,41]=0.6,s[70,42]=0.9,s[70,43]=0.9,s[70,44]=-1.1,s[70,45]=-0.9,s[70,46]=-0.9,s[70,47]=0.8,s[70,48]=1.0,s[70,49]=-1.2,s[70,50]=0.4,s[70,51]=-0.6,s[70,52]=-0.4,s[70,53]=0.3,s[70,54]=1.0,s[70,55]=0.3,s[70,56]=0.1,s[70,57]=0.0,s[70,58]=0.6,s[70,59]=0.3,s[70,60]=-0.8
s[71,1]=-1.0,s[71,2]=0.5,s[71,3]=0.6,s[71,4]=-1.2,s[71,5]=-1.1,s[71,6]=0.0,s[71,7]=-0.4,s[71,8]=0.6,s[71,9]=0.6,s[71,10]=0.9,s[71,11]=-0.9,s[71,12]=0.5,s[71,13]=-1.2,s[71,14]=-0.9,s[71,15]=0.3,s[71,16]=1.1,s[71,17]=-0.2,s[71,18]=-0.8,s[71,19]=0.4,s[71,20]=0.9,s[71,21]=0.2,s[71,22]=-0.8,s[71,23]=-0.5,s[71,24]=-1.1,s[71,25]=-0.7,s[71,26]=0.7,s[71,27]=1.1,s[71,28]=-0.3,s[71,29]=0.4,s[71,30]=0.8,s[71,31]=0.1,s[71,32]=0.4,s[71,33]=0.3,s[71,34]=-1.1,s[71,35]=0.5,s[71,36]=-1.2,s[71,37]=0.0,s[71,38]=0.8,s[71,39]=-1.1,s[71,40]=1.2,s[71,41]=0.6,s[71,42]=-0.6,s[71,43]=0.1,s[71,44]=0.9,s[71,45]=-0.8,s[71,46]=0.5,s[71,47]=1.0,s[71,48]=-1.0,s[71,49]=0.6,s[71,50]=-0.2,s[71,51]=0.2,s[71,52]=-0.1,s[71,53]=1.2,s[71,54]=-0.6,s[71,55]=-1.1,s[71,56]=-1.2,s[71,57]=-1.2,s[71,58]=-0.6,s[71,59]=0.4,s[71,60]=-0.7
s[72,1]=-0.3,s[72,2]=-0.9,s[72,3]=-0.4,s[72,4]=-0.8,s[72,5]=-1.1,s[72,6]=0.8,s[72,7]=-0.6,s[72,8]=0.1,s[72,9]=-0.7,s[72,10]=1.2,s[72,11]=0.4,s[72,12]=-0.7,s[72,13]=0.8,s[72,14]=-0.7,s[72,15]=1.1,s[72,16]=0.9,s[72,17]=0.7,s[72,18]=-0.7,s[72,19]=-1.2,s[72,20]=-0.9,s[72,21]=1.1,s[72,22]=-0.6,s[72,23]=0.1,s[72,24]=-0.5,s[72,25]=0.9,s[72,26]=-1.1,s[72,27]=1.2,s[72,28]=0.5,s[72,29]=0.2,s[72,30]=-0.9,s[72,31]=-0.9,s[72,32]=0.3,s[72,33]=-0.2,s[72,34]=0.5,s[72,35]=-1.0,s[72,36]=0.1,s[72,37]=0.7,s[72,38]=0.6,s[72,39]=0.7,s[72,40]=1.1,s[72,41]=0.0,s[72,42]=-0.9,s[72,43]=1.0,s[72,44]=0.5,s[72,45]=1.1,s[72,46]=-1.2,s[72,47]=1.1,s[72,48]=0.0,s[72,49]=0.4,s[72,50]=-0.6,s[72,51]=-1.0,s[72,52]=-0.6,s[72,53]=-0.3,s[72,54]=-0.6,s[72,55]=0.7,s[72,56]=-0.7,s[72,57]=0.5,s[72,58]=-0.7,s[72,59]=-0.3,s[72,60]=-1.1
s[73,1]=-0.3,s[73,2]=0.7,s[73,3]=-0.8,s[73,4]=0.8,s[73,5]=1.2,s[73,6]=0.9,s[73,7]=-0.7,s[73,8]=0.4,s[73,9]=-0.2,s[73,10]=0.4,s[73,11]=0.6,s[73,12]=-0.2,s[73,13]=-0.9,s[73,14]=0.7,s[73,15]=1.2,s[73,16]=-0.8,s[73,17]=0.5,s[73,18]=0.4,s[73,19]=-0.7,s[73,20]=0.6,s[73,21]=0.7,s[73,22]=-1.1,s[73,23]=-0.6,s[73,24]=-0.8,s[73,25]=-0.6,s[73,26]=0.5,s[73,27]=0.3,s[73,28]=0.4,s[73,29]=0.4,s[73,30]=0.7
s[73,31]=-0.5,s[73,32]=-0.2,s[73,33]=-0.9,s[73,34]=0.1,s[73,35]=0.9,s[73,36]=-1.0,s[73,37]=0.3,s[73,38]=0.8,s[73,39]=0.1,s[73,40]=0.4,s[73,41]=-1.0,s[73,42]=0.1,s[73,43]=0.6,s[73,44]=1.1,s[73,45]=0.0,s[73,46]=0.4,s[73,47]=-0.6,s[73,48]=0.7,s[73,49]=0.7,s[73,50]=1.2,s[73,51]=0.0,s[73,52]=0.0,s[73,53]=-1.2,s[73,54]=-0.1,s[73,55]=-0.6,s[73,56]=-0.8,s[73,57]=-0.8,s[73,58]=0.6,s[73,59]=-0.9,s[73,60]=0.3
s[74,1]=-0.4,s[74,2]=1.0,s[74,3]=1.1,s[74,4]=0.8,s[74,5]=0.9,s[74,6]=1.1,s[74,7]=0.8,s[74,8]=1.1,s[74,9]=-0.6,s[74,10]=-0.9,s[74,11]=1.1,s[74,12]=-1.0,s[74,13]=-1.2,s[74,14]=0.2,s[74,15]=1.2,s[74,16]=0.2,s[74,17]=-0.4,s[74,18]=0.5,s[74,19]=1.2,s[74,20]=1.0,s[74,21]=1.2,s[74,22]=-0.5,s[74,23]=0.1,s[74,24]=0.8,s[74,25]=-1.1,s[74,26]=-0.6,s[74,27]=-0.6,s[74,28]=0.2,s[74,29]=-0.1,s[74,30]=-0.8
s[74,31]=-0.7,s[74,32]=-0.6,s[74,33]=1.0,s[74,34]=0.6,s[74,35]=1.1,s[74,36]=0.3,s[74,37]=1.0,s[74,38]=-1.2,s[74,39]=0.4,s[74,40]=-1.0,s[74,41]=0.1,s[74,42]=-0.7,s[74,43]=-0.9,s[74,44]=-0.4,s[74,45]=0.8,s[74,46]=-0.2,s[74,47]=-1.1,s[74,48]=-0.2,s[74,49]=0.9,s[74,50]=0.7,s[74,51]=-0.4,s[74,52]=-0.1,s[74,53]=0.4,s[74,54]=-1.0,s[74,55]=0.8,s[74,56]=-0.3,s[74,57]=-1.2,s[74,58]=-0.2,s[74,59]=-1.0,s[74,60]=-0.2
s[75,1]=0.9,s[75,2]=0.6,s[75,3]=0.8,s[75,4]=-1.1,s[75,5]=-0.1,s[75,6]=0.6,s[75,7]=0.0,s[75,8]=-0.9,s[75,9]=0.7,s[75,10]=-1.1,s[75,11]=-1.2,s[75,12]=0.3,s[75,13]=1.0,s[75,14]=-0.7,s[75,15]=-0.3,s[75,16]=0.6,s[75,17]=0.4,s[75,18]=1.2,s[75,19]=1.2,s[75,20]=-0.5,s[75,21]=-1.0,s[75,22]=-0.6,s[75,23]=-0.2,s[75,24]=-0.6,s[75,25]=-0.4,s[75,26]=0.2,s[75,27]=0.8,s[75,28]=0.9,s[75,29]=-0.3,s[75,30]=-1.0
s[75,31]=-0.1,s[75,32]=0.3,s[75,33]=0.8,s[75,34]=0.5,s[75,35]=0.3,s[75,36]=-1.2,s[75,37]=0.6,s[75,38]=0.4,s[75,39]=-0.3,s[75,40]=-1.1,s[75,41]=-0.3,s[75,42]=-0.5,s[75,43]=-0.6,s[75,44]=-0.7,s[75,45]=-1.0,s[75,46]=0.6,s[75,47]=1.1,s[75,48]=-1.2,s[75,49]=-0.5,s[75,50]=-0.2,s[75,51]=-0.8,s[75,52]=0.5,s[75,53]=-1.2,s[75,54]=1.0,s[75,55]=1.2,s[75,56]=1.1,s[75,57]=-0.2,s[75,58]=0.2,s[75,59]=-0.9,s[75,60]=-0.4
s[76,1]=0.2,s[76,2]=-0.5,s[76,3]=0.1,s[76,4]=-0.1,s[76,5]=-0.5,s[76,6]=0.4,s[76,7]=0.5,s[76,8]=-0.3,s[76,9]=0.1,s[76,10]=0.9,s[76,11]=-0.9,s[76,12]=1.2,s[76,13]=1.2,s[76,14]=0.4,s[76,15]=-0.5,s[76,16]=0.7,s[76,17]=0.5,s[76,18]=0.7,s[76,19]=-0.9,s[76,20]=0.6,s[76,21]=0.5,s[76,22]=0.1,s[76,23]=0.4,s[76,24]=-0.4,s[76,25]=1.1,s[76,26]=0.2,s[76,27]=-0.2,s[76,28]=-0.3,s[76,29]=-0.9,s[76,30]=-1.1
s[76,31]=-0.2,s[76,32]=0.1,s[76,33]=0.3,s[76,34]=0.3,s[76,35]=-0.7,s[76,36]=-1.2,s[76,37]=1.1,s[76,38]=0.6,s[76,39]=0.4,s[76,40]=1.1,s[76,41]=-0.5,s[76,42]=-0.7,s[76,43]=0.5,s[76,44]=0.5,s[76,45]=1.1,s[76,46]=-0.4,s[76,47]=0.9,s[76,48]=1.1,s[76,49]=-0.6,s[76,50]=-0.9,s[76,51]=1.1,s[76,52]=-1.2,s[76,53]=0.5,s[76,54]=-1.1,s[76,55]=-0.9,s[76,56]=-1.2,s[76,57]=-1.1,s[76,58]=-0.9,s[76,59]=0.2,s[76,60]=-0.4
s[77,1]=0.6,s[77,2]=-0.9,s[77,3]=0.9,s[77,4]=-0.6,s[77,5]=-0.6,s[77,6]=-0.3,s[77,7]=-0.1,s[77,8]=-1.2,s[77,9]=-1.1,s[77,10]=0.5,s[77,11]=0.6,s[77,12]=-0.2,s[77,13]=0.3,s[77,14]=0.1,s[77,15]=-0.6,s[77,16]=1.1,s[77,17]=-1.2,s[77,18]=-1.1,s[77,19]=-0.7,s[77,20]=0.9,s[77,21]=-0.6,s[77,22]=-1.1,s[77,23]=1.2,s[77,24]=0.0,s[77,25]=0.2,s[77,26]=-0.3,s[77,27]=-0.1,s[77,28]=-1.0,s[77,29]=1.2,s[77,30]=0.7
s[77,31]=0.4,s[77,32]=0.2,s[77,33]=-0.4,s[77,34]=-1.1,s[77,35]=1.0,s[77,36]=0.0,s[77,37]=-0.4,s[77,38]=0.4,s[77,39]=0.1,s[77,40]=-0.7,s[77,41]=1.0,s[77,42]=-0.2,s[77,43]=-0.8,s[77,44]=-1.0,s[77,45]=-0.2,s[77,46]=-0.7,s[77,47]=-0.8,s[77,48]=-0.2,s[77,49]=-1.0,s[77,50]=-0.8,s[77,51]=0.6,s[77,52]=-0.5,s[77,53]=-0.9,s[77,54]=-0.4,s[77,55]=0.3,s[77,56]=-1.2,s[77,57]=0.2,s[77,58]=1.2,s[77,59]=0.4,s[77,60]=0.9
s[78,1]=1.1,s[78,2]=-0.6,s[78,3]=1.2,s[78,4]=1.0,s[78,5]=0.9,s[78,6]=0.7,s[78,7]=0.5,s[78,8]=-1.1,s[78,9]=-1.2,s[78,10]=0.0,s[78,11]=-1.2,s[78,12]=-1.1,s[78,13]=-0.2,s[78,14]=0.4,s[78,15]=-0.1,s[78,16]=-0.9,s[78,17]=0.6,s[78,18]=-0.4,s[78,19]=1.2,s[78,20]=-0.3,s[78,21]=-1.1,s[78,22]=-0.1,s[78,23]=0.2,s[78,24]=-0.6,s[78,25]=0.6,s[78,26]=0.2,s[78,27]=-1.0,s[78,28]=-0.4,s[78,29]=-1.1,s[78,30]=1.0
s[78,31]=0.7,s[78,32]=-0.6,s[78,33]=-0.8,s[78,34]=0.5,s[78,35]=0.9,s[78,36]=0.7,s[78,37]=-0.6,s[78,38]=0.7,s[78,39]=-0.2,s[78,40]=0.7,s[78,41]=0.0,s[78,42]=0.5,s[78,43]=0.3,s[78,44]=0.2,s[78,45]=0.1,s[78,46]=-1.2,s[78,47]=-1.1,s[78,48]=0.8,s[78,49]=0.0,s[78,50]=-0.4,s[78,51]=1.1,s[78,52]=0.3,s[78,53]=-0.5,s[78,54]=-1.2,s[78,55]=-1.0,s[78,56]=-0.1,s[78,57]=-0.5,s[78,58]=-0.8,s[78,59]=-0.8,s[78,60]=-0.6
s[79,1]=0.4,s[79,2]=-1.0,s[79,3]=-0.9,s[79,4]=1.1,s[79,5]=0.4,s[79,6]=0.0,s[79,7]=0.1,s[79,8]=1.2,s[79,9]=-0.6,s[79,10]=0.4,s[79,11]=1.1,s[79,12]=-1.2,s[79,13]=0.4,s[79,14]=0.7,s[79,15]=1.1,s[79,16]=-0.6,s[79,17]=-0.5,s[79,18]=-1.1,s[79,19]=-1.0,s[79,20]=-0.4,s[79,21]=0.8,s[79,22]=-0.8,s[79,23]=1.1,s[79,24]=1.2,s[79,25]=0.4,s[79,26]=-0.8,s[79,27]=-0.3,s[79,28]=1.1,s[79,29]=-0.1,s[79,30]=0.1
s[79,31]=1.2,s[79,32]=-1.0,s[79,33]=-0.6,s[79,34]=0.4,s[79,35]=0.0,s[79,36]=0.1,s[79,37]=-0.1,s[79,38]=0.2,s[79,39]=0.0,s[79,40]=1.2,s[79,41]=0.2,s[79,42]=0.1,s[79,43]=-0.9,s[79,44]=-0.6,s[79,45]=-0.7,s[79,46]=-0.9,s[79,47]=-0.7,s[79,48]=0.5,s[79,49]=-0.3,s[79,50]=-0.2,s[79,51]=-0.8,s[79,52]=0.9,s[79,53]=0.8,s[79,54]=-0.6,s[79,55]=0.7,s[79,56]=-0.2,s[79,57]=-0.1,s[79,58]=-0.8,s[79,59]=-1.2,s[79,60]=0.1
s[80,1]=-0.8,s[80,2]=1.0,s[80,3]=-0.9,s[80,4]=0.2,s[80,5]=-0.3,s[80,6]=-0.9,s[80,7]=0.8,s[80,8]=0.4,s[80,9]=0.4,s[80,10]=0.3,s[80,11]=-1.0,s[80,12]=0.0,s[80,13]=-1.2,s[80,14]=1.2,s[80,15]=0.3,s[80,16]=1.1,s[80,17]=-1.1,s[80,18]=-0.2,s[80,19]=-1.2,s[80,20]=-1.0,s[80,21]=0.9,s[80,22]=-0.1,s[80,23]=0.8,s[80,24]=-1.1,s[80,25]=-0.2,s[80,26]=-0.5,s[80,27]=0.8,s[80,28]=-0.1,s[80,29]=-0.4,s[80,30]=-0.2
s[80,31]=0.8,s[80,32]=0.4,s[80,33]=-1.2,s[80,34]=-1.0,s[80,35]=0.9,s[80,36]=0.6,s[80,37]=0.8,s[80,38]=-0.5,s[80,39]=-0.9,s[80,40]=0.8,s[80,41]=0.8,s[80,42]=0.6,s[80,43]=-1.0,s[80,44]=1.0,s[80,45]=0.0,s[80,46]=-0.2,s[80,47]=0.4,s[80,48]=0.0,s[80,49]=1.0,s[80,50]=-0.6,s[80,51]=-1.1,s[80,52]=1.2,s[80,53]=0.4,s[80,54]=0.8,s[80,55]=0.2,s[80,56]=0.8,s[80,57]=0.6,s[80,58]=0.2,s[80,59]=-0.9,s[80,60]=0.0
s[81,1]=1.0,s[81,2]=-0.3,s[81,3]=-0.5,s[81,4]=-0.9,s[81,5]=1.1,s[81,6]=-0.3,s[81,7]=-0.1,s[81,8]=0.1,s[81,9]=1.0,s[81,10]=-1.0,s[81,11]=0.5,s[81,12]=-0.5,s[81,13]=1.2,s[81,14]=0.9,s[81,15]=-0.5,s[81,16]=-0.6,s[81,17]=1.0,s[81,18]=1.1,s[81,19]=-0.4,s[81,20]=-0.9,s[81,21]=0.9,s[81,22]=0.0,s[81,23]=-0.9,s[81,24]=-0.4,s[81,25]=1.0,s[81,26]=-1.0,s[81,27]=-0.3,s[81,28]=-1.2,s[81,29]=-0.1,s[81,30]=-0.6
s[81,31]=-0.3,s[81,32]=-0.6,s[81,33]=0.9,s[81,34]=1.1,s[81,35]=-0.5,s[81,36]=-1.0,s[81,37]=0.7,s[81,38]=0.2,s[81,39]=0.8,s[81,40]=-1.1,s[81,41]=-1.1,s[81,42]=0.3,s[81,43]=0.0,s[81,44]=-0.6,s[81,45]=-0.6,s[81,46]=1.0,s[81,47]=0.1,s[81,48]=-1.0,s[81,49]=-0.9,s[81,50]=-1.1,s[81,51]=-0.1,s[81,52]=-1.1,s[81,53]=-1.2,s[81,54]=1.1,s[81,55]=0.8,s[81,56]=0.3,s[81,57]=-1.1,s[81,58]=-0.4,s[81,59]=-0.5,s[81,60]=0.2
s[82,1]=-0.1,s[82,2]=0.5,s[82,3]=-0.3,s[82,4]=0.7,s[82,5]=-0.6,s[82,6]=-0.8,s[82,7]=-1.2,s[82,8]=-1.2,s[82,9]=0.8,s[82,10]=1.1,s[82,11]=1.0,s[82,12]=-0.4,s[82,13]=-0.1,s[82,14]=-0.3,s[82,15]=0.6,s[82,16]=-0.9,s[82,17]=0.2,s[82,18]=-1.2,s[82,19]=-0.2,s[82,20]=-1.2,s[82,21]=0.0,s[82,22]=0.4,s[82,23]=0.4,s[82,24]=-0.9,s[82,25]=0.2,s[82,26]=-0.1,s[82,27]=1.0,s[82,28]=1.1,s[82,29]=-1.1,s[82,30]=0.3
s[82,31]=0.5,s[82,32]=-0.8,s[82,33]=-0.2,s[82,34]=0.1,s[82,35]=0.7,s[82,36]=-0.6,s[82,37]=-0.3,s[82,38]=-0.6,s[82,39]=0.7,s[82,40]=0.5,s[82,41]=-0.2,s[82,42]=0.5,s[82,43]=-0.7,s[82,44]=0.7,s[82,45]=0.7,s[82,46]=0.6,s[82,47]=0.9,s[82,48]=-0.4,s[82,49]=-1.1,s[82,50]=0.8,s[82,51]=0.0,s[82,52]=1.0,s[82,53]=-0.6,s[82,54]=1.0,s[82,55]=0.3,s[82,56]=-0.6,s[82,57]=1.0,s[82,58]=0.5,s[82,59]=-0.2,s[82,60]=0.9
s[83,1]=-0.1,s[83,2]=0.0,s[83,3]=-0.8,s[83,4]=0.7,s[83,5]=0.2,s[83,6]=1.2,s[83,7]=-0.5,s[83,8]=0.7,s[83,9]=1.1,s[83,10]=1.2,s[83,11]=0.0,s[83,12]=0.1,s[83,13]=0.5,s[83,14]=-0.2,s[83,15]=0.5,s[83,16]=1.1,s[83,17]=-0.1,s[83,18]=-0.5,s[83,19]=-1.1,s[83,20]=0.7,s[83,21]=0.6,s[83,22]=-1.1,s[83,23]=0.4,s[83,24]=-0.5,s[83,25]=0.1,s[83,26]=-1.0,s[83,27]=-1.2,s[83,28]=0.1,s[83,29]=0.5,s[83,30]=0.8
s[83,31]=-0.6,s[83,32]=1.1,s[83,33]=-0.8,s[83,34]=-1.1,s[83,35]=-0.9,s[83,36]=0.8,s[83,37]=1.1,s[83,38]=-0.4,s[83,39]=-0.4,s[83,40]=-0.5,s[83,41]=-0.2,s[83,42]=1.2,s[83,43]=0.5,s[83,44]=1.1,s[83,45]=-0.8,s[83,46]=0.3,s[83,47]=0.0,s[83,48]=1.2,s[83,49]=0.4,s[83,50]=0.7,s[83,51]=-1.2,s[83,52]=0.6,s[83,53]=-0.5,s[83,54]=-0.4,s[83,55]=1.1,s[83,56]=-0.9,s[83,57]=0.2,s[83,58]=1.0,s[83,59]=0.9,s[83,60]=-0.1
s[84,1]=0.7,s[84,2]=-0.5,s[84,3]=-0.6,s[84,4]=-0.1,s[84,5]=-0.8,s[84,6]=0.2,s[84,7]=1.0,s[84,8]=0.1,s[84,9]=-0.2,s[84,10]=0.9,s[84,11]=0.4,s[84,12]=1.0,s[84,13]=1.1,s[84,14]=0.8,s[84,15]=0.3,s[84,16]=-0.5,s[84,17]=0.8,s[84,18]=-0.2,s[84,19]=0.6,s[84,20]=0.8,s[84,21]=-0.8,s[84,22]=0.3,s[84,23]=0.5,s[84,24]=-0.8,s[84,25]=0.1,s[84,26]=1.1,s[84,27]=-1.2,s[84,28]=-0.3,s[84,29]=-0.6,s[84,30]=0.1
s[84,31]=-1.0,s[84,32]=-0.5,s[84,33]=0.4,s[84,34]=0.0,s[84,35]=-0.8,s[84,36]=-0.7,s[84,37]=0.2,s[84,38]=0.5,s[84,39]=-0.2,s[84,40]=-0.4,s[84,41]=0.7,s[84,42]=-0.3,s[84,43]=-0.1,s[84,44]=0.2,s[84,45]=-0.7,s[84,46]=-0.8,s[84,47]=0.8,s[84,48]=-0.1,s[84,49]=-1.2,s[84,50]=0.6,s[84,51]=-0.5,s[84,52]=-0.6,s[84,53]=-0.9,s[84,54]=-0.4,s[84,55]=0.1,s[84,56]=-0.1,s[84,57]=0.5,s[84,58]=0.1,s[84,59]=-0.4,s[84,60]=-0.1
s[85,1]=0.4,s[85,2]=1.2,s[85,3]=-0.7,s[85,4]=-1.2,s[85,5]=-1.0,s[85,6]=0.2,s[85,7]=0.5,s[85,8]=1.0,s[85,9]=-1.2,s[85,10]=0.0,s[85,11]=0.1,s[85,12]=1.0,s[85,13]=0.3,s[85,14]=0.1,s[85,15]=-1.2,s[85,16]=-1.0,s[85,17]=-0.7,s[85,18]=1.1,s[85,19]=-0.8,s[85,20]=1.0,s[85,21]=-0.2,s[85,22]=-1.0,s[85,23]=-1.0,s[85,24]=0.7,s[85,25]=0.1,s[85,26]=-0.6,s[85,27]=-0.3,s[85,28]=1.2,s[85,29]=0.7,s[85,30]=0.4
s[85,31]=0.8,s[85,32]=0.2,s[85,33]=0.2,s[85,34]=0.3,s[85,35]=-0.1,s[85,36]=1.1,s[85,37]=-0.8,s[85,38]=0.0,s[85,39]=-0.4,s[85,40]=-0.7,s[85,41]=-0.7,s[85,42]=-0.2,s[85,43]=0.0,s[85,44]=1.1,s[85,45]=-0.1,s[85,46]=-1.1,s[85,47]=0.9,s[85,48]=0.3,s[85,49]=-0.7,s[85,50]=-0.6,s[85,51]=0.6,s[85,52]=-0.6,s[85,53]=-1.0,s[85,54]=0.3,s[85,55]=0.5,s[85,56]=-0.1,s[85,57]=-0.7,s[85,58]=-0.3,s[85,59]=0.6,s[85,60]=1.2
s[86,1]=-1.0,s[86,2]=0.5,s[86,3]=0.0,s[86,4]=-1.0,s[86,5]=0.1,s[86,6]=0.1,s[86,7]=-0.8,s[86,8]=-1.2,s[86,9]=1.0,s[86,10]=-0.4,s[86,11]=-0.3,s[86,12]=0.9,s[86,13]=1.0,s[86,14]=-0.4,s[86,15]=-1.2,s[86,16]=1.0,s[86,17]=-0.5,s[86,18]=-0.3,s[86,19]=1.0,s[86,20]=-0.9,s[86,21]=-0.5,s[86,22]=1.1,s[86,23]=0.3,s[86,24]=-0.5,s[86,25]=0.8,s[86,26]=0.8,s[86,27]=-0.1,s[86,28]=-0.2,s[86,29]=0.2,s[86,30]=0.0
s[86,31]=1.1,s[86,32]=-0.4,s[86,33]=1.1,s[86,34]=-1.1,s[86,35]=-0.7,s[86,36]=-0.5,s[86,37]=-1.0,s[86,38]=-0.1,s[86,39]=-0.8,s[86,40]=-0.1,s[86,41]=0.2,s[86,42]=-0.1,s[86,43]=-0.9,s[86,44]=-0.1,s[86,45]=-1.1,s[86,46]=0.1,s[86,47]=0.3,s[86,48]=-0.4,s[86,49]=-1.1,s[86,50]=0.5,s[86,51]=1.0,s[86,52]=-0.9,s[86,53]=-0.3,s[86,54]=-0.2,s[86,55]=0.2,s[86,56]=-0.8,s[86,57]=-0.2,s[86,58]=-1.2,s[86,59]=-1.0,s[86,60]=0.3
s[87,1]=1.0,s[87,2]=-0.1,s[87,3]=0.0,s[87,4]=-1.0,s[87,5]=1.1,s[87,6]=0.3,s[87,7]=-1.2,s[87,8]=-0.1,s[87,9]=1.0,s[87,10]=0.0,s[87,11]=0.2,s[87,12]=0.3,s[87,13]=1.1,s[87,14]=-0.6,s[87,15]=0.0,s[87,16]=-0.5,s[87,17]=0.0,s[87,18]=0.8,s[87,19]=-1.2,s[87,20]=0.3,s[87,21]=-0.1,s[87,22]=-0.9,s[87,23]=0.7,s[87,24]=1.2,s[87,25]=-0.3,s[87,26]=1.1,s[87,27]=0.8,s[87,28]=1.0,s[87,29]=1.0,s[87,30]=0.0
s[87,31]=-0.5,s[87,32]=1.0,s[87,33]=-0.2,s[87,34]=-0.1,s[87,35]=0.1,s[87,36]=-0.1,s[87,37]=-0.9,s[87,38]=0.0,s[87,39]=-0.2,s[87,40]=-0.4,s[87,41]=0.5,s[87,42]=-0.5,s[87,43]=-0.5,s[87,44]=-0.3,s[87,45]=-1.2,s[87,46]=-0.1,s[87,47]=-0.8,s[87,48]=-0.5,s[87,49]=0.8,s[87,50]=0.4,s[87,51]=-0.9,s[87,52]=-0.1,s[87,53]=0.7,s[87,54]=0.3,s[87,55]=-0.6,s[87,56]=-1.2,s[87,57]=-0.7,s[87,58]=1.0,s[87,59]=-1.2,s[87,60]=0.8
s[88,1]=-0.2,s[88,2]=-0.5,s[88,3]=1.1,s[88,4]=-0.1,s[88,5]=0.8,s[88,6]=0.6,s[88,7]=0.0,s[88,8]=0.6,s[88,9]=-0.7,s[88,10]=1.2,s[88,11]=0.3,s[88,12]=1.2,s[88,13]=0.8,s[88,14]=-0.7,s[88,15]=-0.2,s[88,16]=1.1,s[88,17]=-0.9,s[88,18]=-1.2,s[88,19]=0.0,s[88,20]=0.5,s[88,21]=-0.9,s[88,22]=0.3,s[88,23]=0.5,s[88,24]=-0.5,s[88,25]=0.7,s[88,26]=0.1,s[88,27]=0.2,s[88,28]=1.1,s[88,29]=-0.7,s[88,30]=0.2
s[88,31]=-1.1,s[88,32]=-0.5,s[88,33]=-0.4,s[88,34]=0.5,s[88,35]=0.2,s[88,36]=0.1,s[88,37]=-0.1,s[88,38]=0.3,s[88,39]=-0.1,s[88,40]=-0.4,s[88,41]=-0.8,s[88,42]=-0.9,s[88,43]=-0.6,s[88,44]=0.5,s[88,45]=0.0,s[88,46]=-0.4,s[88,47]=0.2,s[88,48]=-0.6,s[88,49]=-0.5,s[88,50]=0.2,s[88,51]=1.0,s[88,52]=-0.8,s[88,53]=-1.0,s[88,54]=-0.1,s[88,55]=-1.1,s[88,56]=-0.3,s[88,57]=-0.7,s[88,58]=0.0,s[88,59]=0.5,s[88,60]=0.4
s[89,1]=0.3,s[89,2]=-0.9,s[89,3]=0.7,s[89,4]=0.9,s[89,5]=1.0,s[89,6]=-0.3,s[89,7]=-0.2,s[89,8]=-1.1,s[89,9]=-1.1,s[89,10]=-1.0,s[89,11]=1.2,s[89,12]=1.2,s[89,13]=0.8,s[89,14]=0.4,s[89,15]=1.1,s[89,16]=0.5,s[89,17]=-1.0,s[89,18]=-0.8,s[89,19]=-0.1,s[89,20]=-0.9,s[89,21]=0.1,s[89,22]=-0.5,s[89,23]=0.1,s[89,24]=-0.5,s[89,25]=0.8,s[89,26]=1.2,s[89,27]=-0.9,s[89,28]=-0.8,s[89,29]=-0.9,s[89,30]=0.8
s[89,31]=-0.9,s[89,32]=-0.1,s[89,33]=-0.3,s[89,34]=-0.9,s[89,35]=-1.0,s[89,36]=0.5,s[89,37]=-0.7,s[89,38]=1.0,s[89,39]=0.9,s[89,40]=0.6,s[89,41]=-0.9,s[89,42]=-0.9,s[89,43]=0.2,s[89,44]=0.9,s[89,45]=-0.2,s[89,46]=-0.3,s[89,47]=-1.0,s[89,48]=1.2,s[89,49]=1.2,s[89,50]=0.9,s[89,51]=0.1,s[89,52]=1.2,s[89,53]=0.5,s[89,54]=0.5,s[89,55]=-1.1,s[89,56]=-0.2,s[89,57]=0.7,s[89,58]=0.3,s[89,59]=-0.3,s[89,60]=1.0
s[90,1]=0.8,s[90,2]=0.1,s[90,3]=-0.7,s[90,4]=-0.9,s[90,5]=0.4,s[90,6]=1.2,s[90,7]=0.8,s[90,8]=1.2,s[90,9]=-1.1,s[90,10]=0.4,s[90,11]=0.8,s[90,12]=-0.3,s[90,13]=-0.1,s[90,14]=1.2,s[90,15]=-1.1,s[90,16]=-0.6,s[90,17]=-0.3,s[90,18]=0.9,s[90,19]=-0.5,s[90,20]=0.3,s[90,21]=-1.1,s[90,22]=-0.6,s[90,23]=-0.2,s[90,24]=-0.9,s[90,25]=-0.6,s[90,26]=-1.1,s[90,27]=-0.9,s[90,28]=0.7,s[90,29]=-0.2,s[90,30]=-0.8
s[90,31]=-0.7,s[90,32]=-0.8,s[90,33]=0.2,s[90,34]=-1.2,s[90,35]=0.4,s[90,36]=0.9,s[90,37]=-0.3,s[90,38]=-1.2,s[90,39]=-0.3,s[90,40]=-1.2,s[90,41]=-0.7,s[90,42]=0.5,s[90,43]=0.0,s[90,44]=-0.7,s[90,45]=0.9,s[90,46]=0.3,s[90,47]=0.0,s[90,48]=-0.2,s[90,49]=0.6,s[90,50]=1.2,s[90,51]=0.4,s[90,52]=0.7,s[90,53]=0.3,s[90,54]=0.1,s[90,55]=-0.6,s[90,56]=1.0,s[90,57]=0.4,s[90,58]=0.5,s[90,59]=-1.2,s[90,60]=0.4
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float ppz = @ppz
float ppw = @ppw
float pxx = 0
float pyy = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
pyy = y
float pzz = ppz
x = x+0.1*(s[@sel,1] + s[@sel,2]*x + s[@sel,3]*x*x + s[@sel,4]*x*y + s[@sel,5]*x*ppz + s[@sel,6]*x*ppw + s[@sel,7]*y + s[@sel,8]*y*y + \
s[@sel,9]*y*ppz + s[@sel,10]*y*ppw + s[@sel,11]*ppz + s[@sel,12]*ppz*ppz + s[@sel,13]*ppz*ppw + s[@sel,14]*ppw + s[@sel,15]*ppw*ppw)
y = y+0.1*(s[@sel,16] + s[@sel,17]*pxx + s[@sel,18]*pxx*pxx + s[@sel,19]*pxx*y + s[@sel,20]*pxx*ppz + s[@sel,21]*pxx*ppw + s[@sel,22]*y + s[@sel,23]*y*y + \
s[@sel,24]*y*ppz + s[@sel,25]*y*ppw + s[@sel,26]*ppz + s[@sel,27]*ppz*ppz + s[@sel,28]*ppz*ppw + s[@sel,29]*ppw + s[@sel,30]*ppw*ppw)
ppz = ppz+0.1*(s[@sel,31] + s[@sel,32]*pxx + s[@sel,33]*pxx*pxx + s[@sel,34]*pxx*pyy + s[@sel,35]*pxx*ppz + s[@sel,36]*pxx*ppw + s[@sel,37]*pyy + s[@sel,38]*pyy*pyy + \
s[@sel,39]*pyy*ppz + s[@sel,40]*pyy*ppw + s[@sel,41]*ppz + s[@sel,42]*ppz*ppz + s[@sel,43]*ppz*ppw + s[@sel,44]*ppw + s[@sel,45]*ppw*ppw)
ppw = ppw+0.1*(s[@sel,46] + s[@sel,47]*pxx + s[@sel,48]*pxx*pxx + s[@sel,49]*pxx*pyy + s[@sel,50]*pxx*pzz + s[@sel,51]*pxx*ppw + s[@sel,52]*pyy + s[@sel,53]*pyy*pyy + \
s[@sel,54]*pyy*pzz + s[@sel,55]*pyy*ppw + s[@sel,56]*pzz + s[@sel,57]*pzz*pzz + s[@sel,58]*pzz*ppw + s[@sel,59]*ppw + s[@sel,60]*ppw*ppw)
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y) + ppz*@pw + ppw*@p4)
float d = @distscale*|pz-(x + sgn*flip(y) + ppz*@pw + ppw*@p4)|
return d
endfunc
private:
float s[91,61]
default:
title = "Sprott4D_ODE"
heading
text="Strange attractors from simultaneous ordinary differential \
equations using Euler's finite difference method to calculate."
endheading
heading
text="Sprott 4D ODE quadratic attractors"
endheading
heading
text=" x -> x + 0.1*(Quadratic in x, y, z and w)"
endheading
heading
text=" y -> y + 0.1*(Quadratic in x, y, z and w)"
endheading
heading
text=" z -> z + 0.1*(Quadratic in x, y, z and w)"
endheading
heading
text=" w -> w + 0.1*(Quadratic in x, y, z and w)"
endheading
int param v_trapshapesprott4d_ode
caption = "Version (Trap Shape Sprott4D_ODE)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesprott4D_ode < 100
endparam
param sel
caption = "Sprott selector"
default = 0
enum = "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" \
"11" "12" "13" "14" "15" "16" "17" "18" "19" "20" \
"21" "22" "23" "24" "25" "26" "27" "28" "29" "30" \
"31" "32" "33" "34" "35" "36" "37" "38" "39" "40" \
"41" "42" "43" "44" "45" "46" "47" "48" "49" "50" \
"51" "52" "53" "54" "55" "56" "57" "58" "59" "60" \
"61" "62" "63" "64" "65" "66" "67" "68" "69" "70" \
"71" "72" "73" "74" "75" "76" "77" "78" "79" "80" \
"81" "82" "83" "84" "85" "86" "87" "88" "89" "90"
hint = "Each Sprott selector uses a different strange attractor."
endparam
heading
text = "'Initialize Height' sets the starting z value for the attractor."
endheading
float param ppz
caption = "Initialize Height"
default = 0.0
endparam
heading
text = "'Initialize 4th dim' sets the starting w value for the attractor."
endheading
float param ppw
caption = "Initialize 4th dim"
default = 0.0
endparam
heading
text = "'Height weight' determines the weight of the final z value which is added \
to the trap distance."
endheading
complex param pw
caption = "Height weight"
default = (0,0)
endparam
heading
text = "'4D weight' determines the weight of the final w value which is added \
to the trap distance."
endheading
complex param p4
caption = "4D weight"
default = (0,0)
endparam
float param distscale
caption = "Distance scale"
default = 1
endparam
float param s
caption = "Attractor scale"
default = 0.5
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 100
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSprott3D_ODE(common.ulb:TrapShape) {
; This shape uses a Sprott strange attractor.
; The Sprott attractors were developed by Julien C. Sprott, and are
; based upon polynomials and linear differential equations of polynomials.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSprott3D_ODE(Generic pparent)
TrapShape.TrapShape(pparent)
so[0,1]=-1.2,so[0,2]=-0.7,so[0,3]=0.9,so[0,4]=0.5,so[0,5]=0.9,so[0,6]=-0.1,so[0,7]=-0.2,so[0,8]=-0.5,so[0,9]=-1.1,so[0,10]=0.5,so[0,11]=-1.0,so[0,12]=1.0,so[0,13]=-0.8,so[0,14]=0.6
so[0,15]=0.6,so[0,16]=1.2,so[0,17]=-0.1,so[0,18]=1.1,so[0,19]=1.1,so[0,20]=0.6,so[0,21]=0.3,so[0,22]=0.6,so[0,23]=-1.1,so[0,24]=-0.7,so[0,25]=-0.1,so[0,26]=-1.0,so[0,27]=-0.2,so[0,28]=-0.2,so[0,29]=-0.1,so[0,30]=0.1
so[1,1]=1.0,so[1,2]=-1.1,so[1,3]=-0.6,so[1,4]=-1.0,so[1,5]=0.2,so[1,6]=0.4,so[1,7]=1.0,so[1,8]=0.8,so[1,9]=0.5,so[1,10]=-0.8,so[1,11]=0.1,so[1,12]=-0.1,so[1,13]=-1.2,so[1,14]=-0.9
so[1,15]=0.3,so[1,16]=1.0,so[1,17]=-0.9,so[1,18]=-0.5,so[1,19]=1.1,so[1,20]=1.0,so[1,21]=0.1,so[1,22]=-1.0,so[1,23]=1.0,so[1,24]=-0.9,so[1,25]=-0.4,so[1,26]=-0.6,so[1,27]=0.3,so[1,28]=-0.6,so[1,29]=0.1,so[1,30]=0.7
so[2,1]=-1.0,so[2,2]=-0.3,so[2,3]=0.2,so[2,4]=-0.9,so[2,5]=0.7,so[2,6]=-0.1,so[2,7]=0.3,so[2,8]=1.1,so[2,9]=-0.8,so[2,10]=-0.5,so[2,11]=-1.1,so[2,12]=1.2,so[2,13]=-1.0,so[2,14]=-0.6
so[2,15]=0.6,so[2,16]=1.2,so[2,17]=-0.1,so[2,18]=0.5,so[2,19]=0.5,so[2,20]=0.8,so[2,21]=-1.2,so[2,22]=-0.8,so[2,23]=-1.1,so[2,24]=1.1,so[2,25]=0.7,so[2,26]=0.5,so[2,27]=0.0,so[2,28]=-1.1,so[2,29]=-0.5,so[2,30]=0.6
so[3,1]=-0.8,so[3,2]=-0.5,so[3,3]=0.5,so[3,4]=0.2,so[3,5]=0.2,so[3,6]=-1.1,so[3,7]=-0.8,so[3,8]=-1.0,so[3,9]=-1.1,so[3,10]=0.4,so[3,11]=-1.0,so[3,12]=-0.3,so[3,13]=0.6,so[3,14]=1.1
so[3,15]=0.7,so[3,16]=0.4,so[3,17]=0.1,so[3,18]=1.0,so[3,19]=1.0,so[3,20]=-0.7,so[3,21]=1.1,so[3,22]=-1.0,so[3,23]=-0.9,so[3,24]=-0.9,so[3,25]=-0.7,so[3,26]=-0.3,so[3,27]=-0.2,so[3,28]=-0.3,so[3,29]=-1.0,so[3,30]=0.1
so[4,1]=-0.3,so[4,2]=-0.9,so[4,3]=1.2,so[4,4]=0.1,so[4,5]=1.1,so[4,6]=-1.1,so[4,7]=-0.1,so[4,8]=0.4,so[4,9]=0.4,so[4,10]=-0.6,so[4,11]=0.8,so[4,12]=-0.2,so[4,13]=-0.1,so[4,14]=1.0
so[4,15]=-1.1,so[4,16]=0.3,so[4,17]=-0.5,so[4,18]=-1.0,so[4,19]=1.2,so[4,20]=0.1,so[4,21]=-0.7,so[4,22]=0.1,so[4,23]=-0.3,so[4,24]=0.1,so[4,25]=0.6,so[4,26]=0.6,so[4,27]=0.7,so[4,28]=1.1,so[4,29]=-0.8,so[4,30]=-0.4
so[5,1]=-1.1,so[5,2]=0.1,so[5,3]=0.9,so[5,4]=0.1,so[5,5]=0.2,so[5,6]=0.6,so[5,7]=0.2,so[5,8]=0.0,so[5,9]=-0.2,so[5,10]=-0.2,so[5,11]=-0.3,so[5,12]=-1.1,so[5,13]=0.6,so[5,14]=0.8
so[5,15]=-0.1,so[5,16]=-0.1,so[5,17]=0.3,so[5,18]=0.2,so[5,19]=0.8,so[5,20]=-0.7,so[5,21]=0.6,so[5,22]=-1.1,so[5,23]=0.8,so[5,24]=-0.9,so[5,25]=0.1,so[5,26]=0.1,so[5,27]=-0.4,so[5,28]=0.8,so[5,29]=-0.7,so[5,30]=0.6
so[6,1]=0.7,so[6,2]=-0.2,so[6,3]=-1.2,so[6,4]=0.4,so[6,5]=0.3,so[6,6]=-1.0,so[6,7]=0.2,so[6,8]=-1.0,so[6,9]=-1.2,so[6,10]=1.2,so[6,11]=0.5,so[6,12]=0.8,so[6,13]=-1.1,so[6,14]=-0.6
so[6,15]=-0.3,so[6,16]=0.4,so[6,17]=-0.2,so[6,18]=-0.1,so[6,19]=-1.2,so[6,20]=0.1,so[6,21]=0.1,so[6,22]=0.8,so[6,23]=1.1,so[6,24]=0.5,so[6,25]=1.0,so[6,26]=0.0,so[6,27]=-0.8,so[6,28]=-0.3,so[6,29]=-0.6,so[6,30]=0.4
so[7,1]=0.3,so[7,2]=0.1,so[7,3]=0.6,so[7,4]=-0.5,so[7,5]=0.2,so[7,6]=0.5,so[7,7]=1.2,so[7,8]=0.0,so[7,9]=-0.1,so[7,10]=-1.1,so[7,11]=0.9,so[7,12]=-0.9,so[7,13]=-1.0,so[7,14]=0.0
so[7,15]=0.3,so[7,16]=-1.2,so[7,17]=0.7,so[7,18]=1.0,so[7,19]=0.9,so[7,20]=0.2,so[7,21]=-0.5,so[7,22]=-0.1,so[7,23]=0.6,so[7,24]=0.0,so[7,25]=1.1,so[7,26]=-1.2,so[7,27]=-0.8,so[7,28]=0.9,so[7,29]=1.2,so[7,30]=-0.4
so[8,1]=-0.3,so[8,2]=0.4,so[8,3]=0.3,so[8,4]=-1.1,so[8,5]=1.0,so[8,6]=0.7,so[8,7]=0.8,so[8,8]=0.2,so[8,9]=0.4,so[8,10]=-0.9,so[8,11]=0.1,so[8,12]=-0.6,so[8,13]=1.1,so[8,14]=-0.3
so[8,15]=0.2,so[8,16]=0.2,so[8,17]=-0.4,so[8,18]=0.5,so[8,19]=0.9,so[8,20]=-0.3,so[8,21]=1.0,so[8,22]=-0.7,so[8,23]=1.0,so[8,24]=-0.5,so[8,25]=0.0,so[8,26]=-1.2,so[8,27]=-0.6,so[8,28]=0.5,so[8,29]=-0.8,so[8,30]=0.5
so[9,1]=0.7,so[9,2]=0.2,so[9,3]=0.5,so[9,4]=-0.6,so[9,5]=0.4,so[9,6]=0.8,so[9,7]=1.1,so[9,8]=-0.8,so[9,9]=-1.2,so[9,10]=-1.0,so[9,11]=-0.5,so[9,12]=0.4,so[9,13]=0.8,so[9,14]=-0.1
so[9,15]=-0.2,so[9,16]=-0.5,so[9,17]=-0.6,so[9,18]=-0.4,so[9,19]=-0.3,so[9,20]=0.7,so[9,21]=0.6,so[9,22]=1.1,so[9,23]=0.3,so[9,24]=0.6,so[9,25]=0.0,so[9,26]=-1.2,so[9,27]=-0.5,so[9,28]=-0.9,so[9,29]=-1.1,so[9,30]=0.8
so[10,1]=-0.1,so[10,2]=-1.0,so[10,3]=-0.4,so[10,4]=-0.5,so[10,5]=1.0,so[10,6]=-0.6,so[10,7]=1.1,so[10,8]=1.2,so[10,9]=-0.9,so[10,10]=-0.4,so[10,11]=-1.2,so[10,12]=0.7,so[10,13]=-0.1,so[10,14]=0.8
so[10,15]=-0.5,so[10,16]=-0.8,so[10,17]=-0.9,so[10,18]=-0.9,so[10,19]=0.6,so[10,20]=1.1,so[10,21]=0.0,so[10,22]=1.0,so[10,23]=0.3,so[10,24]=-0.9,so[10,25]=0.5,so[10,26]=-1.1,so[10,27]=-0.3,so[10,28]=-0.8,so[10,29]=-0.9,so[10,30]=-0.6
so[11,1]=0.4,so[11,2]=-1.0,so[11,3]=0.8,so[11,4]=1.0,so[11,5]=1.1,so[11,6]=-0.5,so[11,7]=-0.1,so[11,8]=-0.8,so[11,9]=-1.1,so[11,10]=-0.4,so[11,11]=0.5,so[11,12]=-0.6,so[11,13]=-0.2,so[11,14]=-0.5
so[11,15]=-0.3,so[11,16]=-0.7,so[11,17]=0.3,so[11,18]=1.2,so[11,19]=1.2,so[11,20]=0.1,so[11,21]=1.2,so[11,22]=0.1,so[11,23]=-0.5,so[11,24]=0.3,so[11,25]=-0.9,so[11,26]=0.2,so[11,27]=-1.2,so[11,28]=-0.8,so[11,29]=0.3,so[11,30]=1.0
so[12,1]=-0.3,so[12,2]=-0.4,so[12,3]=-0.2,so[12,4]=-0.8,so[12,5]=-0.2,so[12,6]=-0.1,so[12,7]=-0.4,so[12,8]=0.2,so[12,9]=0.3,so[12,10]=0.4,so[12,11]=0.8,so[12,12]=1.0,so[12,13]=-0.5,so[12,14]=-0.5,so[12,15]=-0.7
so[12,16]=-1.1,so[12,17]=-0.1,so[12,18]=-0.1,so[12,19]=-1.1,so[12,20]=0.5,so[12,21]=-0.2,so[12,22]=0.0,so[12,23]=-0.5,so[12,24]=-1.0,so[12,25]=-0.6,so[12,26]=1.1,so[12,27]=0.2,so[12,28]=-0.1,so[12,29]=-0.6,so[12,30]=0.3
so[13,1]=-0.5,so[13,2]=0.2,so[13,3]=0.3,so[13,4]=0.2,so[13,5]=-0.5,so[13,6]=-1.0,so[13,7]=1.1,so[13,8]=0.6,so[13,9]=-0.1,so[13,10]=-1.2,so[13,11]=0.3,so[13,12]=-0.9,so[13,13]=-1.2,so[13,14]=-1.2,so[13,15]=0.7
so[13,16]=0.1,so[13,17]=1.1,so[13,18]=0.3,so[13,19]=1.1,so[13,20]=-0.9,so[13,21]=-0.3,so[13,22]=1.0,so[13,23]=0.4,so[13,24]=1.0,so[13,25]=0.8,so[13,26]=-0.4,so[13,27]=0.7,so[13,28]=0.1,so[13,29]=-0.2,so[13,30]=-0.5
so[14,1]=0.4,so[14,2]=0.7,so[14,3]=0.9,so[14,4]=0.3,so[14,5]=-1.1,so[14,6]=0.9,so[14,7]=0.5,so[14,8]=0.7,so[14,9]=0.9,so[14,10]=-1.2,so[14,11]=-0.2,so[14,12]=-0.8,so[14,13]=-0.9,so[14,14]=0.7,so[14,15]=0.6
so[14,16]=0.1,so[14,17]=-1.1,so[14,18]=-0.5,so[14,19]=-0.3,so[14,20]=0.6,so[14,21]=0.5,so[14,22]=1.2,so[14,23]=-1.0,so[14,24]=0.0,so[14,25]=0.9,so[14,26]=-1.1,so[14,27]=-0.2,so[14,28]=0.2,so[14,29]=-0.7,so[14,30]=0.9
so[15,1]=0.4,so[15,2]=0.5,so[15,3]=-0.6,so[15,4]=0.3,so[15,5]=-0.1,so[15,6]=-0.6,so[15,7]=1.0,so[15,8]=0.2,so[15,9]=0.7,so[15,10]=-0.3,so[15,11]=-0.9,so[15,12]=1.1,so[15,13]=1.2,so[15,14]=0.5,so[15,15]=0.1
so[15,16]=-0.7,so[15,17]=0.6,so[15,18]=0.4,so[15,19]=-1.1,so[15,20]=-1.1,so[15,21]=1.0,so[15,22]=-0.8,so[15,23]=-0.8,so[15,24]=0.6,so[15,25]=-0.5,so[15,26]=-0.7,so[15,27]=-0.6,so[15,28]=0.9,so[15,29]=0.9,so[15,30]=0.4
so[16,1]=0.3,so[16,2]=-1.1,so[16,3]=0.4,so[16,4]=0.2,so[16,5]=-0.5,so[16,6]=0.9,so[16,7]=-0.2,so[16,8]=-1.1,so[16,9]=0.9,so[16,10]=-0.7,so[16,11]=-1.0,so[16,12]=-1.0,so[16,13]=1.2,so[16,14]=0.6,so[16,15]=0.9
so[16,16]=0.0,so[16,17]=-0.9,so[16,18]=-0.9,so[16,19]=0.0,so[16,20]=-0.3,so[16,21]=-1.1,so[16,22]=1.1,so[16,23]=0.2,so[16,24]=0.1,so[16,25]=0.2,so[16,26]=-0.7,so[16,27]=-0.1,so[16,28]=-1.0,so[16,29]=0.3,so[16,30]=-0.7
so[17,1]=-1.1,so[17,2]=-0.2,so[17,3]=-0.5,so[17,4]=1.0,so[17,5]=0.6,so[17,6]=0.0,so[17,7]=0.4,so[17,8]=-1.2,so[17,9]=-1.1,so[17,10]=0.1,so[17,11]=0.4,so[17,12]=1.2,so[17,13]=-1.0,so[17,14]=-0.1,so[17,15]=0.8
so[17,16]=0.1,so[17,17]=0.4,so[17,18]=-0.2,so[17,19]=0.7,so[17,20]=-0.8,so[17,21]=-0.9,so[17,22]=0.9,so[17,23]=-0.6,so[17,24]=0.8,so[17,25]=-0.5,so[17,26]=0.4,so[17,27]=0.9,so[17,28]=-0.5,so[17,29]=0.3,so[17,30]=-0.1
so[18,1]=-0.4,so[18,2]=-0.2,so[18,3]=0.7,so[18,4]=1.2,so[18,5]=0.8,so[18,6]=-1.2,so[18,7]=1.0,so[18,8]=-0.9,so[18,9]=-0.9,so[18,10]=-1.1,so[18,11]=-0.7,so[18,12]=0.0,so[18,13]=0.2,so[18,14]=-0.5,so[18,15]=0.8
so[18,16]=-1.0,so[18,17]=-0.9,so[18,18]=0.3,so[18,19]=-0.4,so[18,20]=1.2,so[18,21]=1.2,so[18,22]=1.2,so[18,23]=-0.3,so[18,24]=0.3,so[18,25]=0.5,so[18,26]=-0.5,so[18,27]=1.0,so[18,28]=0.5,so[18,29]=-0.9,so[18,30]=0.1
so[19,1]=-0.8,so[19,2]=0.9,so[19,3]=0.2,so[19,4]=-0.8,so[19,5]=0.4,so[19,6]=-0.8,so[19,7]=0.6,so[19,8]=0.1,so[19,9]=1.1,so[19,10]=0.6,so[19,11]=0.4,so[19,12]=0.8,so[19,13]=-0.2,so[19,14]=-0.6,so[19,15]=0.3
so[19,16]=-1.0,so[19,17]=-0.9,so[19,18]=-1.1,so[19,19]=-0.5,so[19,20]=0.9,so[19,21]=-0.8,so[19,22]=-1.2,so[19,23]=-1.2,so[19,24]=-0.9,so[19,25]=-1.2,so[19,26]=-0.2,so[19,27]=1.2,so[19,28]=0.8,so[19,29]=0.5,so[19,30]=0.7
so[20,1]=0.7,so[20,2]=-1.0,so[20,3]=-0.3,so[20,4]=0.5,so[20,5]=0.1,so[20,6]=0.3,so[20,7]=-0.7,so[20,8]=1.1,so[20,9]=-1.2,so[20,10]=-0.3,so[20,11]=1.2,so[20,12]=1.2,so[20,13]=-0.7,so[20,14]=1.0,so[20,15]=0.8
so[20,16]=-0.5,so[20,17]=1.0,so[20,18]=-0.6,so[20,19]=0.4,so[20,20]=-1.1,so[20,21]=-0.4,so[20,22]=1.1,so[20,23]=-1.2,so[20,24]=0.7,so[20,25]=0.9,so[20,26]=1.2,so[20,27]=1.0,so[20,28]=0.1,so[20,29]=0.3,so[20,30]=-0.6
so[21,1]=-0.7,so[21,2]=0.7,so[21,3]=0.8,so[21,4]=0.2,so[21,5]=1.0,so[21,6]=-0.8,so[21,7]=0.6,so[21,8]=-1.1,so[21,9]=-0.8,so[21,10]=1.1,so[21,11]=0.0,so[21,12]=1.1,so[21,13]=0.9,so[21,14]=0.9,so[21,15]=0.9
so[21,16]=0.1,so[21,17]=-0.6,so[21,18]=0.9,so[21,19]=0.1,so[21,20]=1.2,so[21,21]=0.5,so[21,22]=1.0,so[21,23]=1.2,so[21,24]=0.4,so[21,25]=-0.5,so[21,26]=0.9,so[21,27]=-0.5,so[21,28]=-1.0,so[21,29]=-0.3,so[21,30]=0.0
so[22,1]=0.2,so[22,2]=-0.3,so[22,3]=-0.8,so[22,4]=-0.4,so[22,5]=-0.1,so[22,6]=1.1,so[22,7]=0.1,so[22,8]=1.0,so[22,9]=0.1,so[22,10]=-1.1,so[22,11]=-1.1,so[22,12]=0.0,so[22,13]=0.8,so[22,14]=-0.3,so[22,15]=-0.8
so[22,16]=-0.9,so[22,17]=-0.1,so[22,18]=-0.5,so[22,19]=-1.1,so[22,20]=1.0,so[22,21]=-0.7,so[22,22]=0.0,so[22,23]=0.3,so[22,24]=-0.6,so[22,25]=0.0,so[22,26]=0.6,so[22,27]=-0.1,so[22,28]=-1.1,so[22,29]=-0.8,so[22,30]=-0.4
so[23,1]=-1.2,so[23,2]=0.5,so[23,3]=-0.5,so[23,4]=0.0,so[23,5]=0.4,so[23,6]=0.7,so[23,7]=0.3,so[23,8]=-0.3,so[23,9]=0.5,so[23,10]=1.0,so[23,11]=-0.7,so[23,12]=0.5,so[23,13]=0.1,so[23,14]=-1.2,so[23,15]=0.2
so[23,16]=-0.3,so[23,17]=0.8,so[23,18]=0.4,so[23,19]=-0.3,so[23,20]=-0.6,so[23,21]=1.1,so[23,22]=-1.0,so[23,23]=0.2,so[23,24]=0.9,so[23,25]=-0.4,so[23,26]=1.2,so[23,27]=-0.6,so[23,28]=1.2,so[23,29]=0.5,so[23,30]=0.8
so[24,1]=-1.1,so[24,2]=0.3,so[24,3]=0.4,so[24,4]=0.5,so[24,5]=0.7,so[24,6]=0.4,so[24,7]=0.8,so[24,8]=0.4,so[24,9]=0.4,so[24,10]=-0.7,so[24,11]=-0.7,so[24,12]=0.5,so[24,13]=-1.1,so[24,14]=0.3,so[24,15]=0.6
so[24,16]=-0.6,so[24,17]=-0.2,so[24,18]=0.9,so[24,19]=-1.2,so[24,20]=-0.6,so[24,21]=0.5,so[24,22]=-0.8,so[24,23]=1.1,so[24,24]=0.3,so[24,25]=0.9,so[24,26]=1.2,so[24,27]=-0.1,so[24,28]=0.9,so[24,29]=-0.6,so[24,30]=-0.9
so[25,1]=-0.3,so[25,2]=-0.1,so[25,3]=0.2,so[25,4]=0.9,so[25,5]=1.1,so[25,6]=1.1,so[25,7]=0.0,so[25,8]=0.2,so[25,9]=0.3,so[25,10]=0.3,so[25,11]=0.6,so[25,12]=-0.9,so[25,13]=0.1,so[25,14]=-1.0,so[25,15]=0.2
so[25,16]=0.6,so[25,17]=-0.3,so[25,18]=1.2,so[25,19]=0.8,so[25,20]=0.7,so[25,21]=0.3,so[25,22]=1.2,so[25,23]=-0.6,so[25,24]=-1.2,so[25,25]=-0.1,so[25,26]=0.6,so[25,27]=0.9,so[25,28]=-1.0,so[25,29]=-1.1,so[25,30]=0.0
so[26,1]=1.1,so[26,2]=-0.1,so[26,3]=-0.4,so[26,4]=-1.2,so[26,5]=0.6,so[26,6]=0.9,so[26,7]=-1.1,so[26,8]=-1.0,so[26,9]=-0.9,so[26,10]=0.6,so[26,11]=1.1,so[26,12]=0.9,so[26,13]=0.0,so[26,14]=1.2,so[26,15]=1.2
so[26,16]=0.2,so[26,17]=-0.1,so[26,18]=0.9,so[26,19]=0.3,so[26,20]=-1.0,so[26,21]=0.0,so[26,22]=1.1,so[26,23]=-0.2,so[26,24]=0.9,so[26,25]=-1.2,so[26,26]=0.2,so[26,27]=0.8,so[26,28]=-1.2,so[26,29]=-0.9,so[26,30]=0.7
so[27,1]=-0.6,so[27,2]=-1.2,so[27,3]=0.5,so[27,4]=-0.9,so[27,5]=-1.0,so[27,6]=-0.8,so[27,7]=-0.4,so[27,8]=-0.9,so[27,9]=0.0,so[27,10]=-1.0,so[27,11]=-0.8,so[27,12]=-0.6,so[27,13]=0.3,so[27,14]=1.0,so[27,15]=-1.2
so[27,16]=-0.4,so[27,17]=-1.1,so[27,18]=-0.1,so[27,19]=1.1,so[27,20]=0.7,so[27,21]=-0.2,so[27,22]=1.0,so[27,23]=0.2,so[27,24]=0.8,so[27,25]=0.7,so[27,26]=-1.1,so[27,27]=1.2,so[27,28]=-1.0,so[27,29]=0.9,so[27,30]=-0.4
so[28,1]=-0.2,so[28,2]=-1.0,so[28,3]=0.8,so[28,4]=0.5,so[28,5]=-1.0,so[28,6]=0.6,so[28,7]=0.9,so[28,8]=-0.2,so[28,9]=0.1,so[28,10]=-1.1,so[28,11]=-1.2,so[28,12]=-0.5,so[28,13]=0.7,so[28,14]=-0.1,so[28,15]=-0.4
so[28,16]=-0.4,so[28,17]=-0.4,so[28,18]=-0.7,so[28,19]=0.9,so[28,20]=0.3,so[28,21]=-1.2,so[28,22]=-0.4,so[28,23]=-0.1,so[28,24]=1.2,so[28,25]=1.0,so[28,26]=-1.2,so[28,27]=1.2,so[28,28]=-0.8,so[28,29]=-0.5,so[28,30]=0.4
so[29,1]=-1.0,so[29,2]=-1.1,so[29,3]=0.5,so[29,4]=-0.2,so[29,5]=1.0,so[29,6]=0.0,so[29,7]=0.1,so[29,8]=1.0,so[29,9]=-0.9,so[29,10]=0.4,so[29,11]=-0.6,so[29,12]=-1.2,so[29,13]=-0.9,so[29,14]=-1.2,so[29,15]=0.9
so[29,16]=1.1,so[29,17]=0.9,so[29,18]=-0.5,so[29,19]=-0.3,so[29,20]=-1.0,so[29,21]=-0.3,so[29,22]=0.9,so[29,23]=-0.5,so[29,24]=-1.1,so[29,25]=-1.2,so[29,26]=-0.7,so[29,27]=0.7,so[29,28]=1.2,so[29,29]=1.0,so[29,30]=-0.7
so[30,1]=-1.0,so[30,2]=0.9,so[30,3]=0.4,so[30,4]=1.1,so[30,5]=-1.1,so[30,6]=-0.9,so[30,7]=0.8,so[30,8]=0.4,so[30,9]=1.1,so[30,10]=0.0,so[30,11]=-0.5,so[30,12]=-0.5,so[30,13]=-0.3,so[30,14]=-1.2,so[30,15]=0.9
so[30,16]=-1.2,so[30,17]=-0.8,so[30,18]=1.1,so[30,19]=-1.0,so[30,20]=0.7,so[30,21]=-1.0,so[30,22]=1.0,so[30,23]=0.5,so[30,24]=-0.8,so[30,25]=1.1,so[30,26]=1.2,so[30,27]=-0.1,so[30,28]=0.8,so[30,29]=-1.2,so[30,30]=-0.8
so[31,1]=0.1,so[31,2]=0.7,so[31,3]=-0.8,so[31,4]=-1.2,so[31,5]=1.2,so[31,6]=0.8,so[31,7]=-0.3,so[31,8]=0.6,so[31,9]=0.8,so[31,10]=-0.2,so[31,11]=0.9,so[31,12]=-1.1,so[31,13]=-1.0,so[31,14]=0.4,so[31,15]=1.0
so[31,16]=-0.3,so[31,17]=-0.1,so[31,18]=-1.0,so[31,19]=0.0,so[31,20]=0.8,so[31,21]=-0.9,so[31,22]=-0.4,so[31,23]=-0.5,so[31,24]=-0.1,so[31,25]=0.7,so[31,26]=0.1,so[31,27]=0.7,so[31,28]=-0.5,so[31,29]=-0.3,so[31,30]=-1.0
so[32,1]=1.1,so[32,2]=-0.6,so[32,3]=-1.1,so[32,4]=-0.2,so[32,5]=-0.7,so[32,6]=0.7,so[32,7]=0.3,so[32,8]=0.9,so[32,9]=-0.4,so[32,10]=-0.4,so[32,11]=-0.3,so[32,12]=-0.7,so[32,13]=0.7,so[32,14]=0.0,so[32,15]=-0.8
so[32,16]=0.7,so[32,17]=0.1,so[32,18]=-1.0,so[32,19]=-0.5,so[32,20]=0.2,so[32,21]=-0.6,so[32,22]=0.3,so[32,23]=0.8,so[32,24]=-0.3,so[32,25]=0.7,so[32,26]=-0.1,so[32,27]=1.1,so[32,28]=0.8,so[32,29]=0.7,so[32,30]=-0.2
so[33,1]=0.9,so[33,2]=1.1,so[33,3]=0.8,so[33,4]=-0.7,so[33,5]=-0.5,so[33,6]=0.6,so[33,7]=-0.8,so[33,8]=0.3,so[33,9]=1.0,so[33,10]=-0.7,so[33,11]=0.5,so[33,12]=0.7,so[33,13]=0.6,so[33,14]=0.5,so[33,15]=0.5,so[33,16]=-1.0,so[33,17]=0.5,so[33,18]=-0.5,so[33,19]=-1.1,so[33,20]=-0.5,so[33,21]=0.7,so[33,22]=0.9,so[33,23]=-0.2,so[33,24]=-1.0,so[33,25]=1.2,so[33,26]=1.2,so[33,27]=1.2,so[33,28]=0.7,so[33,29]=-0.4,so[33,30]=-1.0
so[34,1]=-0.9,so[34,2]=-0.6,so[34,3]=-0.9,so[34,4]=1.0,so[34,5]=-0.9,so[34,6]=0.8,so[34,7]=1.1,so[34,8]=-1.2,so[34,9]=0.4,so[34,10]=-0.8,so[34,11]=1.0,so[34,12]=-0.4,so[34,13]=-1.1,so[34,14]=-1.1,so[34,15]=0.4,so[34,16]=-0.3,so[34,17]=0.3,so[34,18]=-0.7,so[34,19]=0.1,so[34,20]=0.0,so[34,21]=0.0,so[34,22]=-0.2,so[34,23]=0.6,so[34,24]=0.3,so[34,25]=0.9,so[34,26]=1.0,so[34,27]=0.8,so[34,28]=1.1,so[34,29]=-1.1,so[34,30]=0.2
so[35,1]=-0.3,so[35,2]=-1.1,so[35,3]=0.1,so[35,4]=0.9,so[35,5]=0.0,so[35,6]=-0.2,so[35,7]=-1.1,so[35,8]=-0.4,so[35,9]=0.9,so[35,10]=0.8,so[35,11]=0.3,so[35,12]=1.2,so[35,13]=0.5,so[35,14]=0.4,so[35,15]=0.1,so[35,16]=0.1,so[35,17]=-0.1,so[35,18]=-0.9,so[35,19]=1.1,so[35,20]=0.3,so[35,21]=0.1,so[35,22]=0.1,so[35,23]=0.4,so[35,24]=0.8,so[35,25]=-0.4,so[35,26]=-1.0,so[35,27]=0.0,so[35,28]=1.0,so[35,29]=0.0,so[35,30]=-0.4
so[36,1]=0.3,so[36,2]=0.6,so[36,3]=0.5,so[36,4]=-0.9,so[36,5]=-0.6,so[36,6]=-1.0,so[36,7]=0.6,so[36,8]=1.1,so[36,9]=-1.2,so[36,10]=-1.1,so[36,11]=-0.1,so[36,12]=0.9,so[36,13]=0.8,so[36,14]=1.1,so[36,15]=0.3,so[36,16]=0.0,so[36,17]=-0.2,so[36,18]=0.8,so[36,19]=0.0,so[36,20]=1.0,so[36,21]=0.1,so[36,22]=0.0,so[36,23]=0.1,so[36,24]=-0.9,so[36,25]=1.0,so[36,26]=-0.1,so[36,27]=-0.6,so[36,28]=-0.7,so[36,29]=-0.2,so[36,30]=1.2
so[37,1]=0.1,so[37,2]=-0.4,so[37,3]=-0.3,so[37,4]=0.7,so[37,5]=-0.7,so[37,6]=-0.2,so[37,7]=0.3,so[37,8]=-1.2,so[37,9]=1.0,so[37,10]=-0.3,so[37,11]=0.4,so[37,12]=-0.3,so[37,13]=-0.7,so[37,14]=0.0,so[37,15]=0.4,so[37,16]=0.5,so[37,17]=0.9,so[37,18]=-0.7,so[37,19]=0.8,so[37,20]=-0.8,so[37,21]=-0.4,so[37,22]=-0.4,so[37,23]=-0.4,so[37,24]=0.8,so[37,25]=1.2,so[37,26]=-1.1,so[37,27]=-0.4,so[37,28]=0.6,so[37,29]=-0.4,so[37,30]=-0.7
so[38,1]=-0.3,so[38,2]=0.7,so[38,3]=0.0,so[38,4]=-0.1,so[38,5]=0.3,so[38,6]=0.3,so[38,7]=0.8,so[38,8]=-0.9,so[38,9]=0.4,so[38,10]=-0.8,so[38,11]=0.4,so[38,12]=-0.3,so[38,13]=-0.2,so[38,14]=-0.7,so[38,15]=0.5,so[38,16]=0.8,so[38,17]=-1.2,so[38,18]=-0.9,so[38,19]=1.0,so[38,20]=0.9,so[38,21]=-0.3,so[38,22]=0.4,so[38,23]=1.1,so[38,24]=-1.2,so[38,25]=-1.0,so[38,26]=0.2,so[38,27]=-1.0,so[38,28]=0.2,so[38,29]=-0.5,so[38,30]=1.1
so[39,1]=-1.1,so[39,2]=0.8,so[39,3]=0.8,so[39,4]=-0.4,so[39,5]=-0.6,so[39,6]=0.6,so[39,7]=-1.2,so[39,8]=-1.2,so[39,9]=0.6,so[39,10]=0.8,so[39,11]=-0.8,so[39,12]=-0.9,so[39,13]=0.0,so[39,14]=1.0,so[39,15]=0.3,so[39,16]=-0.1,so[39,17]=0.2,so[39,18]=1.2,so[39,19]=0.5,so[39,20]=0.9,so[39,21]=0.3,so[39,22]=0.6,so[39,23]=-0.2,so[39,24]=0.8,so[39,25]=-1.2,so[39,26]=-0.9,so[39,27]=-0.1,so[39,28]=-0.9,so[39,29]=-0.2,so[39,30]=0.6
so[40,1]=0.0,so[40,2]=0.3,so[40,3]=-1.0,so[40,4]=1.1,so[40,5]=-0.7,so[40,6]=-1.0,so[40,7]=-0.3,so[40,8]=0.3,so[40,9]=0.2,so[40,10]=-1.2,so[40,11]=-0.1,so[40,12]=0.0,so[40,13]=0.9,so[40,14]=0.7,so[40,15]=0.9,so[40,16]=-0.4,so[40,17]=0.1,so[40,18]=-0.5,so[40,19]=-1.0,so[40,20]=-0.7,so[40,21]=0.1,so[40,22]=-1.1,so[40,23]=-0.8,so[40,24]=-1.0,so[40,25]=-0.8,so[40,26]=1.2,so[40,27]=0.2,so[40,28]=1.0,so[40,29]=-0.6,so[40,30]=-1.0
so[41,1]=0.8,so[41,2]=-0.5,so[41,3]=0.9,so[41,4]=-1.1,so[41,5]=1.1,so[41,6]=-1.2,so[41,7]=-1.1,so[41,8]=-0.8,so[41,9]=0.1,so[41,10]=-0.4,so[41,11]=0.0,so[41,12]=0.5,so[41,13]=0.2,so[41,14]=-0.5,so[41,15]=-0.5,so[41,16]=1.0,so[41,17]=-0.7,so[41,18]=0.4,so[41,19]=1.2,so[41,20]=0.1,so[41,21]=0.8,so[41,22]=-0.8,so[41,23]=-0.4,so[41,24]=1.0,so[41,25]=-0.9,so[41,26]=-0.4,so[41,27]=-0.6,so[41,28]=0.3,so[41,29]=-0.8,so[41,30]=-0.3
so[42,1]=1.2,so[42,2]=-0.9,so[42,3]=0.0,so[42,4]=-0.4,so[42,5]=-1.1,so[42,6]=0.3,so[42,7]=-0.5,so[42,8]=0.4,so[42,9]=0.5,so[42,10]=0.3,so[42,11]=-1.0,so[42,12]=1.0,so[42,13]=0.4,so[42,14]=1.0,so[42,15]=0.7,so[42,16]=-0.7,so[42,17]=0.5,so[42,18]=0.6,so[42,19]=0.4,so[42,20]=0.6,so[42,21]=-0.2,so[42,22]=-0.9,so[42,23]=1.1,so[42,24]=-0.4,so[42,25]=-0.9,so[42,26]=0.5,so[42,27]=-0.4,so[42,28]=-0.5,so[42,29]=0.3,so[42,30]=-0.1
so[43,1]=1.0,so[43,2]=0.5,so[43,3]=-0.4,so[43,4]=-0.9,so[43,5]=0.8,so[43,6]=1.1,so[43,7]=-1.1,so[43,8]=-0.2,so[43,9]=0.6,so[43,10]=0.9,so[43,11]=-0.3,so[43,12]=0.4,so[43,13]=1.1,so[43,14]=1.0,so[43,15]=0.2,so[43,16]=-0.7,so[43,17]=-0.2,so[43,18]=0.8,so[43,19]=-1.0,so[43,20]=0.5,so[43,21]=1.1,so[43,22]=0.6,so[43,23]=0.1,so[43,24]=0.6,so[43,25]=-0.3,so[43,26]=1.0,so[43,27]=-0.2,so[43,28]=-1.0,so[43,29]=0.7,so[43,30]=-0.8
so[44,1]=-0.5,so[44,2]=-1.2,so[44,3]=0.3,so[44,4]=-1.2,so[44,5]=0.3,so[44,6]=-0.5,so[44,7]=1.2,so[44,8]=-1.0,so[44,9]=-0.4,so[44,10]=-0.5,so[44,11]=-1.2,so[44,12]=0.8,so[44,13]=1.2,so[44,14]=-0.5,so[44,15]=1.1,so[44,16]=0.4,so[44,17]=0.7,so[44,18]=0.9,so[44,19]=-0.9,so[44,20]=-0.9,so[44,21]=0.5,so[44,22]=-1.1,so[44,23]=0.4,so[44,24]=0.4,so[44,25]=0.5,so[44,26]=-0.1,so[44,27]=-1.2,so[44,28]=0.2,so[44,29]=-0.8,so[44,30]=-0.6
so[45,1]=0.0,so[45,2]=0.1,so[45,3]=1.2,so[45,4]=-0.4,so[45,5]=0.5,so[45,6]=0.4,so[45,7]=-1.1,so[45,8]=0.1,so[45,9]=-0.2,so[45,10]=0.0,so[45,11]=-1.1,so[45,12]=0.4,so[45,13]=0.7,so[45,14]=0.3,so[45,15]=-1.1,so[45,16]=0.5,so[45,17]=-1.2,so[45,18]=-1.0,so[45,19]=-1.1,so[45,20]=-1.2,so[45,21]=0.2,so[45,22]=0.8,so[45,23]=0.1,so[45,24]=0.0,so[45,25]=0.3,so[45,26]=0.5,so[45,27]=0.6,so[45,28]=0.2,so[45,29]=-0.7,so[45,30]=0.4
so[46,1]=1.2,so[46,2]=0.0,so[46,3]=0.7,so[46,4]=-0.7,so[46,5]=-0.9,so[46,6]=0.3,so[46,7]=-1.1,so[46,8]=1.1,so[46,9]=-0.2,so[46,10]=-0.4,so[46,11]=0.0,so[46,12]=-0.5,so[46,13]=0.8,so[46,14]=-1.2,so[46,15]=-1.1,so[46,16]=-0.2,so[46,17]=-0.5,so[46,18]=-0.1,so[46,19]=0.6,so[46,20]=-0.6,so[46,21]=-0.5,so[46,22]=0.7,so[46,23]=1.2,so[46,24]=0.8,so[46,25]=0.5,so[46,26]=0.0,so[46,27]=1.1,so[46,28]=0.8,so[46,29]=0.4,so[46,30]=-0.9
so[47,1]=-0.1,so[47,2]=-0.8,so[47,3]=0.4,so[47,4]=0.6,so[47,5]=-0.4,so[47,6]=1.1,so[47,7]=0.2,so[47,8]=-0.1,so[47,9]=-0.1,so[47,10]=1.2,so[47,11]=0.2,so[47,12]=-1.2,so[47,13]=1.1,so[47,14]=-1.2,so[47,15]=1.2,so[47,16]=-0.2,so[47,17]=0.7,so[47,18]=-0.3,so[47,19]=0.4,so[47,20]=-0.8,so[47,21]=-0.5,so[47,22]=0.4,so[47,23]=0.7,so[47,24]=0.4,so[47,25]=1.2,so[47,26]=-0.2,so[47,27]=1.0,so[47,28]=0.6,so[47,29]=0.4,so[47,30]=-0.3
so[48,1]=1.1,so[48,2]=-0.4,so[48,3]=0.4,so[48,4]=0.8,so[48,5]=0.0,so[48,6]=-0.4,so[48,7]=-1.1,so[48,8]=-1.1,so[48,9]=-0.2,so[48,10]=-1.2,so[48,11]=-0.3,so[48,12]=-0.7,so[48,13]=1.2,so[48,14]=0.4,so[48,15]=0.2,so[48,16]=0.0,so[48,17]=0.5,so[48,18]=-0.5,so[48,19]=0.9,so[48,20]=-0.9,so[48,21]=-0.5,so[48,22]=0.7,so[48,23]=0.7,so[48,24]=-1.0,so[48,25]=0.3,so[48,26]=-0.2,so[48,27]=0.2,so[48,28]=-1.0,so[48,29]=0.3,so[48,30]=-0.3
so[49,1]=1.2,so[49,2]=0.5,so[49,3]=-0.2,so[49,4]=-1.0,so[49,5]=-0.1,so[49,6]=-0.6,so[49,7]=0.3,so[49,8]=-0.1,so[49,9]=0.6,so[49,10]=-0.9,so[49,11]=-0.5,so[49,12]=-0.7,so[49,13]=0.7,so[49,14]=0.7,so[49,15]=1.1,so[49,16]=-1.2,so[49,17]=0.4,so[49,18]=-0.2,so[49,19]=-0.9,so[49,20]=0.4,so[49,21]=-0.4,so[49,22]=-0.7,so[49,23]=-0.5,so[49,24]=-1.1,so[49,25]=0.8,so[49,26]=-0.3,so[49,27]=0.9,so[49,28]=-1.1,so[49,29]=-0.4,so[49,30]=0.4
so[50,1]=-0.1,so[50,2]=0.3,so[50,3]=-0.1,so[50,4]=-0.5,so[50,5]=0.0,so[50,6]=0.9,so[50,7]=-0.7,so[50,8]=-0.5,so[50,9]=-1.2,so[50,10]=-0.2,so[50,11]=-1.0,so[50,12]=1.2,so[50,13]=0.9,so[50,14]=0.4,so[50,15]=0.2,so[50,16]=-0.9,so[50,17]=0.3,so[50,18]=0.7,so[50,19]=-0.4,so[50,20]=0.7,so[50,21]=-0.4,so[50,22]=1.2,so[50,23]=-0.2,so[50,24]=-1.2,so[50,25]=0.4,so[50,26]=-0.4,so[50,27]=0.4,so[50,28]=-1.0,so[50,29]=-0.3,so[50,30]=0.6
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float ppz = @ppz
float pxx = 0
float pyy = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
pyy = y
x = x + 0.1*(so[@sd,1] + so[@sd,2]*x + so[@sd,3]*x*x + so[@sd,4]*x*y \
+ so[@sd,5]*x*ppz + so[@sd,6]*y + so[@sd,7]*y*y + \
so[@sd,8]*y*ppz + so[@sd,9]*ppz + so[@sd,10]*ppz*ppz)
y = y + 0.1*(so[@sd,11] + so[@sd,12]*pxx + so[@sd,13]*pxx*pxx + so[@sd,14]*pxx*y \
+ so[@sd,15]*pxx*ppz + so[@sd,16]*y + so[@sd,17]*y*y + \
so[@sd,18]*y*ppz + so[@sd,19]*ppz + so[@sd,20]*ppz*ppz)
ppz = ppz + 0.1*(so[@sd,21] + so[@sd,22]*pxx + so[@sd,23]*pxx*pxx + so[@sd,24]*pxx*pyy + \
so[@sd,25]*pxx*ppz + so[@sd,26]*pyy + so[@sd,27]*pyy*pyy + \
so[@sd,28]*pyy*ppz + so[@sd,29]*ppz + so[@sd,30]*ppz*ppz)
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y) + ppz*@pw)
float d = @distscale*|pz-(x + sgn*flip(y) + ppz*@pw)|
return d
endfunc
private:
float so[51,31]
default:
title = "Sprott3D_ODE"
heading
text="Strange attractors from simultaneous ordinary differential \
equations using Euler's finite difference method to calculate."
endheading
heading
text="Sprott 3D ODE quadratic attractors"
endheading
heading
text=" x -> x + 0.1*(Quadratic in x, y and z)"
endheading
heading
text=" y -> y + 0.1*(Quadratic in x, y and z)"
endheading
heading
text=" z -> z + 0.1*(Quadratic in x, y and z)"
endheading
int param v_trapshapesprott3d_ode
caption = "Version (Trap Shape Sprott3D_ODE)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesprott3d_ode < 101
endparam
param sd
caption = "Sprott selector"
default = 0
enum = "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" \
"15" "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" \
"30" "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" \
"45" "46" "47" "48" "49" "50"
hint = "Each Sprott selector uses a different strange attractor."
endparam
heading
text = "'Initialize Height' sets the starting z value for the attractor."
endheading
float param ppz
caption = "Initialize Height"
default = 0.5
endparam
heading
text = "'Height weight' determines the weight of the final z value which is added \
to the trap distance."
endheading
complex param pw
caption = "Height weight"
default = (0.5,0)
endparam
float param distscale
caption = "Distance scale"
default = 0.1
endparam
float param s
caption = "Attractor scale"
default = 2.0
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 50
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSprottQuad(common.ulb:TrapShape) {
; This shape uses a Sprott strange attractor.
; The Sprott attractors were developed by Julien C. Sprott, and are
; based upon polynomials and linear differential equations of polynomials.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSprottQuad(Generic pparent)
TrapShape.TrapShape(pparent)
qd[0,1]=1,qd[0,2]=-1.1,qd[0,3]=-0.2,qd[0,4]=-0.1,qd[0,5]=-0.4,qd[0,6]=0.1,qd[0,7]=-0.3,qd[0,8]=0.8,qd[0,9]=-0.1,qd[0,10]=0.3,qd[0,11]=-1,qd[0,12]=-0.9
qd[1,1]=0.9,qd[1,2]=-0.1,qd[1,3]=0.2,qd[1,4]=0.5,qd[1,5]=-0.6,qd[1,6]=-1.0,qd[1,7]=-0.9,qd[1,8]=-0.8,qd[1,9]=1.0,qd[1,10]=-0.2,qd[1,11]=0.4,qd[1,12]=-0.2
qd[2,1]=-0.8,qd[2,2]=1.1,qd[2,3]=0.5,qd[2,4]=1.1,qd[2,5]=1.1,qd[2,6]=1.1,qd[2,7]=-0.6,qd[2,8]=-0.1,qd[2,9]=-0.6,qd[2,10]=-0.1,qd[2,11]=0.2,qd[2,12]=0.5
qd[3,1]=-0.8,qd[3,2]=-0.7,qd[3,3]=0.4,qd[3,4]=0.8,qd[3,5]=0.4,qd[3,6]=1.1,qd[3,7]=0.9,qd[3,8]=0.9,qd[3,9]=0.4,qd[3,10]=0.6,qd[3,11]=0.9,qd[3,12]=0.1
qd[4,1]=0.9,qd[4,2]=0.5,qd[4,3]=-1.2,qd[4,4]=0.0,qd[4,5]=-0.3,qd[4,6]=0.0,qd[4,7]=0.2,qd[4,8]=0.4,qd[4,9]=0.9,qd[4,10]=-0.1,qd[4,11]=-1.1,qd[4,12]=-0.1
qd[5,1]=0.6,qd[5,2]=-0.1,qd[5,3]=-0.5,qd[5,4]=-1.2,qd[5,5]=-0.3,qd[5,6]=-0.6,qd[5,7]=0.8,qd[5,8]=0.4,qd[5,9]=-0.1,qd[5,10]=1.0,qd[5,11]=-0.8,qd[5,12]=-1.0
qd[6,1]=-0.8,qd[6,2]=0.5,qd[6,3]=0.5,qd[6,4]=-0.7,qd[6,5]=-0.9,qd[6,6]=1.0,qd[6,7]=-0.1,qd[6,8]=-0.4,qd[6,9]=1.1,qd[6,10]=-0.4,qd[6,11]=0.0,qd[6,12]=-0.3
qd[7,1]=-0.6,qd[7,2]=0.8,qd[7,3]=0.4,qd[7,4]=-0.8,qd[7,5]=-1.0,qd[7,6]=-1.1,qd[7,7]=-0.8,qd[7,8]=1.0,qd[7,9]=0.3,qd[7,10]=1.0,qd[7,11]=0.8,qd[7,12]=0.4
qd[8,1]=-0.9,qd[8,2]=-0.4,qd[8,3]=-1.1,qd[8,4]=-0.4,qd[8,5]=0.8,qd[8,6]=0.9,qd[8,7]=0.9,qd[8,8]=-0.2,qd[8,9]=-1.1,qd[8,10]=-0.7,qd[8,11]=-0.2,qd[8,12]=0.1
qd[9,1]=-0.2,qd[9,2]=0.8,qd[9,3]=-0.4,qd[9,4]=-0.3,qd[9,5]=-0.8,qd[9,6]=1.0,qd[9,7]=0.5,qd[9,8]=-0.9,qd[9,9]=0.9,qd[9,10]=-0.6,qd[9,11]=0.4,qd[9,12]=-0.3
qd[10,1]=0.7,qd[10,2]=-0.3,qd[10,3]=-1.1,qd[10,4]=0.5,qd[10,5]=0.3,qd[10,6]=-0.7,qd[10,7]=0.0,qd[10,8]=0.9,qd[10,9]=-0.4,qd[10,10]=0.3,qd[10,11]=0.7,qd[10,12]=0.2
qd[11,1]=1.1,qd[11,2]=-0.4,qd[11,3]=-0.1,qd[11,4]=-1.1,qd[11,5]=-0.8,qd[11,6]=-0.9,qd[11,7]=-0.7,qd[11,8]=-0.7,qd[11,9]=0.7,qd[11,10]=0.4,qd[11,11]=0.0,qd[11,12]=-0.1
qd[12,1]=-1.2,qd[12,2]=-0.1,qd[12,3]=-0.5,qd[12,4]=0.6,qd[12,5]=-1.0,qd[12,6]=-0.3,qd[12,7]=-0.6,qd[12,8]=-0.2,qd[12,9]=-0.8,qd[12,10]=-0.7,qd[12,11]=-0.4,qd[12,12]=0.1
qd[13,1]=0.2,qd[13,2]=1.0,qd[13,3]=-0.3,qd[13,4]=0.9,qd[13,5]=0.6,qd[13,6]=-0.5,qd[13,7]=0.6,qd[13,8]=1.0,qd[13,9]=-1.0,qd[13,10]=-0.1,qd[13,11]=-1.2,qd[13,12]=0.8
qd[14,1]=-0.6,qd[14,2]=-0.5,qd[14,3]=0.7,qd[14,4]=0.4,qd[14,5]=-0.7,qd[14,6]=-0.1,qd[14,7]=0.7,qd[14,8]=0.4,qd[14,9]=-0.7,qd[14,10]=1.0,qd[14,11]=0.1,qd[14,12]=-0.1
qd[15,1]=0.6,qd[15,2]=-0.3,qd[15,3]=-0.1,qd[15,4]=-1.1,qd[15,5]=-1.1,qd[15,6]=0.5,qd[15,7]=-0.1,qd[15,8]=0.1,qd[15,9]=0.7,qd[15,10]=0.9,qd[15,11]=-0.8,qd[15,12]=1.0
qd[16,1]=-0.4,qd[16,2]=-1.0,qd[16,3]=-0.7,qd[16,4]=-0.7,qd[16,5]=-1.1,qd[16,6]=-0.1,qd[16,7]=1.2,qd[16,8]=-0.5,qd[16,9]=-0.7,qd[16,10]=0.3,qd[16,11]=0.5,qd[16,12]=-0.6
qd[17,1]=-0.7,qd[17,2]=0.7,qd[17,3]=1.0,qd[17,4]=-0.5,qd[17,5]=0.7,qd[17,6]=0.3,qd[17,7]=0.8,qd[17,8]=-0.9,qd[17,9]=-0.8,qd[17,10]=-1.0,qd[17,11]=-0.6,qd[17,12]=-1.1
qd[18,1]=0.8,qd[18,2]=0.3,qd[18,3]=0.0,qd[18,4]=0.2,qd[18,5]=0.3,qd[18,6]=-0.8,qd[18,7]=-0.4,qd[18,8]=-1.2,qd[18,9]=-0.9,qd[18,10]=-1.1,qd[18,11]=-0.2,qd[18,12]=0.2
qd[19,1]=0.3,qd[19,2]=1.0,qd[19,3]=-0.4,qd[19,4]=0.9,qd[19,5]=0.3,qd[19,6]=-0.5,qd[19,7]=0.0,qd[19,8]=-1.0,qd[19,9]=-1.2,qd[19,10]=0.1,qd[19,11]=-0.9,qd[19,12]=0.0
qd[20,1]=1.2,qd[20,2]=-0.2,qd[20,3]=-0.9,qd[20,4]=1.1,qd[20,5]=0.5,qd[20,6]=-0.5,qd[20,7]=0.3,qd[20,8]=-0.5,qd[20,9]=-1.2,qd[20,10]=0.6,qd[20,11]=-0.1,qd[20,12]=-0.4
qd[21,1]=0.2,qd[21,2]=0.3,qd[21,3]=0.4,qd[21,4]=-0.1,qd[21,5]=1.2,qd[21,6]=-0.5,qd[21,7]=-0.4,qd[21,8]=-1.1,qd[21,9]=0.5,qd[21,10]=-1.2,qd[21,11]=1.2,qd[21,12]=0.3
qd[22,1]=1.1,qd[22,2]=0.4,qd[22,3]=-0.3,qd[22,4]=-0.2,qd[22,5]=0.4,qd[22,6]=-1.0,qd[22,7]=0.6,qd[22,8]=-0.4,qd[22,9]=-0.5,qd[22,10]=1.2,qd[22,11]=-0.9,qd[22,12]=1.0
qd[23,1]=-1.1,qd[23,2]=0.9,qd[23,3]=1.1,qd[23,4]=0.4,qd[23,5]=-1.2,qd[23,6]=1.0,qd[23,7]=0.3,qd[23,8]=0.3,qd[23,9]=0.3,qd[23,10]=-0.7,qd[23,11]=0.6,qd[23,12]=-0.9
qd[24,1]=-0.1,qd[24,2]=-0.4,qd[24,3]=-0.8,qd[24,4]=-0.8,qd[24,5]=0.9,qd[24,6]=-0.2,qd[24,7]=0.9,qd[24,8]=-0.2,qd[24,9]=-0.9,qd[24,10]=-0.9,qd[24,11]=-0.4,qd[24,12]=-1.2
qd[25,1]=-0.7,qd[25,2]=-0.2,qd[25,3]=-0.4,qd[25,4]=0.4,qd[25,5]=-0.9,qd[25,6]=0.9,qd[25,7]=0.3,qd[25,8]=-0.3,qd[25,9]=-1.1,qd[25,10]=-0.2,qd[25,11]=0.0,qd[25,12]=-0.4
qd[26,1]=-0.6,qd[26,2]=1.1,qd[26,3]=-0.2,qd[26,4]=0.7,qd[26,5]=-0.1,qd[26,6]=1.1,qd[26,7]=-1.2,qd[26,8]=0.0,qd[26,9]=1.1,qd[26,10]=0.3,qd[26,11]=0.7,qd[26,12]=0.8
qd[27,1]=0.1,qd[27,2]=-0.7,qd[27,3]=0.2,qd[27,4]=-0.2,qd[27,5]=0.1,qd[27,6]=1.2,qd[27,7]=-0.5,qd[27,8]=-0.9,qd[27,9]=0.5,qd[27,10]=0.4,qd[27,11]=-1.0,qd[27,12]=0.2
qd[28,1]=0.7,qd[28,2]=-0.6,qd[28,3]=-0.2,qd[28,4]=0.1,qd[28,5]=0.2,qd[28,6]=-0.2,qd[28,7]=-0.8,qd[28,8]=-0.7,qd[28,9]=0.6,qd[28,10]=1.2,qd[28,11]=0.4,qd[28,12]=1.2
qd[29,1]=-0.4,qd[29,2]=-0.1,qd[29,3]=-0.2,qd[29,4]=-0.4,qd[29,5]=-1.2,qd[29,6]=0.8,qd[29,7]=-0.7,qd[29,8]=-0.1,qd[29,9]=0.6,qd[29,10]=0.5,qd[29,11]=-0.9,qd[29,12]=0.7
qd[30,1]=-0.9,qd[30,2]=0.4,qd[30,3]=-0.6,qd[30,4]=-0.7,qd[30,5]=1.1,qd[30,6]=0.9,qd[30,7]=0.2,qd[30,8]=-1.0,qd[30,9]=0.3,qd[30,10]=1.1,qd[30,11]=0.3,qd[30,12]=0.0
qd[31,1]=-0.6,qd[31,2]=-0.4,qd[31,3]=1.1,qd[31,4]=-1.0,qd[31,5]=-0.6,qd[31,6]=1.2,qd[31,7]=0.4,qd[31,8]=0.3,qd[31,9]=-0.1,qd[31,10]=-0.8,qd[31,11]=0.9,qd[31,12]=0.1,
qd[32,1]=0.2,qd[32,2]=-0.2,qd[32,3]=-0.3,qd[32,4]=-1.1,qd[32,5]=-0.3,qd[32,6]=-0.9,qd[32,7]=0.4,qd[32,8]=1.0,qd[32,9]=0.5,qd[32,10]=1.1,qd[32,11]=-0.7,qd[32,12]=-1.2
qd[33,1]=1.0,qd[33,2]=-0.8,qd[33,3]=-0.9,qd[33,4]=-0.3,qd[33,5]=-0.8,qd[33,6]=-0.1,qd[33,7]=0.3,qd[33,8]=-0.3,qd[33,9]=0.1,qd[33,10]=-0.1,qd[33,11]=0.1,qd[33,12]=-1.1
qd[34,1]=0.0,qd[34,2]=-0.9,qd[34,3]=0.0,qd[34,4]=-0.8,qd[34,5]=0.6,qd[34,6]=0.9,qd[34,7]=0.2,qd[34,8]=-0.9,qd[34,9]=-1.0,qd[34,10]=-1.2,qd[34,11]=-0.8,qd[34,12]=-1.2
qd[35,1]=0.2,qd[35,2]=0.4,qd[35,3]=-1.2,qd[35,4]=-0.6,qd[35,5]=-1.2,qd[35,6]=0.6,qd[35,7]=0.4,qd[35,8]=-1.1,qd[35,9]=1.2,qd[35,10]=-0.9,qd[35,11]=-0.4,qd[35,12]=-0.1
qd[36,1]=0.7,qd[36,2]=0.5,qd[36,3]=-1.2,qd[36,4]=-0.6,qd[36,5]=0.3,qd[36,6]=0.2,qd[36,7]=-1.2,qd[36,8]=-0.6,qd[36,9]=0.2,qd[36,10]=-0.7,qd[36,11]=-0.1,qd[36,12]=0.8
qd[37,1]=0.3,qd[37,2]=-0.3,qd[37,3]=-1.1,qd[37,4]=-1.0,qd[37,5]=0.5,qd[37,6]=-0.8,qd[37,7]=0.8,qd[37,8]=1.1,qd[37,9]=0.8,qd[37,10]=0.1,qd[37,11]=-0.9,qd[37,12]=0.1
qd[38,1]=-0.8,qd[38,2]=-1.1,qd[38,3]=-0.1,qd[38,4]=-0.5,qd[38,5]=-0.2,qd[38,6]=0.6,qd[38,7]=0.0,qd[38,8]=-0.8,qd[38,9]=-0.3,qd[38,10]=1.2,qd[38,11]=-1.0,qd[38,12]=1.1
qd[39,1]=0.5,qd[39,2]=0.3,qd[39,3]=-0.7,qd[39,4]=-0.2,qd[39,5]=-0.3,qd[39,6]=1.1,qd[39,7]=0.8,qd[39,8]=1.1,qd[39,9]=-1.0,qd[39,10]=-0.1,qd[39,11]=0.4,qd[39,12]=-0.6
qd[40,1]=-0.5,qd[40,2]=0.4,qd[40,3]=0.6,qd[40,4]=0.8,qd[40,5]=-0.3,qd[40,6]=-1.2,qd[40,7]=0.7,qd[40,8]=-0.5,qd[40,9]=-0.7,qd[40,10]=-1.0,qd[40,11]=0.1,qd[40,12]=-0.5
qd[41,1]=1.1,qd[41,2]=0.3,qd[41,3]=-1.2,qd[41,4]=1.0,qd[41,5]=0.7,qd[41,6]=-1.2,qd[41,7]=0.8,qd[41,8]=-0.7,qd[41,9]=0.1,qd[41,10]=-0.2,qd[41,11]=-1.0,qd[41,12]=1.0
qd[42,1]=-0.6,qd[42,2]=-0.2,qd[42,3]=1.0,qd[42,4]=0.9,qd[42,5]=-1.1,qd[42,6]=-0.6,qd[42,7]=0.3,qd[42,8]=0.7,qd[42,9]=-0.7,qd[42,10]=0.0,qd[42,11]=0.1,qd[42,12]=-0.6
qd[43,1]=0.6,qd[43,2]=-0.6,qd[43,3]=-0.5,qd[43,4]=0.2,qd[43,5]=-0.7,qd[43,6]=0.3,qd[43,7]=-0.5,qd[43,8]=0.8,qd[43,9]=-0.5,qd[43,10]=-1.1,qd[43,11]=-0.2,qd[43,12]=1.2
qd[44,1]=0.0,qd[44,2]=0.2,qd[44,3]=0.1,qd[44,4]=-0.9,qd[44,5]=-0.9,qd[44,6]=-1.2,qd[44,7]=-0.8,qd[44,8]=-1.0,qd[44,9]=0.4,qd[44,10]=0.1,qd[44,11]=0.6,qd[44,12]=0.4
qd[45,1]=-1.2,qd[45,2]=1.0,qd[45,3]=1.2,qd[45,4]=-0.8,qd[45,5]=-1.1,qd[45,6]=0.4,qd[45,7]=-0.2,qd[45,8]=0.6,qd[45,9]=-0.2,qd[45,10]=0.5,qd[45,11]=-1.0,qd[45,12]=-0.2
qd[46,1]=-0.2,qd[46,2]=-1.1,qd[46,3]=-0.5,qd[46,4]=0.1,qd[46,5]=0.9,qd[46,6]=0.3,qd[46,7]=0.5,qd[46,8]=-0.6,qd[46,9]=-1.0,qd[46,10]=0.8,qd[46,11]=-0.7,qd[46,12]=-0.7
qd[47,1]=-0.3,qd[47,2]=-0.3,qd[47,3]=0.7,qd[47,4]=-0.9,qd[47,5]=1.0,qd[47,6]=0.8,qd[47,7]=-0.7,qd[47,8]=-0.9,qd[47,9]=0.5,qd[47,10]=0.8,qd[47,11]=0.1,qd[47,12]=0.2
qd[48,1]=-0.8,qd[48,2]=-0.8,qd[48,3]=1.2,qd[48,4]=0.7,qd[48,5]=-0.7,qd[48,6]=0.1,qd[48,7]=1.0,qd[48,8]=-0.8,qd[48,9]=-0.6,qd[48,10]=0.5,qd[48,11]=1.0,qd[48,12]=-0.5
qd[49,1]=-0.3,qd[49,2]=-0.9,qd[49,3]=0.6,qd[49,4]=-0.2,qd[49,5]=-0.1,qd[49,6]=0.4,qd[49,7]=0.5,qd[49,8]=-1.1,qd[49,9]=1.0,qd[49,10]=-1.2,qd[49,11]=0.0,qd[49,12]=-1.0
qd[50,1]=-0.9,qd[50,2]=-0.2,qd[50,3]=1.1,qd[50,4]=0.5,qd[50,5]=0.5,qd[50,6]=-0.8,qd[50,7]=0.3,qd[50,8]=0.2,qd[50,9]=0.0,qd[50,10]=0.3,qd[50,11]=-0.6,qd[50,12]=-1.1
qd[51,1]=-1.1,qd[51,2]=0.0,qd[51,3]=1.0,qd[51,4]=0.0,qd[51,5]=0.4,qd[51,6]=0.1,qd[51,7]=-0.3,qd[51,8]=-0.7,qd[51,9]=-0.6,qd[51,10]=0.7,qd[51,11]=-0.8,qd[51,12]=0.9
qd[52,1]=0.0,qd[52,2]=-0.5,qd[52,3]=-0.2,qd[52,4]=-1.0,qd[52,5]=-1.2,qd[52,6]=-1.0,qd[52,7]=0.7,qd[52,8]=-0.3,qd[52,9]=-0.8,qd[52,10]=0.4,qd[52,11]=0.0,qd[52,12]=-0.5
qd[53,1]=-0.1,qd[53,2]=0.5,qd[53,3]=-0.1,qd[53,4]=-1.0,qd[53,5]=-0.6,qd[53,6]=-0.5,qd[53,7]=-0.6,qd[53,8]=-0.4,qd[53,9]=0.4,qd[53,10]=-0.8,qd[53,11]=-1.2,qd[53,12]=0.5
qd[54,1]=0.1,qd[54,2]=-0.8,qd[54,3]=0.6,qd[54,4]=0.1,qd[54,5]=1.1,qd[54,6]=0.6,qd[54,7]=0.3,qd[54,8]=-0.8,qd[54,9]=-1.0,qd[54,10]=-0.5,qd[54,11]=-0.5,qd[54,12]=-1.1
qd[55,1]=-1.1,qd[55,2]=0.1,qd[55,3]=1.1,qd[55,4]=0.9,qd[55,5]=0.3,qd[55,6]=-0.3,qd[55,7]=0.9,qd[55,8]=-1.1,qd[55,9]=-0.5,qd[55,10]=0.7,qd[55,11]=0.6,qd[55,12]=-0.2
qd[56,1]=-0.9,qd[56,2]=0.4,qd[56,3]=1.2,qd[56,4]=-1.2,qd[56,5]=0.8,qd[56,6]=0.5,qd[56,7]=-0.5,qd[56,8]=0.5,qd[56,9]=0.8,qd[56,10]=-0.4,qd[56,11]=-1.0,qd[56,12]=-1.1
qd[57,1]=0.8,qd[57,2]=-0.3,qd[57,3]=0.4,qd[57,4]=-1.0,qd[57,5]=-0.5,qd[57,6]=0.3,qd[57,7]=-1.1,qd[57,8]=0.0,qd[57,9]=0.3,qd[57,10]=0.1,qd[57,11]=-0.8,qd[57,12]=0.7
qd[58,1]=-0.2,qd[58,2]=-1.2,qd[58,3]=1.2,qd[58,4]=1.1,qd[58,5]=-1.0,qd[58,6]=0.9,qd[58,7]=0.1,qd[58,8]=-0.5,qd[58,9]=0.7,qd[58,10]=-1.2,qd[58,11]=-0.6,qd[58,12]=1.2
qd[59,1]=-0.1,qd[59,2]=-1.0,qd[59,3]=-0.7,qd[59,4]=0.9,qd[59,5]=0.4,qd[59,6]=-0.1,qd[59,7]=-0.6,qd[59,8]=0.4,qd[59,9]=0.6,qd[59,10]=1.0,qd[59,11]=-0.7,qd[59,12]=1.1
qd[60,1]=-0.4,qd[60,2]=-0.3,qd[60,3]=0.1,qd[60,4]=0.7,qd[60,5]=1.0,qd[60,6]=0.6,qd[60,7]=-0.3,qd[60,8]=1.0,qd[60,9]=-0.8,qd[60,10]=-0.5,qd[60,11]=0.5,qd[60,12]=0.8
qd[61,1]=0.4,qd[61,2]=-0.7,qd[61,3]=0.7,qd[61,4]=0.0,qd[61,5]=1.1,qd[61,6]=0.9,qd[61,7]=0.2,qd[61,8]=-0.9,qd[61,9]=-1.1,qd[61,10]=-0.4,qd[61,11]=-0.1,qd[61,12]=0.1
qd[62,1]=0.7,qd[62,2]=-0.2,qd[62,3]=-0.6,qd[62,4]=0.9,qd[62,5]=0.0,qd[62,6]=0.3,qd[62,7]=1.2,qd[62,8]=0.3,qd[62,9]=-0.6,qd[62,10]=-0.6,qd[62,11]=0.3,qd[62,12]=-1.0
qd[63,1]=1.0,qd[63,2]=0.7,qd[63,3]=-0.7,qd[63,4]=-0.2,qd[63,5]=0.9,qd[63,6]=0.1,qd[63,7]=0.9,qd[63,8]=1.0,qd[63,9]=-0.9,qd[63,10]=1.0,qd[63,11]=-0.2,qd[63,12]=-0.3
qd[64,1]=-0.7,qd[64,2]=1.1,qd[64,3]=0.9,qd[64,4]=1.1,qd[64,5]=0.3,qd[64,6]=-0.2,qd[64,7]=0.3,qd[64,8]=-1.1,qd[64,9]=-1.0,qd[64,10]=0.4,qd[64,11]=-0.6,qd[64,12]=-0.5
qd[65,1]=0.5,qd[65,2]=-0.2,qd[65,3]=-0.1,qd[65,4]=-0.6,qd[65,5]=0.3,qd[65,6]=0.7,qd[65,7]=1.0,qd[65,8]=0.6,qd[65,9]=-0.2,qd[65,10]=-1.2,qd[65,11]=0.3,qd[65,12]=-0.6
qd[66,1]=1.0,qd[66,2]=-0.8,qd[66,3]=-0.5,qd[66,4]=0.2,qd[66,5]=0.1,qd[66,6]=-0.4,qd[66,7]=-0.7,qd[66,8]=-0.4,qd[66,9]=1.1,qd[66,10]=-1.1,qd[66,11]=-0.5,qd[66,12]=-0.5
qd[67,1]=1.1,qd[67,2]=-0.4,qd[67,3]=-0.2,qd[67,4]=-0.6,qd[67,5]=0.4,qd[67,6]=-0.8,qd[67,7]=0.5,qd[67,8]=-0.9,qd[67,9]=-0.6,qd[67,10]=0.1,qd[67,11]=1.2,qd[67,12]=0.7
qd[68,1]=-0.2,qd[68,2]=-0.5,qd[68,3]=-0.1,qd[68,4]=-0.1,qd[68,5]=0.7,qd[68,6]=0.3,qd[68,7]=1.1,qd[68,8]=0.9,qd[68,9]=-0.8,qd[68,10]=0.2,qd[68,11]=0.2,qd[68,12]=-0.5
qd[69,1]=1.1,qd[69,2]=-0.9,qd[69,3]=0.4,qd[69,4]=-0.7,qd[69,5]=0.2,qd[69,6]=0.0,qd[69,7]=0.4,qd[69,8]=1.2,qd[69,9]=0.8,qd[69,10]=-0.7,qd[69,11]=-0.8,qd[69,12]=0.1
qd[70,1]=-0.8,qd[70,2]=0.3,qd[70,3]=0.4,qd[70,4]=-1.1,qd[70,5]=-0.1,qd[70,6]=1.2,qd[70,7]=-0.9,qd[70,8]=-0.7,qd[70,9]=1.2,qd[70,10]=-1.1,qd[70,11]=-0.2,qd[70,12]=0.3
qd[71,1]=-0.3,qd[71,2]=-1.2,qd[71,3]=0.5,qd[71,4]=-0.8,qd[71,5]=0.2,qd[71,6]=1.1,qd[71,7]=1.2,qd[71,8]=-0.8,qd[71,9]=0.9,qd[71,10]=-1.1,qd[71,11]=-1.1,qd[71,12]=1.2,
qd[72,1]=-0.3,qd[72,2]=-1.2,qd[72,3]=0.7,qd[72,4]=0.3,qd[72,5]=0.4,qd[72,6]=0.6,qd[72,7]=0.1,qd[72,8]=0.7,qd[72,9]=-0.6,qd[72,10]=-0.6,qd[72,11]=0.7,qd[72,12]=0.8
qd[73,1]=-1.1,qd[73,2]=0.2,qd[73,3]=0.2,qd[73,4]=-1.1,qd[73,5]=-0.6,qd[73,6]=1.1,qd[73,7]=-0.1,qd[73,8]=0.5,qd[73,9]=1.2,qd[73,10]=0.9,qd[73,11]=0.8,qd[73,12]=-0.7
qd[74,1]=0.9,qd[74,2]=0.5,qd[74,3]=-1.1,qd[74,4]=-0.5,qd[74,5]=0.0,qd[74,6]=-1.2,qd[74,7]=0.2,qd[74,8]=1.2,qd[74,9]=-0.5,qd[74,10]=-0.3,qd[74,11]=-0.3,qd[74,12]=-0.8
qd[75,1]=0.8,qd[75,2]=0.7,qd[75,3]=-1.2,qd[75,4]=0.4,qd[75,5]=-0.1,qd[75,6]=-1.2,qd[75,7]=-0.7,qd[75,8]=-0.1,qd[75,9]=-1.0,qd[75,10]=0.0,qd[75,11]=-1.0,qd[75,12]=-0.3
qd[76,1]=-0.8,qd[76,2]=1.0,qd[76,3]=0.9,qd[76,4]=-1.1,qd[76,5]=-0.9,qd[76,6]=0.4,qd[76,7]=0.6,qd[76,8]=-0.1,qd[76,9]=0.8,qd[76,10]=-0.5,qd[76,11]=-0.2,qd[76,12]=-0.3
qd[77,1]=-0.7,qd[77,2]=-1.1,qd[77,3]=0.5,qd[77,4]=0.1,qd[77,5]=-0.6,qd[77,6]=0.6,qd[77,7]=-0.1,qd[77,8]=1.1,qd[77,9]=0.0,qd[77,10]=-1.2,qd[77,11]=-0.1,qd[77,12]=0.4
qd[78,1]=0.5,qd[78,2]=-1.1,qd[78,3]=-1.1,qd[78,4]=0.0,qd[78,5]=-0.5,qd[78,6]=0.0,qd[78,7]=0.7,qd[78,8]=1.2,qd[78,9]=-0.9,qd[78,10]=-0.2,qd[78,11]=0.5,qd[78,12]=-1.0
qd[79,1]=-0.4,qd[79,2]=-0.3,qd[79,3]=0.3,qd[79,4]=-0.1,qd[79,5]=-1.0,qd[79,6]=1.0,qd[79,7]=-0.7,qd[79,8]=-0.7,qd[79,9]=1.0,qd[79,10]=-1.2,qd[79,11]=0.5,qd[79,12]=0.8
qd[80,1]=0.6,qd[80,2]=-0.3,qd[80,3]=0.0,qd[80,4]=0.4,qd[80,5]=-0.8,qd[80,6]=-0.3,qd[80,7]=-0.7,qd[80,8]=-0.9,qd[80,9]=-0.3,qd[80,10]=0.2,qd[80,11]=1.1,qd[80,12]=1.1
qd[81,1]=-0.3,qd[81,2]=-0.7,qd[81,3]=0.2,qd[81,4]=-0.7,qd[81,5]=-0.3,qd[81,6]=0.5,qd[81,7]=1.2,qd[81,8]=-0.1,qd[81,9]=-0.8,qd[81,10]=-1.1,qd[81,11]=-0.1,qd[81,12]=-0.8
qd[82,1]=0.2,qd[82,2]=-0.4,qd[82,3]=-0.9,qd[82,4]=-0.2,qd[82,5]=1.2,qd[82,6]=1.2,qd[82,7]=0.3,qd[82,8]=-0.7,qd[82,9]=-1.1,qd[82,10]=-0.2,qd[82,11]=-0.2,qd[82,12]=-0.7
qd[83,1]=1.2,qd[83,2]=-0.7,qd[83,3]=-0.5,qd[83,4]=0.1,qd[83,5]=0.2,qd[83,6]=-1.1,qd[83,7]=0.3,qd[83,8]=-1.0,qd[83,9]=0.6,qd[83,10]=-0.3,qd[83,11]=0.2,qd[83,12]=-1.1
qd[84,1]=0.7,qd[84,2]=-1.2,qd[84,3]=0.9,qd[84,4]=0.0,qd[84,5]=-0.7,qd[84,6]=0.2,qd[84,7]=-0.7,qd[84,8]=1.2,qd[84,9]=0.5,qd[84,10]=1.0,qd[84,11]=-0.4,qd[84,12]=1.2
qd[85,1]=1.1,qd[85,2]=-0.4,qd[85,3]=-0.7,qd[85,4]=0.4,qd[85,5]=0.7,qd[85,6]=-0.4,qd[85,7]=-0.3,qd[85,8]=0.5,qd[85,9]=-0.2,qd[85,10]=0.6,qd[85,11]=0.0,qd[85,12]=0.8
qd[86,1]=1.2,qd[86,2]=-0.3,qd[86,3]=-0.1,qd[86,4]=-0.9,qd[86,5]=0.6,qd[86,6]=0.0,qd[86,7]=0.6,qd[86,8]=0.6,qd[86,9]=0.9,qd[86,10]=-0.6,qd[86,11]=-1.2,qd[86,12]=0.4
qd[87,1]=0.3,qd[87,2]=-1.0,qd[87,3]=0.3,qd[87,4]=-0.1,qd[87,5]=-1.0,qd[87,6]=1.1,qd[87,7]=-0.8,qd[87,8]=-0.4,qd[87,9]=0.6,qd[87,10]=0.0,qd[87,11]=0.6,qd[87,12]=1.0
qd[88,1]=-0.3,qd[88,2]=0.0,qd[88,3]=-0.3,qd[88,4]=0.8,qd[88,5]=-0.8,qd[88,6]=0.8,qd[88,7]=0.7,qd[88,8]=1.1,qd[88,9]=-0.5,qd[88,10]=0.0,qd[88,11]=0.6,qd[88,12]=-1.0
qd[89,1]=0.4,qd[89,2]=0.8,qd[89,3]=-0.3,qd[89,4]=-0.2,qd[89,5]=-1.2,qd[89,6]=-0.2,qd[89,7]=0.0,qd[89,8]=0.0,qd[89,9]=1.2,qd[89,10]=1.2,qd[89,11]=0.5,qd[89,12]=-1.1
qd[90,1]=0.5,qd[90,2]=-0.4,qd[90,3]=-0.8,qd[90,4]=-1.0,qd[90,5]=0.0,qd[90,6]=-0.7,qd[90,7]=0.0,qd[90,8]=-0.5,qd[90,9]=-1.1,qd[90,10]=1.0,qd[90,11]=0.8,qd[90,12]=0.1
qd[91,1]=-0.6,qd[91,2]=0.1,qd[91,3]=-0.3,qd[91,4]=-0.8,qd[91,5]=-0.5,qd[91,6]=0.2,qd[91,7]=-1.1,qd[91,8]=0.3,qd[91,9]=0.6,qd[91,10]=1.0,qd[91,11]=-0.2,qd[91,12]=0.9
qd[92,1]=1.0,qd[92,2]=0.3,qd[92,3]=-0.5,qd[92,4]=0.6,qd[92,5]=-1.2,qd[92,6]=-0.1,qd[92,7]=-1.0,qd[92,8]=-0.3,qd[92,9]=0.0,qd[92,10]=-1.2,qd[92,11]=0.4,qd[92,12]=0.1,
qd[93,1]=-0.1,qd[93,2]=-1.2,qd[93,3]=-1.1,qd[93,4]=-0.3,qd[93,5]=0.9,qd[93,6]=-0.7,qd[93,7]=1.0,qd[93,8]=0.1,qd[93,9]=0.3,qd[93,10]=-0.6,qd[93,11]=0.4,qd[93,12]=-0.5
qd[94,1]=-1.2,qd[94,2]=0.8,qd[94,3]=0.1,qd[94,4]=1.1,qd[94,5]=-0.7,qd[94,6]=1.2,qd[94,7]=-0.5,qd[94,8]=0.7,qd[94,9]=-0.4,qd[94,10]=0.9,qd[94,11]=-1.2,qd[94,12]=-0.3
qd[95,1]=0.2,qd[95,2]=-0.4,qd[95,3]=-0.9,qd[95,4]=0.0,qd[95,5]=0.6,qd[95,6]=0.4,qd[95,7]=0.5,qd[95,8]=0.7,qd[95,9]=-1.1,qd[95,10]=0.4,qd[95,11]=-0.2,qd[95,12]=-1.1
qd[96,1]=0.8,qd[96,2]=0.2,qd[96,3]=-1.1,qd[96,4]=0.7,qd[96,5]=-1.2,qd[96,6]=-1.0,qd[96,7]=0.0,qd[96,8]=-0.3,qd[96,9]=1.1,qd[96,10]=-0.8,qd[96,11]=-0.5,qd[96,12]=0.9
qd[97,1]=0.7,qd[97,2]=-0.7,qd[97,3]=1.2,qd[97,4]=0.1,qd[97,5]=-1.0,qd[97,6]=0.1,qd[97,7]=0.5,qd[97,8]=1.1,qd[97,9]=-0.9,qd[97,10]=0.9,qd[97,11]=0.6,qd[97,12]=-1.2
qd[98,1]=1.0,qd[98,2]=-0.1,qd[98,3]=-0.8,qd[98,4]=0.0,qd[98,5]=0.7,qd[98,6]=-0.6,qd[98,7]=0.6,qd[98,8]=0.2,qd[98,9]=-0.2,qd[98,10]=0.8,qd[98,11]=1.0,qd[98,12]=-0.4
qd[99,1]=0.2,qd[99,2]=-0.9,qd[99,3]=0.1,qd[99,4]=0.5,qd[99,5]=0.0,qd[99,6]=0.8,qd[99,7]=-1.0,qd[99,8]=-0.4,qd[99,9]=0.9,qd[99,10]=-0.2,qd[99,11]=0.6,qd[99,12]=0.0
qd[100,1]=-1.0,qd[100,2]=-0.4,qd[100,3]=-0.3,qd[100,4]=0.9,qd[100,5]=0.8,qd[100,6]=1.0,qd[100,7]=-1.2,qd[100,8]=0.5,qd[100,9]=0.3,qd[100,10]=-0.4,qd[100,11]=0.1,qd[100,12]=0.1
qd[101,1]=0.1,qd[101,2]=1.2,qd[101,3]=0.7,qd[101,4]=-0.3,qd[101,5]=0.8,qd[101,6]=-0.7,qd[101,7]=-0.6,qd[101,8]=-0.9,qd[101,9]=1.0,qd[101,10]=-0.7,qd[101,11]=-0.1,qd[101,12]=1.2
qd[102,1]=-0.6,qd[102,2]=-0.2,qd[102,3]=0.1,qd[102,4]=0.2,qd[102,5]=-0.4,qd[102,6]=1.1,qd[102,7]=0.8,qd[102,8]=-1.1,qd[102,9]=-0.2,qd[102,10]=-0.6,qd[102,11]=-0.3,qd[102,12]=-0.9
qd[103,1]=0.7,qd[103,2]=-0.1,qd[103,3]=-0.9,qd[103,4]=0.2,qd[103,5]=0.8,qd[103,6]=-0.6,qd[103,7]=-0.4,qd[103,8]=-1.2,qd[103,9]=1.0,qd[103,10]=0.8,qd[103,11]=0.3,qd[103,12]=0.4
qd[104,1]=0.1,qd[104,2]=-1.2,qd[104,3]=-0.6,qd[104,4]=0.9,qd[104,5]=1.1,qd[104,6]=-0.6,qd[104,7]=0.3,qd[104,8]=-0.7,qd[104,9]=-0.8,qd[104,10]=-0.7,qd[104,11]=0.0,qd[104,12]=-0.8
qd[105,1]=1.0,qd[105,2]=0.0,qd[105,3]=-0.1,qd[105,4]=0.0,qd[105,5]=-0.3,qd[105,6]=-0.2,qd[105,7]=0.7,qd[105,8]=0.3,qd[105,9]=0.4,qd[105,10]=1.1,qd[105,11]=0.3,qd[105,12]=-0.3
qd[106,1]=-0.4,qd[106,2]=-1.2,qd[106,3]=-0.1,qd[106,4]=-0.5,qd[106,5]=-0.6,qd[106,6]=0.0,qd[106,7]=-0.3,qd[106,8]=1.1,qd[106,9]=0.7,qd[106,10]=0.3,qd[106,11]=-0.6,qd[106,12]=0.5
qd[107,1]=0.1,qd[107,2]=0.2,qd[107,3]=-0.3,qd[107,4]=1.2,qd[107,5]=1.1,qd[107,6]=0.5,qd[107,7]=0.7,qd[107,8]=0.5,qd[107,9]=-1.1,qd[107,10]=0.4,qd[107,11]=-0.2,qd[107,12]=-1.2
qd[108,1]=0.2,qd[108,2]=-0.1,qd[108,3]=-0.2,qd[108,4]=0.3,qd[108,5]=0.4,qd[108,6]=-0.8,qd[108,7]=-0.7,qd[108,8]=-1.2,qd[108,9]=-0.1,qd[108,10]=-0.6,qd[108,11]=-0.7,qd[108,12]=1.0
qd[109,1]=0.3,qd[109,2]=0.5,qd[109,3]=-0.5,qd[109,4]=-1.0,qd[109,5]=0.4,qd[109,6]=1.2,qd[109,7]=-0.8,qd[109,8]=-1.0,qd[109,9]=0.5,qd[109,10]=0.2,qd[109,11]=-0.3,qd[109,12]=0.5
qd[110,1]=0.2,qd[110,2]=-0.1,qd[110,3]=-0.3,qd[110,4]=1.0,qd[110,5]=0.9,qd[110,6]=-1.1,qd[110,7]=1.2,qd[110,8]=0.6,qd[110,9]=-0.3,qd[110,10]=-0.3,qd[110,11]=-0.6,qd[110,12]=-0.7
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = qd[@sd,1] + qd[@sd,2]*x + qd[@sd,3]*x*x + qd[@sd,4]*x*y \
+ qd[@sd,5]*y + qd[@sd,6]*y*y
y = qd[@sd,7] + qd[@sd,8]*pxx + qd[@sd,9]*pxx*pxx + qd[@sd,10]*pxx*y \
+ qd[@sd,11]*y + qd[@sd,12]*y*y
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
private:
float qd[111,13]
default:
title = "SprottQuad"
heading
text="Sprott 2D Quadratic Attractors"
endheading
heading
text=" x -> Quadratic in x and y"
endheading
heading
text=" y -> Quadratic in x and y"
endheading
int param v_trapshapesprottquad
caption = "Version (Trap Shape SprottQuad)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesprottquad < 101
endparam
param sd
caption = "Sprott selector"
default = 0
enum = "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" \
"15" "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" \
"30" "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" \
"45" "46" "47" "48" "49" "50" "51" "52" "53" "54" "55" "56" "57" "58" "59" \
"60" "61" "62" "63" "64" "65" "66" "67" "69" "69" "70" "71" "72" "73" "74" \
"75" "76" "77" "78" "79" "80" "81" "82" "83" "84" "85" "86" "87" "88" "89" \
"90" "91" "92" "93" "94" "95" "96" "97" "98" "99" "100" "101" "102" "103" \
"104" "105" "106" "107" "108" "109" "110"
hint = "Each Sprott selector uses a different strange attractor."
endparam
float param distscale
caption = "Distance scale"
default = 1.0
endparam
float param s
caption = "Attractor scale"
default = 0.5
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 20
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeThreeply(common.ulb:TrapShape) {
; This shape is the Threeply strange attractor.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeThreeply(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
if x != 0
x = y - x/abs(x)*(abs(sin(x)*cos(@h2) + @h3 \
- x*sin(@h1 + @h2 + @h3)))
else
x = y - (abs(sin(x)*cos(@h2) + @h3 \
- x*sin(@h1 + @h2 + @h3)))
endif
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Threeply"
heading
text = "Threeply attractor"
endheading
heading
text = "x->y-sign(x)*(abs(sin(x)*cos(h2)+\
h3-x*sin(h1+h2+h3)))"
endheading
heading
text = "y->h1-x"
endheading
int param v_trapshapethreeply
caption = "Version (Trap Shape Threeply)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapethreeply < 101
endparam
float param h1
caption = "Threeply param 1"
default = -55
endparam
float param h2
caption = "Threeply param 2"
default = -1
endparam
float param h3
caption = "Threeply param 3"
default = 0.8
endparam
float param distscale
caption = "Distance scale"
default = 0.0002
endparam
float param s
caption = "Attractor scale"
default = 100
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 100
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeZito(common.ulb:TrapShape) {
; This shape uses the Zito strange attractor.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeZito(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = x*y +@h1*x - y
y= pxx + y
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Zito"
heading
text = "Zito attractor"
endheading
heading
text = "x -> x*y + a*x - y"
endheading
heading
text = "y -> x + y"
endheading
int param v_trapshapezito
caption = "Version (Trap Shape Zito)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapezito < 101
endparam
float param h1
caption = "Zito param"
default = 0.357
endparam
float param distscale
caption = "Distance scale"
default = 1
endparam
float param s
caption = "Attractor scale"
default = 2
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 10
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_SpokesNRings(common.ulb:TrapShape) {
; This trap creates rings and spokes shapes.
; This variant of the ampersand function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"
$define debug
; Constructor
func REB_TrapShapeAmpersand(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
if !@cmplx
x = real(@fn1(pz))
y = imag(@fn2(pz))
else
x = real(@fn1(pz))
y = imag(@fn1(pz))
endif
if @ref == "pz"
d = (y^2-x^2)*(x-@a1)*(@a2*x-@a3)-@a4*(x^2+y^2-@a5*x)^2+cabs(pz)*@offset
else
d = (y^2-x^2)*(x-@a1)*(@a2*x-@a3)-@a4*(x^2+y^2-@a5*x)^2+@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)
float qy = 0
float qb = 6*x^2 - 3*x - 3
float qc = 6*x^4 - 13*x^3 + 19*x^2
if @negroot
qy = ((-qb - (qb^2 - 16*qc)^0.5)/(8))^0.5
else
qy = ((-qb + (qb^2 - 16*qc)^0.5)/(8))^0.5
endif
m_LastZ = @a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(@a*(x + sgn*flip(qy))))
else
d = cabs(pz - @a*(x + sgn*flip(qy)))
endif
endif
return d
endfunc
default:
title = "Ampersand"
int param v_trapshapeampersand
caption = "Version (Trap Shape Ampersand)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeampersand < 101
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
bool param adv
caption = "advanced"
default = false
visible = @altformula
endparam
float param a1
caption = "parameter a1"
default = 1
visible = @adv && @altformula
endparam
float param a2
caption = "parameter a2"
default = 2
visible = @adv && @altformula
endparam
float param a3
caption = "parameter a3"
default = 3
visible = @adv
endparam
float param a4
caption = "parameter a4"
default = 4
visible = @adv && @altformula
endparam
float param a5
caption = "parameter a5"
default = 2
visible = @adv && @altformula
endparam
bool param cmplx
caption = "Apply to complex"
default = false
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = !@cmplx && @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
param negroot
caption = "Quad Neg Root"
default = true
visible = !@altformula
endparam
}
class REB_TrapShapeSpiricOfPerseus(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSpiricOfPerseus(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
complex qy = 0
if @negroot
qy = -(2*(x^2+@c^2)^0.5 -x^2 - 1 + @b^2 - @c^2)^0.5
else
qy = (2*(x^2+@c^2)^0.5 -x^2 - 1 + @b^2 - @c^2)^0.5
endif
m_LastZ = 3*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(3*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 3*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Spiric Of Perseus"
int param v_SpiricOfPerseus
caption = "Version (Spiric Of Perseus)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_SpiricOfPerseus < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "Spiric 1 parameter"
default = 0.3
endparam
float param c
caption = "Spiric 2 parameter"
default = 0.6
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = true
endparam
}
class REB_TrapShapeGranvillesEgg(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeGranvillesEgg(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
complex qy = 0
if @negroot
qy = -((x-@b)*(1-x)/x^2)^0.5
else
qy = ((x-@b)*(1-x)/x^2)^0.5
endif
m_LastZ = @a*(x + sgn*flip(qy))/2
if @absval
d = abs(cabs(pz) - cabs(@a*(x + sgn*flip(qy)))/2)
else
d = cabs(pz - @a*(x + sgn*flip(qy))/2)
endif
return d
endfunc
default:
title = "Granville's Egg"
int param v_GranvillesEgg
caption = "Version (Granville's Egg)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_GranvillesEgg < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "Granville parameter"
default = 0.1
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = true
endparam
}
class REB_TrapShapeGudermannian(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeGudermannian(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = atan(exp(x))
m_LastZ = 5*@a*(x + sgn*flip(qy))/2
if @absval
d = abs(cabs(pz) - cabs(5*@a*(x + sgn*flip(qy)))/2)
else
d = cabs(pz - 5*@a*(x + sgn*flip(qy))/2)
endif
return d
endfunc
default:
title = "Gudermannian"
int param v_Gudermannian
caption = "Version (Gudermannian)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Gudermannian < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeHeatCapacity(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHeatCapacity(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = x + @b/x^2
m_LastZ = @a*(x + sgn*flip(qy))/2
if @absval
d = abs(cabs(pz) - cabs(@a*(x + sgn*flip(qy)))/2)
else
d = cabs(pz - @a*(x + sgn*flip(qy))/2)
endif
return d
endfunc
default:
title = "Heat Capacity"
int param v_HeatCapacity
caption = "Version (Heat Capacity)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_HeatCapacity < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "Heat Capacity parameter"
default = 0.01
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeHoerlFunction(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHoerlFunction(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = x^@b*exp(x)
m_LastZ = 2.5*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(2.5*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 2.5*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Hoerl Function"
int param v_HoerlFunction
caption = "Version (Hoerl Function)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_HoerlFunction < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "Hoerl parameter"
default = 0.5
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeBesace(common.ulb:TrapShape) {
public:
import "common.ulb"
$define debug
; Constructor
func REB_TrapShapeBesace(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = (y+@aa*x^2)^2-x^2+x^4-cabs(pz)*@offset
else
d = (y+@aa*x^2)^2-x^2+x^4-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
int sgn = 1
if @sgn
sgn = -1
endif
d = 0
x = real(pz)
complex qy = 0
if @negroot
qy = -sqrt(x^2-x^4) - @b*x^2
else
qy = sqrt(x^2-x^4) - @b*x^2
endif
m_LastZ = @a*(x + sgn*flip(qy))/2
if @absval
d = abs(cabs(pz) - cabs(@a*(x + sgn*flip(qy)))/2)
else
d = cabs(pz - @a*(x + sgn*flip(qy))/2)
endif
endif
return d
endfunc
default:
title = "Besace"
int param v_Besace
caption = "Version (Besace)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_besace < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.2
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "Besace parameter"
default = 2
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "Besace parameter"
default = 100
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
param negroot
caption = "Quad Neg Root"
default = true
visible = !@altformula
endparam
}
class REB_TrapShapeKulpsQuartic(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKulpsQuartic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = 0
if @negroot
qy = -sqrt(1/(1+x^2))
else
qy = sqrt(1/(1+x^2))
endif
m_LastZ = 2.5*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(2.5*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 2.5*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Kulp's Quartic"
int param v_KulpsQuartic
caption = "Version (Kulp's Quartic)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_KulpsQuartic < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = true
endparam
}
class REB_TrapShapeKiepertsCurve(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKiepertsCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
complex qy = 0
if @negroot
qy = -sqrt((1-x^2)^3)
else
qy = sqrt((1-x^2)^3)
endif
m_LastZ = 3*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(3*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 3*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Kiepert's Curve"
int param v_KiepertsCurve
caption = "Version (Kiepert's Curve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_KiepertsCurve < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = true
endparam
}
class REB_TrapShapeLennardJones(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLennardJones(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = 0
qy = x^(-12) - x^(-6)
m_LastZ = 5*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(5*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 5*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Lennard-Jones Potential"
int param v_LennardJones
caption = "Version (Lennard-Jones Potential)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_LennardJones < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeFunction(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeFunction(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = 0
qy = real(@fn(x))
m_LastZ = 5*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(5*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 5*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Function"
int param v_Function
caption = "Version (Function)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Function < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
func fn
caption = "Function"
default = sin()
endfunc
}
class REB_TrapShapeCubicSpiral(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCubicspiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = 0
qy = x^3
m_LastZ = 4*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(4*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 4*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Cubic Spiral"
int param v_CubicSpiral
caption = "Version (Cubic Spiral)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_CubicSpiral < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeGauss(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeGauss(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
float x = real(pz)
float qy = 0
qy = (1/(@sigma*sqrt(2*#pi)))*exp(-x^2/(2*@sigma^2))
m_LastZ = 4*@a*(x + sgn*flip(qy))
if @absval
d = abs(cabs(pz) - cabs(4*@a*(x + sgn*flip(qy))))
else
d = cabs(pz - 4*@a*(x + sgn*flip(qy)))
endif
return d
endfunc
default:
title = "Gauss Curve"
int param v_Gauss
caption = "Version (Gauss Curve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Gauss < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param sigma
caption = "Sigma"
default = 1
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeOphiuride(common.ulb:TrapShape) {
; This shape uses the ophiuride function.
; This variant of the ophuiride function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeOphiuride(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = (0.01*@b*sin(theta)-@a*cos(theta))*tan(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Ophiuride"
int param v_trapshapeophiuride
caption = "Version (Trap Shape Ophiuride)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeophiuride < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeREBAstroid(common.ulb:TrapShape) {
; This shape uses the astroid function.
; This variant of the astoid function is different from that used by Damien
; Jones. It has signed and absolute value version of the distance. The function
; also has a complex conjugate variant. The transformed value is the complex
; return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeREBAstroid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
complex as = 0
complex af1 = 0
complex af2 = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
if !@cmplx
x = real(@fn1(pz))
y = imag(@fn2(pz))
else
x = real(@fn1(pz))
y = imag(@fn1(pz))
endif
if @ref == "pz"
d = x^(2/3)+y^(2/3)-@a^(2/3)+cabs(pz)*@offset
else
d = x^(2/3)+y^(2/3)-@a^(2/3)+@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
af1 = @afn1(theta)^real(@pwr)
af2 = @afn2(theta)^imag(@pwr)
as = @ar*(af1+sgn*flip(af2))
m_LastZ = as
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - (as))
endif
endif
return d
endfunc
default:
title = "Astroid REB"
int param v_trapshapeastroidreb
caption = "Version (Trap Shape Astroid REB)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeastroidreb < 102
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.2
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param a
caption = "parameter a"
default = 1
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
bool param cmplx
caption = "Apply to complex"
default = false
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula && !@cmplx
endfunc
float param ar
caption = "Radius"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
complex param pwr
caption = "Power"
default = (3,3)
hint = "Affects shape and scale of trap."
visible = !@altformula
endparam
func afn1
caption = "Function #1"
default = cos()
visible = !@altformula
endfunc
func afn2
caption = "Function #2"
default = sin()
visible = !@altformula
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeBean(common.ulb:TrapShape) {
; This shape uses the bean function.
; It has signed and absolute value version of the distance. The function
; also has a complex conjugate variant. The transformed value is the complex
; return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBean(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
float theta = 0
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = (x^2+y^2)^2-x^3-y^3-cabs(pz)*@offset
else
d = (x^2+y^2)^2-x^3-y^3-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
complex af1 = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
af1 = @a*(@afn1(theta)^real(@pwr)+@afn2(theta)^imag(@pwr))
if @absval
d = abs(cabs(pz) - cabs(af1*cos(theta) + sgn*flip(af1*sin(theta))))
else
d = cabs(pz - (af1*cos(theta) + sgn*flip(af1*sin(theta))))
endif
m_LastZ = (af1*cos(theta) + sgn*flip(af1*sin(theta)))
endif
return d
endfunc
default:
title = "Bean"
int param v_trapshapebean
caption = "Version (Trap Shape Bean)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapebean < 101
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.2
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
complex param pwr
caption = "Power"
default = (3,3)
hint = "Affects shape and scale of trap."
visible = !@altformula
endparam
func afn1
caption = "Function #1"
default = cos()
visible = !@altformula
endfunc
func afn2
caption = "Function #2"
default = sin()
visible = !@altformula
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeCircle(common.ulb:TrapShape) {
; This shape uses the circle function.
; This variant of the circle function has a signed and absolute value
; version of the distance. The function also has a complex conjugate.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCircle(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*sin(theta)^2 + 0.2*@b*cos(theta)^2
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta) + sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
return d
endfunc
default:
title = "Circle"
int param v_trapshapecircle
caption = "Version (Trap Shape Circle)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecircle < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_AstroidalEllipsoid(common.ulb:TrapShape) {
; This shape uses the 3D Astroidal Ellipsoid function.
public:
import "common.ulb"
; Constructor
func REB_AstroidalEllipsoid(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = (@aa*cos(real(pz))*cos(imag(pz)))^3*@scale2
float y = (@ab*sin(real(pz))*cos(imag(pz)))^3*@scale2
float z = (@ac*sin(imag(pz)))^3*@scale2
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Astroidal Ellipsoid"
heading
text = "This is a 3D parametric surface."
endheading
int param v_AstroidalEllipsoid
caption = "Version (Trap Shape AstroidalEllipsoid)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_AstroidalEllipsoid < 100
endparam
float param xang
caption = "X rotation"
default = -40
endparam
float param yang
caption = "Y rotation"
default = 30
endparam
float param scale2
caption = "prescale"
default = 1.0
endparam
float param scale
caption = "Scale"
default = 0.2
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
float param aa
caption = "param a"
default = 1.0
endparam
float param ab
caption = "param b"
default = 1.0
endparam
float param ac
caption = "param c"
default = 1.0
endparam
}
class REB_AppleSurface(common.ulb:TrapShape) {
; This shape uses the 3D Apple Surface function.
public:
import "common.ulb"
; Constructor
func REB_AppleSurface(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = (cos(real(pz))*(4 + 3.8*cos(imag(pz))))*@ap*@scale2
float y = (sin(real(pz))*(4 + 3.8*cos(imag(pz))))*@ap*@scale2
float z = ((cos(imag(pz)) + sin(imag(pz)) - 1)+\
(1 + sin(imag(pz)))*log(1 - #pi*imag(pz) / 10) +\
7.5*sin(imag(pz)))*@ap*@scale2
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Apple Surface"
heading
text = "This is a 3D parametric surface."
endheading
int param v_AppleSurface
caption = "Version (Trap Shape AppleSurface)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_AppleSurface < 100
endparam
float param xang
caption = "X rotation"
default = -75
endparam
float param yang
caption = "Y rotation"
default = 20
endparam
float param scale2
caption = "Precale"
default = 1.0
endparam
float param scale
caption = "Scale"
default = 0.2
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
float param ap
caption = "param"
default = 0.1
endparam
}
class REB_BowTie(common.ulb:TrapShape) {
; This shape uses the 3D Bow Tie Surface function.
public:
import "common.ulb"
; Constructor
func REB_BowTie(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = sin(real(pz))/(sqrt(2)+sin(imag(pz)))*@scale2
float y = sin(real(pz))/(sqrt(2)+cos(imag(pz)))*@scale2
float z = cos(real(pz))/(sqrt(2)+1)*@scale2
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Bow Tie Surface"
heading
text = "This is a 3D parametric surface."
endheading
int param v_BowTieSurface
caption = "Version (Trap Shape BowTieSurface)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BowTieSurface < 100
endparam
float param xang
caption = "X rotation"
default = -45
endparam
float param yang
caption = "Y rotation"
default = 90
endparam
float param scale2
caption = "Prescale"
default = 1
endparam
float param scale
caption = "Scale"
default = 0.2
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
}
class REB_BowSurface(common.ulb:TrapShape) {
; This shape uses the 3D Bow Surface function.
public:
import "common.ulb"
; Constructor
func REB_BowSurface(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = ((2 + @T*sin(2*#pi*real(pz)))*sin(4*#pi*imag(pz)))*@scale2
float y = (2 + @T*sin(2*#pi*real(pz)))*cos(4*#pi*imag(pz))*@scale2
float z = (@T*cos(2*#pi*real(pz)) + 3*cos(2*#pi*imag(pz))*@scale2)
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Bow Surface"
heading
text = "This is a 3D parametric surface."
endheading
int param v_BowSurface
caption = "Version (Trap Shape BowSurface)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BowSurface < 100
endparam
float param xang
caption = "X rotation"
default = -100
endparam
float param yang
caption = "Y rotation"
default = 30
endparam
float param scale2
caption = "Prescale"
default = 0.5
endparam
float param scale
caption = "Scale"
default = 0.2
endparam
float param T
caption = "Bow thickness"
default = 1
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
}
class REB_BoySurface(common.ulb:TrapShape) {
; This shape uses the 3D Boy Surface function.
public:
import "common.ulb"
; Constructor
func REB_BoySurface(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = (((2/3)*(cos(real(pz))*cos(2*imag(pz))+sqrt(2)*sin(real(pz))*cos(imag(pz)))*cos(real(pz)) \
/(sqrt(2) - sin(2*real(pz))*sin(3*imag(pz)))))*@scale2
float y = (((2/3)*(cos(real(pz))*sin(2*imag(pz))-sqrt(2)*sin(real(pz))*sin(imag(pz)))*cos(real(pz)) \
/(sqrt(2)-sin(2*real(pz))*sin(3*imag(pz)))))*@scale2
float z = ((sqrt(2)*cos(real(pz))^2 / (sqrt(2) - sin(2*real(pz))*sin(2*imag(pz)))))*@scale2
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Boy Surface"
heading
text = "This is a 3D parametric surface."
endheading
int param v_BoySurface
caption = "Version (Trap Shape BowSurface)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BoySurface < 100
endparam
float param xang
caption = "X rotation"
default = -20
endparam
float param yang
caption = "Y rotation"
default = 0
endparam
float param scale2
caption = "Prescale"
default = 1.0
endparam
float param scale
caption = "Scale"
default = 0.2
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
}
class REB_BourMinimalSurface(common.ulb:TrapShape) {
; This shape uses the 3D Bour Minimal Surface function.
public:
import "common.ulb"
; Constructor
func REB_BourMinimalSurface(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = ((real(pz)^(@n-1)* cos((@n-1)*imag(pz))/(2*(@n-1)) - real(pz)^(@n+1)* cos((@n+1)*imag(pz))/(2*(@n+1))))*@scale2
float y = ((real(pz)^(@n-1)* sin((@n-1)*imag(pz))/(2*(@n-1)) + real(pz)^(@n+1)* sin((@n+1)*imag(pz))/(2*(@n+1))))*@scale2
float z = ((real(pz)^@n*cos(@n*imag(pz)) / @n))*@scale2
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Bour Minimal Surface"
heading
text = "This is a 3D parametric surface."
endheading
int param v_BourMinimalSurface
caption = "Version (Trap Shape BourMinimalSurface)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BourMinimalSurface < 100
endparam
float param xang
caption = "X rotation"
default = -20
endparam
float param yang
caption = "Y rotation"
default = 30
endparam
float param scale2
caption = "Prescale"
default = 1.0
endparam
float param scale
caption = "Scale"
default = 0.2
endparam
int param n
caption = "Integer parameter"
default = 3
min = 2
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
}
class REB_BohemianDome(common.ulb:TrapShape) {
; This shape uses the 3D Bohemian Dome Surface function.
public:
import "common.ulb"
; Constructor
func REB_BohemianDome(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = (@ba*cos(real(pz)))*@scale2
float y = (@bb*cos(imag(pz)) + @ba*sin(real(pz)))*@scale2
float z = (@bc*sin(imag(pz)))*@scale2
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Bohemian Dome"
heading
text = "This is a 3D parametric surface."
endheading
int param v_BohemianDome
caption = "Version (Trap Shape Bohemian Dome)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BohemianDome < 100
endparam
float param xang
caption = "X rotation"
default = -30
endparam
float param yang
caption = "Y rotation"
default = 60
endparam
float param scale2
caption = "Precale"
default = 1.0
endparam
float param scale
caption = "Scale"
default = 0.2
endparam
float param ba
caption = "param a"
default = 0.5
endparam
float param bb
caption = "param b"
default = 1.5
endparam
float param bc
caption = "param c"
default = 1.0
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
}
class REB_BanchoffKleinBottle(common.ulb:TrapShape) {
; This shape uses the 3D Banchoff Klein Bottle Surface function.
public:
import "common.ulb"
; Constructor
func REB_BanchoffKleinBottle(Generic pparent)
TrapShape.TrapShape(pparent)
xrot = (0,1)^(@xang/90)
yrot = (0,1)^(@yang/90)
temp = 0
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = (cos(real(pz)/@banc)*(cos(real(pz)/@banb)*(@bana+cos(imag(pz)))+ \
(sin(real(pz)/@banb)*sin(imag(pz))*cos(imag(pz)))))*@bc
float y = (sin(real(pz)/@banc)*(cos(real(pz)/@banb)*(@bana+cos(imag(pz)))+ \
(sin(real(pz)/@banb)*sin(imag(pz))*cos(imag(pz)))))*@bc
float z = (-sin(real(pz)/@banb)*(@bana+cos(imag(pz)))+cos(real(pz)/@banb)*sin(imag(pz))*cos(imag(pz)))*@bc
;
; Y axis rotation
;
temp = x + flip(z)
temp = temp*yrot
x = real(temp)
z = imag(temp)
;
; X axis rotation
;
temp = y + flip(z)
temp = temp*xrot
y = real(temp)
z = imag(temp)
; calculate 3D distance
float d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +z^2)*@scale
if @usez
if @tz == "cabs(z)"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*cabs(pz)-z)^2)*@scale
elseif @tz == "real+imag z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz)+imag(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((imag(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(real(pz))-z)^2)*@scale
elseif @tz == "real z"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*(imag(pz))-z)^2)*@scale
elseif @tz == "angle pz"
d = sqrt((real(pz)-x)^2 + (imag(pz)-y)^2 +(@sz*atan2(pz)-z)^2)*@scale
endif
endif
m_lastZ = x + flip(y)
return d
endfunc
protected:
complex xrot
complex yrot
complex temp
default:
title = "Banchoff Klein Bottle"
heading
text = "This is a 3D parametric surface."
endheading
int param v_BanchoffKleinBottle
caption = "Version (Banchoff Klein Bottle)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BanchoffKleinBottle < 100
endparam
float param xang
caption = "X rotation"
default = -90
endparam
float param yang
caption = "Y rotation"
default = 90
endparam
float param scale
caption = "scale"
default = 0.2
endparam
bool param usez
caption = "fractal z for z value"
default = false
endparam
param tz
caption = "fractal z type"
enum = "cabs(z)" "real+imag z" "real z" "imag z" "angle pz"
default = 0
visible = @usez
endparam
float param sz
caption = "fractal z scale"
default = 1
visible = @usez
endparam
float param bc
caption = "Banchoff scale"
default = 0.5
endparam
float param bana
caption = "Parameter a"
default = 1.414213
endparam
float param banb
caption = "Parameter b"
default = 2.0
endparam
float param banc
caption = "Parameter c"
default = 1.0
endparam
}
class REB_TrapShapeConvexPolygons(common.ulb:TrapShape) {
; This shape uses the Convex Polygons.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCircleCatacaustic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
float af1 = 0
float af2 = 0
complex as = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
af1 = 2*@b*(1-3*2*@b*cos(theta)+2*2*@b*cos(theta)^3)/(-(1+2*(2*@b)^2)+3*2*@b*cos(theta))
af2 = 2*(2*@b)^2*sin(theta)^3/(1+2*(2*@b)^2-3*2*@b*cos(theta))
as = @a*(af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - (as))
endif
m_LastZ = as
return d
endfunc
default:
title = "Circle Catacaustic"
int param v_trapshapecirclecatacaustic
caption = "Version (Trap Shape Circle Catacaustic)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecirclecatacaustic < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeCruciform(common.ulb:TrapShape) {
; This shape uses the cruciform function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCruciform(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
float af1 = 0
float af2 = 0
complex as = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
af1 = 0.1*@a/cos(theta)
af2 = 0.02*@b/sin(theta)
as = (af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - (as))
endif
m_LastZ = as
return d
endfunc
default:
title = "Cruciform"
int param v_trapshapecruciform
caption = "Version (Trap Shape Cruciform)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecruciform < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeCurtateCycloid(common.ulb:TrapShape) {
; This shape uses the curtate cycloid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCurtateCycloid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
complex af1 = 0
complex af2 = 0
complex as = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
af1 = @a*theta - 0.1*@b*@afn2(theta)
af2 = @a - 0.1*@b*@afn1(theta)
as = (af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - (as))
endif
m_LastZ = as
return d
endfunc
default:
title = "Curtate Cycloid"
int param v_trapshapecurtatecycloid
caption = "Version (Trap Shape Curtate Cycloid)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecurtatecycloid < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
func afn1
caption = "Function #1"
default = cos()
endfunc
func afn2
caption = "Function #2"
default = sin()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeCycloid(common.ulb:TrapShape) {
; This shape uses the cycloid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCycloid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = cabs(pz)
if @absval
d = abs(cabs(pz) - cabs(rr*(theta-sin(theta) + sgn*flip(rr*(1-cos(theta))))))
else
d = cabs(pz - (rr*(theta-sin(theta) + sgn*flip(rr*(1-cos(theta))))))
endif
m_LastZ = (rr*(theta-sin(theta) + sgn*flip(rr*(1-cos(theta)))))
return d
endfunc
default:
title = "Cycloid"
int param v_trapshapecycloid
caption = "Version (Trap Shape Cycloid)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecycloid < 102
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeCycloidofSeva(common.ulb:TrapShape) {
; This shape uses the cycloid of Seva function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCycloidofSeva(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.5*@a*(1+2*cos(2*theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Cycloid of Seva"
int param v_trapshapecycloidofseva
caption = "Version (Trap Shape Cycloid Of Seva)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecycloidofseva < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeDeltoidCatacaustic(common.ulb:TrapShape) {
; This shape uses the deltoid catacaustic function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeDeltoidCatacaustic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
complex af1 = 0
complex af2 = 0
complex as = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
af1 = 3*@afn1(theta) + @afn1(3*theta+#pi/2*@b) - @afn1(#pi/2*@b)
af2 = 3*@afn2(theta) + @afn2(3*theta+#pi/2*@b) - @afn2(#pi/2*@b)
as = 0.25*@a*(af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - (as))
endif
m_LastZ = as
return d
endfunc
default:
title = "Deltoid Catacaustic"
int param v_trapshapedeltoidcatacaustic
caption = "Version (Trap Shape Deltoid Catacaustic)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapedeltoidcatacaustic < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
func afn1
caption = "Function #1"
default = cos()
endfunc
func afn2
caption = "Function #2"
default = sin()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeDevilsCurve(common.ulb:TrapShape) {
; This shape uses the devil's curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeDevilsCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = (((0.5*@a*sin(theta))^2-(0.2*@b*cos(theta))^2)/(sin(theta)^2-cos(theta)^2))^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Devils Curve"
int param v_trapshapedevilscurve
caption = "Version (Trap Shape Devils Curve)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapedevilscurve < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeArachnida1(common.ulb:TrapShape) {
; This shape uses the arachnida 1 function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeArachnida1(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = 0
float y = 0
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.25*@a*sin(@pi*theta)/sin((@pi-1)*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Arachnida 1"
int param v_trapshapearachnida1
caption = "Version (Trap Shape Arachnida 1)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapearachnida1 < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
int param pi
caption = "Polar integer"
default = 3
hint = "Affects shape and scale of trap."
endparam
bool param wave
caption = "Add petal wave"
default = false
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeArachnida2(common.ulb:TrapShape) {
; This shape uses the arachnida 2 function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeArachnida2(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.25*@a*sin(@pi*theta)/sin((@pi+1)*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Arachnida 2"
int param v_trapshapearachnida2
caption = "Version (Trap Shape Arachnida 2)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapearachnida2 < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
int param pi
caption = "Polar integer"
default = 3
hint = "Affects shape and scale of trap."
endparam
bool param wave
caption = "Add petal wave"
default = false
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeArchimedes(common.ulb:TrapShape) {
; This shape uses the Archimedes function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeArchimedes(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @b+@a*theta
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Archimedes"
int param v_trapshapearchimedes
caption = "Version (Trap Shape Archimedes)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapearchimedes < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 0.0
hint = "Affects spiral start point"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeAtzemaSpiral(common.ulb:TrapShape) {
; This shape uses the Atzema spiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeAtzemaSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
float af1 = 0.5*@a*(sin(theta)/theta-2*cos(theta)-theta*sin(theta))
float af2 = 0.05*@b*(cos(theta)/theta-2*sin(theta)+theta*cos(theta))
complex as = (af1 + sgn*flip(af2))
IF @absval
d = abs(cabs(pz) - cabs(as))
ELSE
d = cabs(pz - as)
ENDIF
m_LastZ = as
return d
endfunc
default:
title = "Atzema Spiral"
int param v_trapshapeatzemaspiral
caption = "Version (Trap Shape Atzema Spiral)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeatzemaspiral < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeBicorn(common.ulb:TrapShape) {
; This shape uses the bicorn function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBicorn(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = y^2*(@aa^2-x^2)-(x^2+2*@aa*y-@aa^2)^2+cabs(pz)*@offset
else
d = y^2*(@aa^2-x^2)-(x^2+2*@aa*y-@aa^2)^2+@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
float af1 = @a*sin(theta)
float af2 = @a*cos(theta)^2*(2+cos(theta))/(3+sin(theta)^2)
complex as = (af1 + sgn*flip(af2))
IF @absval
d = abs(cabs(pz) - cabs(as))
ELSE
d = cabs(pz - as)
ENDIF
m_LastZ = as
endif
return d
endfunc
default:
title = "Bicorn"
int param v_trapshapebicorn
caption = "Version (Trap Shape Bicorn)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapebicorn < 102
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1.25
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "Bicorn parameter"
default = 1.25
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeBicuspid(common.ulb:TrapShape) {
; This shape uses the bicuspid function.
; This variant of the function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBicuspid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = (x^2-@aa^2)*(x-@aa)^2+(y^2-@aa^2)^2+cabs(pz)*@offset
else
d = (x^2-@aa^2)*(x-@aa)^2+(y^2-@aa^2)^2+@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
int sgn = 1
if @sgn
sgn = -1
endif
y = imag(pz)
float qx = 0
float qb = -2*(0.05*@b)^2
float qc = (0.05*@b)^4 - (y^2 - (0.05*@b)^2)^2
if @negroot
qx = ((-qb - (qb^2 - 4*qc)^0.5)/(2))^0.5
else
qx = ((-qb + (qb^2 - 4*qc)^0.5)/(2))^0.5
endif
if @absval
d = abs(cabs(pz) - cabs(2.25*@a*(qx + sgn*flip(y))))
else
d = cabs(pz - 2.25*@a*(qx + sgn*flip(y)))
endif
m_LastZ = 2.25*@a*(qx + sgn*flip(y))
endif
return d
endfunc
default:
title = "Bicuspid"
int param v_trapshapebicuspid
caption = "Version (Trap Shape Bicuspid)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapebicuspid < 101
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 1
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
param negroot
caption = "Quad Reg Root"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeRhodonea(common.ulb:TrapShape) {
; This shape uses the rhodonea function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeRhodonea(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*sin(5*@b*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Rhodonea"
int param v_Rhodonea
caption = "Version (Rhodonea)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Rhodonea < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param @wave
caption = "Add petal wave"
default = false
endparam
float param @wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param @wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeCircleTangent(common.ulb:TrapShape) {
; This shape uses the Circle Tangent function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCircleTangent(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.5*@a*(1+@b/10*sin(theta)^(8*@c))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Circle Tangent"
int param v_CircleTangent
caption = "Version (Circle Tangent)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_CircleTangent < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeBifolium(common.ulb:TrapShape) {
; This shape uses the bifolium function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBifolium(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = (x^2+y^2)^2-(x-@aa*y)*x^2-cabs(pz)*@offset
else
d = (x^2+y^2)^2-(x-@aa*y)*x^2-@offset
endif
m_lastz = x-d + flip(y-d)
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 4*@a*sin(theta)*sin(theta)*cos(theta)
if @v_trapshapebifolium >= 102
rr = 4*@a*sin(@c*theta)^@b*cos(theta)
endif
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Bifolium"
int param v_trapshapebifolium
caption = "Version (Trap Shape Bifolium)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapebifolium < 102
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.2
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "Bifolium param"
default = 5.0
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
visible = !@altformula
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = @v_trapshapebifolium >= 102 && !@altformula
endparam
float param c
caption = "Polar parameter 2"
default = 1
visible = @v_trapshapebifolium >= 102 && !@altformula
endparam
float param b
caption = "Power"
default = 2
visible = @v_trapshapebifolium >= 102 && !@altformula
endparam
bool param @wave
caption = "Add petal wave"
default = false
visible = @v_trapshapebifolium >= 102 && !@altformula
endparam
float param @wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && !@altformula
endparam
float param @wfreq
caption = "Wave frequency"
default = 20
visible = @wave && !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
}
class REB_TrapShapeBotanicCurve(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBotanicCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.5*@a*(1 + @b*sin(@c*theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Botanic Curve"
int param v_BotanicCurve
caption = "Version (Botanic Curve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BotanicCurve < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "Petal Sharpness"
default = 1
endparam
float param c
caption = "Petals"
default = 10
endparam
bool param @wave
caption = "Add petal wave"
default = false
endparam
float param @wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param @wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeObliqueStrophoid(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeObliqueStrophoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*sin(@b-2*theta)/sin(@b-theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Oblique Strophoid"
int param v_ObliqueStrophoid
caption = "Version (Obliquev Strophoid)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_ObliqueStrophoid < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "Strophoid parameter"
default = 0.5
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeFermatsSpiral(common.ulb:TrapShape) {
; This shape uses the FermatsSpiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeFermatsSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 2*@a*theta^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Fermat's Spiral"
int param v_trapshapeFermatsSpiral
caption = "Version (Trap Shape Fermat's Spiral)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeFermatsSpiral < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeAtomSpiral(common.ulb:TrapShape) {
; This shape uses the atom spiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeAtomSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.5*@a*theta/(theta + @b*0.25)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Atom Spiral"
int param v_AtomSpiral
caption = "Version (Atom Spiral)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_AtomSpiral < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeCevasTrisectrix(common.ulb:TrapShape) {
; This shape uses the atom spiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCevasTrisectrix(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = (x^2+y^2)^3-((@aa+1)*x^2-(@aa-1)*y^2)^2-cabs(pz)*@offset
else
d = (x^2+y^2)^3-((@aa+1)*x^2-(@aa-1)*y^2)^2-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 2.5*@a*(1+@b*sin(2*theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Ceva's Trisectrix"
int param v_CevasTrisectrix
caption = "Version (Ceva's Trisectrix)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_CevasTrisectrix < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 2
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
}
class REB_TrapShapeHyperbolicSpiral(common.ulb:TrapShape) {
; This shape uses the HyperbolicSpiralfunction.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHyperbolicSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a/theta
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Hyperbolic Spiral"
int param v_HyperbolicSpiral
caption = "Version (HyperbolicSpiral)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_HyperbolicSpiral < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeNodalCurve(common.ulb:TrapShape) {
; This shape uses the NodalCurve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeNodalCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*tan(@b*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Nodal Curve"
int param v_NodalCurve
caption = "Version (NodalCurve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_NodalCurve < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeGielisCurve(common.ulb:TrapShape) {
; This shape uses the Gielis curve.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeGielisCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*(abs(cos(2*@b*theta))^@pa + abs(sin(2*@b*theta))^@pb)^@pc
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Gielis Curve"
int param v_GielisCurve
caption = "Version (GielisCurve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_GielisCurve < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param pa
caption = "Power a"
default = 10.0
hint = "Affects spread and scale of trap"
endparam
float param pb
caption = "Power b"
default = 10.0
hint = "Affects spread and scale of trap"
endparam
float param pc
caption = "Power c"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param wave
caption = "Add petal wave"
default = false
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeSuperSpiral(common.ulb:TrapShape) {
; This shape uses the SuperSpiral curve.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSuperSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*exp(0.2*@c*theta)*(abs(cos(3*@b*theta))^@pa + abs(sin(3*@b*theta))^@pb)^@pc
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Super Spiral"
int param v_SuperSpiral
caption = "Version (Super Spiral)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_SuperSpiral < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param pa
caption = "Power a"
default = 10.0
hint = "Affects spread and scale of trap"
endparam
float param pb
caption = "Power b"
default = 10.0
hint = "Affects spread and scale of trap"
endparam
float param pc
caption = "Power c"
default = -0.2
hint = "Affects spread and scale of trap"
endparam
bool param @wave
caption = "Add petal wave"
default = false
endparam
float param @wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param @wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeConchoidOfDeSluze(common.ulb:TrapShape) {
; This shape uses the ConchoidOfDeSluze function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeConchoidOfDeSluze(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
if !@cmplx
x = real(@fn1(pz))
y = imag(@fn2(pz))
else
x = real(@fn1(pz))
y = imag(@fn1(pz))
endif
if @ref == "pz"
d = x^3+x*y^2-x^2-y^2-@a1^2*x^2-cabs(pz)*@offset
else
d = x^3+x*y^2-x^2-y^2-@a1^2*x^2-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*(1/cos(theta) - 1.5*@b*cos(theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Conchoid of De Sluze"
int param v_ConchoidOfDeSluze
caption = "Version (ConchoidOfDeSluze)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_ConchoidOfDeSluze < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param a1
caption = "parameter a1"
default = 2
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
bool param cmplx
caption = "Apply to complex"
default = false
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula && !@cmplx
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
}
class REB_TrapShapeEpitrochoid(common.ulb:TrapShape) {
; This shape uses the Epitrochoid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeEquiangularSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*exp(theta*cotan(@b/2))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Equiangular Spiral"
int param v_EquiangularSpiral
caption = "Version (Equiangular Spiral)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_EquiangularSpiral < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeFreethsNephroid(common.ulb:TrapShape) {
; This shape uses the bifolium function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeFreethsNephroid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.5*@a*(1+2*sin(theta/2))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Freeth's Nephroid"
int param v_FreethsNephroid
caption = "Version (FreethsNephroid)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_FreethsNephroid < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeSinusoidalSpiral(common.ulb:TrapShape) {
; This shape uses the Sinusoidal Spiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSinusoidalSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*(cos(2*@b*theta))^1/(2*@b)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Sinusoidal Spiral"
int param v_SinusoidalSpiral
caption = "Version (SinusoidalSpiral)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_SinusoidalSpiral < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeBow(common.ulb:TrapShape) {
; This shape uses the bow function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBow(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = x^4-x^2*y+y^3-cabs(pz)*@offset
else
d = x^4-x^2*y+y^3-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
float af1 = 0.1*@a*(1-tan(theta)^2)*cos(theta)
float af2 = 0.1*@b*(1-tan(theta)^2)*sin(theta)
complex as = (af1 + sgn*flip(af2))
IF @absval
d = abs(cabs(pz) - cabs(as))
ELSE
d = cabs(pz - as)
ENDIF
m_LastZ = as
endif
return d
endfunc
default:
title = "Bow"
int param v_trapshapebow
caption = "Version (Trap Shape Bow)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapebow < 102
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.2
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeButterfly(common.ulb:TrapShape) {
; This shape uses the butterfly function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeButterfly(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = y^6+x^6-x^2-cabs(pz)*@offset
else
d = y^6+x^6-x^2-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
float theta = 0
d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.25*@a*(exp(sin(theta))-2*cos(4*theta)+sin(1/24*(2*theta-#pi)))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Butterfly"
int param v_trapshapebutterfly
caption = "Version (Trap Shape Butterfly)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapebutterfly < 102
endparam
heading
text = "The 'Alternate formula' is a sextic polynomial form while the regular form\
is exponential and uses trigometric functions."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeCapricornoid(common.ulb:TrapShape) {
; This shape uses the Capricornoid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCapricornoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = @aa^2*(x^4+x^2*y^2)-@ab*(x^4+y^4)-@ab*(2*x^2*y^2-2*@aa*y^3+@aa^2*y^2-2*@aa*x^2*y) -cabs(pz)*@offset
else
d = @aa^2*(x^4+x^2*y^2)-@ab*(x^4+y^4)-@ab*(2*x^2*y^2-2*@aa*y^3+@aa^2*y^2-2*@aa*x^2*y)-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.5*@a*sin(theta)/(0.5*@b + 0.35*@c*cos(theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Capricornoid"
int param v_Capricornoid
caption = "Version (Trap Shape Capricornoid)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Capricornoid < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 1.5
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
float param ab
caption = "parameter b"
default = 3
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param c
caption = "3rd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeBulletNose(common.ulb:TrapShape) {
; This shape uses the Bullet Nose function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBulletNose(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = @aa^2*y^2-@ab^2*x^2-x^2*y^2+cabs(pz)*@offset
else
d = @aa^2*y^2-@ab^2*x^2-x^2*y^2+@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
x = r * cos(wtheta)
y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.25*@a*(@b^2*sin(theta)^2-(2*@c)^2*cos(theta)^2)^0.5/(sin(theta)*cos(theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Bullet Nose"
int param v_BulletNose
caption = "Version (Trap Shape Bullet Nose)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BulletNose < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.7
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 1
visible = @altformula
endparam
float param ab
caption = "parameter b"
default = 1
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param c
caption = "3rd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = !@altformula
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && !@altformula
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeTrott(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeTrott(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = 144*(x^4+y^4)-225*(x^2+y^2)+350*x^2*y^2+81-cabs(pz)*@offset
else
d = 144*(x^4+y^4)-225*(x^2+y^2)+350*x^2*y^2+81-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
return d
endfunc
default:
title = "Trott"
int param v_Trott
caption = "Version (Trap Shape Trott)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Trott < 100
endparam
float param scale
caption = "scale"
default = 1
endparam
float param width
caption = "width"
default = 1
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
endparam
func fn1
caption = "Function 1"
default = ident()
endfunc
func fn2
caption = "Function 2"
default = ident()
endfunc
}
class REB_TrapShapeWattsCurve(common.ulb:TrapShape) {
; This shape uses the Watts Curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeWattsCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*(1- @b*(sin(theta) + (@c-cos(theta)^2)^0.5)^2)^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Watts Curve"
int param v_WattsCurve
caption = "Version (Watts Curve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_WattsCurve < 100
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeCardioid(common.ulb:TrapShape) {
; This shape uses the cardiod function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCardioid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = (x^2+y^2-2*@aa*x)^2-4*@aa^2*(x^2+y^2)-cabs(pz)*@offset
else
d = (x^2+y^2-2*@aa*x)^2-4*@aa^2*(x^2+y^2)-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a*(1-cos(theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Cardioid"
int param v_trapshapecardioid
caption = "Version (Trap Shape Cardioid)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecardioid < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.5
visible = @altformula
endparam
float param width
caption = "width"
default = 4
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 0.75
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeCassiniOvals(common.ulb:TrapShape) {
; This shape uses the Cassini ovals function.
; This variant of the function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCassiniOvals(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = x^4+y^4+2*x^2*y^2-2*@aa^2*x^2+2*@aa^2*y^2+@aa^4-@ab^4-cabs(pz)*@offset
else
d = x^4+y^4+2*x^2*y^2-2*@aa^2*x^2+2*@aa^2*y^2+@aa^4-@ab^4-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
if @negroot
rr = 0.5*@a*(cos(2*theta)-((@b*0.1/(@a*0.5))^4-sin(2*theta)^2)^0.5)^0.5
else
rr = 0.5*@a*(cos(2*theta)+((@b*0.1/(@a*0.5))^4-sin(2*theta)^2)^0.5)^0.5
endif
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
endif
return d
endfunc
default:
title = "Cassini Ovals"
int param v_trapshapecassiniovals
caption = "Version (Trap Shape Cassini Ovals)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecassiniovals < 102
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 1
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
float param ab
caption = "parameter b"
default = 1.0
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
param negroot
caption = "Quad Neg Root"
default = false
visible = !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeCayleysSextic(common.ulb:TrapShape) {
; This shape uses the Cayley's sextic function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCayleysSextic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = -@aa^3*x^3-48*@aa*x*(x^2+y^2)^2+64*(x^2+y^2)^3-3*@aa^2*(x^2+y^2)*(5*x^2+9*y^2)-cabs(pz)*@offset
else
d = -@aa^3*x^3-48*@aa*x*(x^2+y^2)^2+64*(x^2+y^2)^3-3*@aa^2*(x^2+y^2)*(5*x^2+9*y^2)-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 1.5*@a*cos(theta)^3
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Cayley's Sextic"
int param v_trapshapecayleyssextic
caption = "Version (Trap Shape Cayley's Sextic)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecayleyssextic < 101
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 1
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
}
class REB_TrapShapeCissoidofDiocles(common.ulb:TrapShape) {
; This shape uses the cissoid of Diocles function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCissoidofDiocles(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = x*(x^2+y^2)-2*@aa*y^2-cabs(pz)*@offset
else
d = x*(x^2+y^2)-2*@aa*y^2-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.2*@a*sin(theta)*tan(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Cissoid of Diocles"
int param v_trapshapecissoidofdiocles
caption = "Version (Trap Shape Cissoid Of Diocles)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecissoidofdiocles < 101
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 1
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 1
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
}
class REB_TrapShapeCochleoid(common.ulb:TrapShape) {
; This shape uses the cochleoid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCochleoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 1.25*@a*sin(theta)/theta
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Cochleoid"
int param v_trapshapecochleoid
caption = "Version (Trap Shape Cochleoid)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecochleoid < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeHeartCurve(common.ulb:TrapShape) {
; This shape uses the Heart Curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeTrochoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float theta = atan2(pz)
float x = @a*(@b*theta-@c*sin(theta))
float y = @a*(@b-@c*cos(theta))
m_lastZ = x + flip(y)
d = cabs(pz-m_lastZ)
return d
endfunc
default:
title = "Trochoid"
int param v_Trochoid
caption = "Version (Trochoid)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Trochoid < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
}
class REB_TrapShapeFishCurve(common.ulb:TrapShape) {
; This shape uses the Heart Curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeFishCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 5*@a*atan2(pz)
float x = @b*(cos(t) - sin(t)^2/sqrt(2))
float y = @b*cos(t)*sin(t)
m_lastZ = x + flip(y)
d = cabs(pz-m_lastZ)
return d
endfunc
default:
title = "Fish Curve"
int param v_FishCurve
caption = "Version (FishCurve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_FishCurve < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
}
class REB_TrapShapeConchoid(common.ulb:TrapShape) {
; This shape uses the conchoid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeConchoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = 0.1*(@a + @b*cos(theta))/cos(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Conchoid"
int param v_trapshapeconchoid
caption = "Version (Trap Shape Conchoid)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeconchoid < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeCotesSpiral(common.ulb:TrapShape) {
; This shape uses the Cote's spiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCotesSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
float rr = @a/cosh(@b*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Cotes' Spiral"
int param v_trapshapecotesspiral
caption = "Version (Trap Shape Cotes' Spiral)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecotesspiral < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeDiamond(common.ulb:TrapShape) {
; This shape uses the diamond function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeDiamond(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
if @absval
d = abs(cabs(pz) - cabs(@a*@adfn(abs((real(pz)*@adj1))+sgn*abs((flip(imag(pz))^@adj2))-1)))
else
d = cabs(pz - @a*@adfn(abs((real(pz)*@adj1))+sgn*abs((flip(imag(pz))^@adj2))-1))
endif
m_LastZ = (@a*@adfn(abs((real(pz)*@adj1))+sgn*abs((flip(imag(pz))^@adj2))-1))
return d
endfunc
default:
title = "Diamond"
int param v_trapshapediamond
caption = "Version (Trap Shape Diamond)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapediamond < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param adj1
caption = "Adjuster 1"
default = 10.0
hint = "Affects spread and scale of trap"
endparam
float param adj2
caption = "Adjuster 2"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
func adfn
caption = "Adjuster function"
default = ident()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeDipoleCurve(common.ulb:TrapShape) {
; This shape uses the dipole function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeDipoleCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*(cos(theta))^2
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Dipole Curve"
int param v_trapshapedipolecurve
caption = "Version (Trap Shape Dipole Curve)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapedipolecurve < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeDumbellCurve(common.ulb:TrapShape) {
; This shape uses the dumbell function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeDumbellCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float cx = 0
float cy = 0
float d = 0
cx = real(pz)
cy = (cx^4-cx^6)^0.5
if @absval
d = abs(cabs(pz) - cabs(4*@a*(cx + sgn*flip(cy))))
else
d = cabs(pz - 4*@a*(cx + sgn*flip(cy)))
endif
m_LastZ = 4*@a*(cx + sgn*flip(cy))
return d
endfunc
default:
title = "Dumbell Curve"
int param v_trapshapedumbellcurve
caption = "Version (Trap Shape Dumbell Curve)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapedumbellcurve < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeEightCurve(common.ulb:TrapShape) {
; This shape uses the eight function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeEightCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*cos(theta)^(-2)*cos(2*theta)^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Eight Curve"
int param v_trapshapeeightcurve
caption = "Version (Trap Shape Eight Curve)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeeightcurve < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeEllipseCatacaustic(common.ulb:TrapShape) {
; This shape uses the ellipse catacaustic function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeEllipseCatacaustic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
complex af1 = 4*@a*(@a-@b)*(@a*@b)*sin(theta)^3/(@a^2+@b^2+(@b^2-@a^2)*cos(2*theta))
complex af2 = 4*@b*(@b^2-@a^2)*cos(theta)^3/(@a^2+@b^2+3*(@b^2-@a^2)*cos(2*theta))
complex as = 0.1*(af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - as)
endif
m_LastZ = as
return d
endfunc
default:
title = "Ellipse Catacaustic"
int param v_trapshapeellipsecatacaustic
caption = "Version (Trap Shape Ellipse Catacaustic)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeellipsecatacaustic < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeEllipseEvolute(common.ulb:TrapShape) {
; This shape uses the ellipse evolute function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeEllipseEvolute(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
complex af1 = (@a^2-(0.7*@b)^2)/@a*@afn1(theta)^(real(@pwr))
complex af2 = ((0.7*@b)^2-@a^2)/(0.7*@b)*@afn2(theta)^(imag(@pwr))
complex as = 0.1*(af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - as)
endif
m_LastZ = as
return d
endfunc
default:
title = "Ellipse Evolute"
int param v_trapshapeellipseevolute
caption = "Version (Trap Shape Ellipse Evolute)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeellipseevolute < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
complex param pwr
caption = "Power"
default = (3,3)
hint = "Affects shape and scale of trap."
endparam
func afn1
caption = "Function #1"
default = cos()
endfunc
func afn2
caption = "Function #2"
default = sin()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeEpicycloid(common.ulb:TrapShape) {
; This shape uses the epicycloid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeEpicycloid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
complex af1 = (5*@a+@b)*@afn1(theta) - @b*@afn1((5*@a+@b)*theta/@b)
complex af2 = (5*@a+@b)*@afn2(theta) - @b*@afn2((5*@a+@b)*theta/@b)
complex as = 0.1*(af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - as)
endif
m_LastZ = as
return d
endfunc
default:
title = "Epicycloid"
int param v_trapshapeepicycloid
caption = "Version (Trap Shape Epicycloid)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeepicycloid < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
func afn1
caption = "Function #1"
default = cos()
endfunc
func afn2
caption = "Function #2"
default = sin()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeEpispiral(common.ulb:TrapShape) {
; This shape uses the epispiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeEpispiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.25*@a/cos(@pn*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Epispiral"
int param v_trapshapeepispiral
caption = "Version (Trap Shape Epispiral)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeepispiral < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
int param pn
caption = "Polar integer"
default = 3
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeFoliumOfDescartes(common.ulb:TrapShape) {
; This shape uses the folium of Descartes function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeFoliumOfDescartes(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.3*@a*tan(theta)/(cos(theta)*(1+tan(theta)^3))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Folium Of Descartes"
int param v_trapshapefoliumofdescartes
caption = "Version (Trap Shape Folium Of Descartes)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapefoliumofdescartes < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeGearCurve(common.ulb:TrapShape) {
; This shape uses the gear curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeGearCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
complex af1 = (0.25*@a+1/(5*@b)*tanh(5*@b*sin(@pn*theta)))*cos(theta)
complex af2 = (0.25*@a+1/(5*@b)*tanh(5*@b*sin(@pn*theta)))*sin(theta)
complex as = (af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - as)
endif
m_LastZ = as
return d
endfunc
default:
title = "Gear Curve"
int param v_trapshapegearcurve
caption = "Version (Trap Shape Gear Curve)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapegearcurve < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
int param pn
caption = "Polar integer"
default = 3
hint = "Affects spread and scale of trap"
endparam
bool param wave
caption = "Add petal wave"
default = false
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeHipopede(common.ulb:TrapShape) {
; This shape uses the hipopede function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHipopede(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = (0.5*@b*(0.5*@a-(0.5*@b)^2*cos(theta)))^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Hipopede"
int param v_trapshapehipopede
caption = "Version (Trap Shape Hipopede)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapehipopede < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeHyperbola(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHyperbola(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.35*@a*(1/cos(2*theta))^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Hyperbola REB"
int param v_trapshapehyperbolareb
caption = "Version (Trap Shape Hyperbola REB)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapehyperbolareb < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeKampyleofEudoxus(common.ulb:TrapShape) {
; This shape uses the kampyle of Eudoxus function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKampyleofEudoxus(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.02*@a/cos(theta)^2
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Kampyle of Eudoxus"
int param v_trapshapekampyleofeudoxus
caption = "Version (Trap Shape Kampyle Of Eudoxus)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapekampyleofeudoxus < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeKappaCurve(common.ulb:TrapShape) {
; This shape uses the kapp a curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKappaCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.1*@a*tan(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Kappa Curve"
int param v_trapshapekappacurve
caption = "Version (Trap Shape Kappa Curve)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapekappacurve < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeKeratoidCusp(common.ulb:TrapShape) {
; This shape uses the keratoid cusp function.
; This variant of the function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKeratoidCusp(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float d = 0
complex cx = real(pz)
complex qa = 1
complex qb = -cx^2
complex qc = -cx^5
if @negroot == true
qy = (-qb - (qb^2 - 4*qa*qc)^0.5)/(2*qa)
else
qy = (-qb + (qb^2 - 4*qa*qc)^0.5)/(2*qa)
endif
if @absval == true
d = abs(cabs(pz) - cabs(2.5*@a*(cx + sgn*flip(qy))))
else
d = cabs(pz - 2.5*@a*(cx + sgn*flip(qy)))
endif
m_LastZ = 2.5*@a*(cx + sgn*flip(qy))
return d
endfunc
default:
title = "Keratoid Cusp"
int param v_trapshapekeratoidcusp
caption = "Version (Trap Shape Keratoid Cusp)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapekeratoidcusp < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = true
endparam
}
class REB_TrapShapeKnotCurve(common.ulb:TrapShape) {
; This shape uses the knot curve function.
; This variant of the function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKnotCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
x = real(@fn1(pz))
y = imag(@fn2(pz))
d = (x^2-1)^2-y^2*(2*y+3)+@offset
d = abs(d)
else
int sgn = 1
if @sgn
sgn = -1
endif
complex cy = imag(pz)
complex qx = 0
complex qa = 1
complex qb = -2
complex qc = 1 - 3*cy^2 - 2*cy^3
if @negroot == true
qx = ((-qb - (qb^2 - 4*qa*qc)^0.5)/(2*qa))^0.5
else
qx = ((-qb + (qb^2 - 4*qa*qc)^0.5)/(2*qa))^0.5
endif
if @absval == true
d = abs(cabs(pz) - cabs(@a*(qx + sgn*flip(cy))))
else
d = cabs(pz - @a*(qx + sgn*flip(cy)))
endif
m_LastZ = @a*(qx + sgn*flip(cy))
endif
return d
endfunc
default:
title = "KnotCurve"
int param v_trapshapeknotcurve
caption = "Version (Trap Shape Knot Curve)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeknotcurve < 101
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@altformula
endparam
param negroot
caption = "Quad Neg Root"
default = true
visible = !@altformula
endparam
}
class REB_TrapShapeLemniscate(common.ulb:TrapShape) {
; This shape uses the lemniscate function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLemniscate(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*(cos(2*theta))^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Lemniscate"
int param v_trapshapelemniscate
caption = "Version (Trap Shape Lemniscate)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapelemniscate < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeArcsOfSamothrace(common.ulb:TrapShape) {
; This shape uses the lemniscate function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeArcsOfSamothrace(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
if !@cmplx
x = real(@fn1(pz))
y = imag(@fn2(pz))
else
x = real(@fn1(pz))
y = imag(@fn1(pz))
endif
if @ref == "pz"
d = x^2*(@a1*x^2-@a2*y^2)^2-y^2*(x^2+y^2)-cabs(pz)*@offset
else
d = x^2*(@a1*x^2-@a2*y^2)^2-y^2*(x^2+y^2)-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*tan(theta)/(1+4*@b*cos(1.25*@c*theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
x = real(pz)
y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
endif
return d
endfunc
default:
title = "Arcs of Samothrace"
int param v_ArcsOfSamothrace
caption = "Version (ArcsOfSamothrace)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_ArcsOfSamothrace < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.2
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
bool param adv
caption = "advanced"
default = false
visible = @altformula
endparam
float param a1
caption = "parameter a1"
default = 3
visible = @adv && @altformula
endparam
float param a2
caption = "parameter a2"
default = 1
visible = @adv && @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
bool param cmplx
caption = "Apply to complex"
default = false
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula && !@cmplx
endfunc
bool param ptraps
caption = "Use as Polar Traps"
default = false
visible = !@altformula
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps && !@altformula
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param c
caption = "3rd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = !@altformula
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && !@altformula
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && !@altformula
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps && !@altformula
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps && !@altformula
endparam
bool param alttheta
caption = "Alternate theta"
default = false
visible = !@altformula
endparam
}
class REB_TrapShapeLimaconOfPascal(common.ulb:TrapShape) {
; This shape uses the limacon of Pascal function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLimaconOfPascal(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.05*@b + @a*cos(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Limacon Of Pascal"
int param v_trapshapelimaconofpascal
caption = "Version (Trap Shape Limacon Of Pascal)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapelimaconofpascal < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeLine(common.ulb:TrapShape) {
; This shape uses the ophiuride function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLine(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
float cx = real(pz)
float cy = cx
if @absval
d = abs(cabs(pz) - cabs(3*@a*(cx + sgn*flip(cy))))
else
d = cabs(pz - 3*@a*(cx + sgn*flip(cy)))
endif
m_LastZ = 3*@a*(cx + sgn*flip(cy))
return d
endfunc
default:
title = "Line"
int param v_trapshapeline
caption = "Version (Trap Shape Line)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeline < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeLinksCurve(common.ulb:TrapShape) {
; This shape uses the links curve function.
; This variant of the function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLinksCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
float cx = real(pz)
float qa = 1
float qb = 2*cx^2-6*cx
float qc = cx^4-2*cx^3+cx^2
if @negroot
qy = ((-qb - (qb^2 - 4*qa*qc)^0.5)/(2*qa))^0.5
else
qy = ((-qb + (qb^2 - 4*qa*qc)^0.5)/(2*qa))^0.5
endif
if @absval
d = abs(cabs(pz) - cabs(@a*(cx + sgn*flip(qy))))
else
d = cabs(pz - @a*(cx + sgn*flip(qy)))
endif
m_LastZ = @a*(cx + sgn*flip(qy))
return d
endfunc
default:
title = "Links Curve"
int param v_trapshapelinkscurve
caption = "Version (Trap Shape Links Curve)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapelinkscurve < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = true
endparam
}
class REB_TrapShapeLituus(common.ulb:TrapShape) {
; This shape uses the lituus function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLituus(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.25*@a/theta^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Lituus"
int param v_trapshapelituus
caption = "Version (Trap Shape Lituus)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapelituus < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeLogSpiral(common.ulb:TrapShape) {
; This shape uses the log spiral function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLogSpiral(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = exp(@a*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Log Spiral"
int param v_trapshapelogspiral
caption = "Version (Trap Shape Log Spiral)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapelogspiral < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeLogSpiralCatacaustic(common.ulb:TrapShape) {
; This shape uses the log spiral catacaustic function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLogSpiralCatacaustic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
complex af1 = 0.2*@b*exp(0.1*@b*theta)*(0.1*@b*cos(theta)-sin(theta))/(1+(0.1*@b)^2)
complex af2 = 0.2*@b*exp(0.1*@b*theta)*(0.1*@b*cos(theta)+sin(theta))/(1+(0.1*@b)^2)
complex as = @a*(af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - as)
endif
m_LastZ = as
return d
endfunc
default:
title = "Log Spiral Catacaustic"
int param v_trapshapelogspiralcatacaustic
caption = "Version (Trap Shape Log Spiral Catacaustic)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapelogspiralcatacaustic < 102
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeMalteseCross(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeMalteseCross(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.2*@a/(cos(theta)*sin(theta)*(cos(theta)^2-sin(theta)^2))^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Maltese Cross"
int param v_trapshapemaltesecross
caption = "Version (Trap Shape Maltese Cross)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapemaltesecross < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeNephroid(common.ulb:TrapShape) {
; This shape uses the nephroid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeNephroid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
complex af1 = 3*@afn1(theta) - @afn1(theta/3)
complex af2 = 3*@afn2(theta) - @afn2(theta/3)
complex as = 0.5*@a*(af1+sgn*flip(af2))
m_LastZ = as
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - (as))
endif
return d
endfunc
default:
title = "Nephroid"
int param v_trapshapenephroid
caption = "Version (Trap Shape Nephroid)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapenephroid < 102
endparam
float param a
caption = "Polar Parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
func afn1
caption = "Function #1"
default = cos()
endfunc
func afn2
caption = "Function #2"
default = sin()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeParabola(common.ulb:TrapShape) {
; This shape uses the parabola function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeParabola(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
float cy = imag(pz)
float cx = 10*@b*cy^2
m_LastZ = 0.65*@a*(cx + sgn*flip(cy))
if @absval
d = abs(cabs(pz) - cabs(0.65*@a*(cx + sgn*flip(cy))))
else
d = cabs(pz - 0.65*@a*(cx + sgn*flip(cy)))
endif
return d
endfunc
default:
title = "Parabola"
int param v_trapshapeparabola
caption = "Version (Trap Shape Parabola)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeparabola < 101
endparam
float param a
caption = "Polar Parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar Parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeTridentOfNewton(common.ulb:TrapShape) {
; This shape uses the Trident Of Newton function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeTridentOfNewton(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
float cx = real(pz)
float cy = cx^2 + @b*cx - @c + 0.02*@d/cx
m_LastZ = @a*(cx + sgn*flip(cy))
if @absval
d = abs(cabs(pz) - cabs(m_LastZ))
else
d = cabs(pz - m_LastZ)
endif
return d
endfunc
default:
title = "Trident Of Newton"
int param v_TridentOfNewton
caption = "Version (Trident Of Newton)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_TridentOfNewton < 100
endparam
float param a
caption = "Polar Parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar Parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd Polar Parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
float param d
caption = "4th Polar Parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeWassenaarCurve(common.ulb:TrapShape) {
; This shape uses the Wassenaar Curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeWassenaarCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
complex cx = real(pz)
complex cy = 0
if @negroot
cy = cx^2 - (1-30*@b*cx^2)^0.5
else
cy = cx^2 + (1-30*@b*cx^2)^0.5
endif
m_LastZ = @a*(cx + sgn*flip(cy))
if @absval
d = abs(cabs(pz) - cabs(m_LastZ))
else
d = cabs(pz - m_LastZ)
endif
return d
endfunc
default:
title = "Wassenaar Curve"
int param v_WassenaarCurve
caption = "Version (Wassenaar Curve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_WassenaarCurve < 100
endparam
float param a
caption = "Polar Parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar Parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = false
endparam
}
class REB_TrapShapeWeibullCurve(common.ulb:TrapShape) {
; This shape uses the Weibull Curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeWeibullCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
complex cx = real(pz)
complex cy = exp(-cx^(@b/10))
m_LastZ = @a*(cx + sgn*flip(cy))
if @absval
d = abs(cabs(pz) - cabs(m_LastZ))
else
d = cabs(pz - m_LastZ)
endif
return d
endfunc
default:
title = "Weibull Curve"
int param v_WeibullCurve
caption = "Version (Weibull Curve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_WeibullCurve < 100
endparam
float param a
caption = "Polar Parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar Parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapePiriform(common.ulb:TrapShape) {
; This shape uses the piriform function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapePiriform(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float theta = 0
int sgn = 1
if @sgn
sgn = -1
endif
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
complex af1 = 0.1*@a*(1+sin(theta))
complex af2 = 0.1*@b*cos(theta)*(1+sin(theta))
complex as = (af1 + sgn*flip(af2))
m_LastZ = as
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - as)
endif
return d
endfunc
default:
title = "Piriform"
int param v_trapshapepiriform
caption = "Version (Trap Shape Piriform)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapepiriform < 102
endparam
float param a
caption = "Polar Parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar Parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapePoinsotSpiral1(common.ulb:TrapShape) {
; This shape uses the Poinsot spiral 1 function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapePoinsotSpiral1(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a/cosh(@pn*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Poinsot Spiral 1"
int param v_trapshapepoinsotspiral1
caption = "Version (Trap Shape Poinsot Spiral 1)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapepoinsotspiral1 < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
int param pn
caption = "Polar integer"
default = 3
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapePoinsotSpiral2(common.ulb:TrapShape) {
; This shape uses the Poinsot spiral 2 function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapePoinsotSpiral2(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a/sinh(@pn*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Poinsot Spiral 2"
int param v_trapshapepoinsotspiral2
caption = "Version (Trap Shape Poinsot Spiral 2)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapepoinsotspiral2 < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
int param pn
caption = "Polar integer"
default = 3
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapePolytrope(common.ulb:TrapShape) {
; This shape uses the polytrope function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapePolytrope(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
float cx = real(pz)
float cy = 1/cx^@pn
if @absval
d = abs(cabs(pz) - cabs(0.00005*@a*(cx + sgn*flip(cy))))
else
d = cabs(pz - 0.00005*@a*(cx + sgn*flip(cy)))
endif
m_LastZ = 0.00005*@a*(cx + sgn*flip(cy))
return d
endfunc
default:
title = "Polytrope"
int param v_trapshapepolytrope
caption = "Version (Trap Shape Polytrope)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapepolytrope < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
int param pn
caption = "Polar integer"
default = 3
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeQuadratrixOfHippias(common.ulb:TrapShape) {
; This shape uses the quadratrix of Hippias function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeQuadratrixOfHippias(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*theta/sin(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Quadratrix of Hippias"
int param v_trapshapequadratrixofhippias
caption = "Version (Trap Shape Quadratrix Of Hippias)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapequadratrixofhippias < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeQuadrifolium(common.ulb:TrapShape) {
; This shape uses the quadrifolium function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeQuadrifolium(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*sin(2*theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Quadrifolium"
int param v_trapshapequadrifolium
caption = "Version (Trap Shape Quadrifolium)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapequadrifolium < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeRose(common.ulb:TrapShape) {
; This shape uses the rose function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeRose(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*cos(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Rose"
int param v_trapshaperose
caption = "Version (Trap Shape Rose)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshaperose < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeSuperRose(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSuperRose(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float theta = 0
float d = 0
float rr = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
rr = @g*sin(@f*theta*(abs(cos(@d*theta))^@a + abs(sin(@d*theta))^@b)^@c)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Super Rose"
int param v_trapshapeSuperRose
caption = "Version (Trap Shape Super Rose)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeSuperRose < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param g
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param a
caption = "Shape 1"
default = 2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "Shape 2"
default = 2
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "Shape 3"
default =3
hint = "Affects spread and scale of trap"
endparam
float param d
caption = "Shape 4"
default = 2
hint = "Affects spread and scale of trap"
endparam
float param f
caption = "Shape 5"
default = 5
hint = "Affects spread and scale of trap"
endparam
bool param @wave
caption = "Add petal wave"
default = false
endparam
float param @wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave
endparam
float param @wfreq
caption = "Wave frequency"
default = 20
visible = @wave
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeRoseOfTroy(common.ulb:TrapShape) {
; This shape uses the rose of Troy function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeRoseOfTroy(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @c*(1+10*@a*sin(4*@b*theta))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Rose of Troy"
int param v_trapshaperoseoftroy
caption = "Version (Trap Shape Rose Of Troy)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshaperoseoftroy < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
float param c
caption = "3rd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeScarabaeus(common.ulb:TrapShape) {
; This shape uses the scarabaeus function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeScarabaeus(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.25*@b*cos(2*theta)-0.5*@a*cos(theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Scarabaeus"
int param v_trapshapescarabaeus
caption = "Version (Trap Shape Scarabaeus)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapescarabaeus < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeSemicubicalParabola(common.ulb:TrapShape) {
; This shape uses the semicubical parabola function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSemicubicalParabola(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*(cos(2*@b*theta))^(1/(2*@b))
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Semicubical Parabola"
int param v_trapshapesemicubicalparabola
caption = "Version (Trap Shape Semicubical Parabola)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesemicubicalparabola < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeSerpentineCurve(common.ulb:TrapShape) {
; This shape uses the serpentine curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSerpentineCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
complex af1 = 0.2*@a*cotan(theta)
complex af2 = 0.2*@b*sin(theta)*cos(theta)
complex as = (af1 + sgn*flip(af2))
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - as)
endif
m_LastZ = pz - as
return d
endfunc
default:
title = "Serpentine Curve"
int param v_trapshapeserpentinecurve
caption = "Version (Trap Shape Serpentine Curve)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeserpentinecurve < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
class REB_TrapShapeStirrupCurve(common.ulb:TrapShape) {
; This shape uses the stirrup curve function.
; This variant of the function involves taking a square root
; so there are two solutions. A signed and absolute value version of
; the distance is also available. The transformed value is the
; complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeStirrupCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
int sgn = 1
if @sgn
sgn = -1
endif
float cy = imag(pz)
float qa = 1
float qb = -2
float qc = 1-cy^2*(cy-1)*(cy-2)*(cy+5)
float qx = 0
if @negroot
qx = ((-qb - (qb^2 - 4*qa*qc)^0.5)/(2*qa))^0.5
else
qx = ((-qb + (qb^2 - 4*qa*qc)^0.5)/(2*qa))^0.5
endif
if @absval
d = abs(cabs(pz) - cabs(@a*(qx + sgn*flip(cy))))
else
d = cabs(pz - @a*(qx + sgn*flip(cy)))
endif
m_LastZ = @a*(qx + sgn*flip(cy))
return d
endfunc
default:
title = "Stirrup Curve"
int param v_trapshapestirrupcurve
caption = "Version (Trap Shape Stirrup Curve)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapestirrupcurve < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
param negroot
caption = "Quad Neg Root"
default = true
endparam
}
class REB_TrapShapeStrophoid(common.ulb:TrapShape) {
; This shape uses the strophoid function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeStrophoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.1*@b*sin(@a-2*theta)/sin(@a-theta)
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Strophoid"
int param v_trapshapestrophoid
caption = "Version (Trap Shape Strophoid)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapestrophoid < 101
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects shape and scale of trap."
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
}
class REB_TrapShapeSwastikaCurve(common.ulb:TrapShape) {
; This shape uses the swastika curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate and a
; polar variant. The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSwastikaCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
rr = 0.25*@a*(sin(theta)*cos(theta)/(sin(theta)^4-cos(theta)^4))^0.5
if !@ptraps
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta)+ sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
else
float x = real(pz)
float y = imag(pz)
if @disttype == 0
d = abs(x-rr*cos(theta) + y-rr*sin(theta))
else
d = (abs(x-rr*cos(theta)) + abs(y-rr*sin(theta)))
endif
m_LastZ = x-rr*cos(theta) + flip(y-rr*sin(theta))
endif
return d
endfunc
default:
title = "Swastika Curve"
int param v_trapshapeswastikacurve
caption = "Version (Trap Shape Swastika Curve)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeswastikacurve < 102
endparam
bool param ptraps
caption = "Use as Polar Traps"
default = false
endparam
param disttype
caption = "Distance type"
default = 0
enum = "Abs total" "Abs parts"
visible = @ptraps
hint = "The distance function must be positive. \
The absolute value can be taken of the \
whole function or of its individual parts."
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
visible = !@ptraps
endparam
param absval
caption = "Absolute Value"
default = false
visible = !@ptraps
endparam
bool param alttheta
caption = "Alternate theta"
default = false
endparam
}
class REB_TrapShapeTeardropCurve(common.ulb:TrapShape) {
; This shape uses the teardrop curve function.
; This variant of the function has a signed and absolute value
; version of the distance. The function also has a complex conjugate variant.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeTeardropCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
if !@alttheta
theta = atan2(pz)
else
theta = atan(imag(pz)/real(pz))
endif
int sgn = 1
if @sgn
sgn = -1
endif
complex af1 = @a*cos(theta)
complex af2 = 0.5*@b*sin(theta)*sin(theta/2)^(@pn-1)
complex as = (af1 + sgn*flip(af2))
m_LastZ = as
if @absval
d = abs(cabs(pz) - cabs(as))
else
d = cabs(pz - (as))
endif
return d
endfunc
default:
title = "Teardrop Curve"
int param v_trapshapeteardropcurve
caption = "Version (Trap Shape Teardrop Curve)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeteardropcurve < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float par
; @param target = sphere to be inverted
; @param inverter = not used.
; @param level = recursion level
; @param gen = index of generator matrix
;------------------------------------------------
Sphere func Inverse(Sphere target, Sphere inverter, int level, int gen)
mob[5] = new Mobius(0,0,0,0)
mob[5].CircToMob(target)
mob[gen].MConj(mob[5],mob[5])
Sphere ns = new Sphere(0,0,0,0,0)
mob[5].MobToCirc(level,gen,ns)
return ns
endfunc
; Top level recursion function
func Recurse()
int l = 0
int ir = 0
int si = 0
int sj = 0
int j = 0
bool done = false
int c = 0
float ddx = 0
float ddy = 0
float ddr = 0
sphere rra
bool continue = false
int ifinal = 0
int istack = 0
int nold = 0
int nfinal = 1
int iii = 0
int k = 0
int lev = 0
if @showcusp == "Both"
j = 3
iii = 2
elseif @showcusp == "Standard"
j = 1
iii = 0
else
j = 2
iii = 1
endif
if @cusptype == "Grandma's Special #2"
if @showcusp == "Both"
j = 4
iii = 3
else
j = 2
iii = 1
endif
endif
if @cusptype == "Maskit"
if @showcuspm == "Both" || (@showcuspm == "Predefined" && \
@showcuspm2 == "Both")
j = 2
iii = 1
else
j = 1
iii = 0
endif
endif
iii = iii + 1
lev = 1
while lev <= mlevel && j < flength
gi = 0
while gi < iend && j < flength
k = 0
while k <= iii && j < flength
ss.sph[j] = Inverse(ss.sph[k],ss.sph[0],lev,gi)
if ss.sph[j].frad >= 0 && abs(ss.sph[j].frad) < fminsphere
j = j - 1
endif
if j > flength
lev = mlevel + 1
k = iii + 1
endif
j = j+1
k = k + 1
endwhile
if j > flength
gi = 5
endif
gi = gi + 1
endwhile
; sort array by circle identity
l = round(j/2)+1
ir = j
continue = true
repeat
if l > 1
l = l-1
rra = ss.sph[l-1]
else
rra = ss.sph[ir-1]
ss.sph[ir-1] = ss.sph[0]
ir = ir-1
if ir == 0
ss.sph[0] = rra
continue = false
endif
endif
if continue == true
si = l
sj = 2*l
endif
while (sj <= ir) && (continue == true)
if sj < ir
ddx = real(ss.sph[sj-1].fcen)-real(ss.sph[sj].fcen)
ddy = imag(ss.sph[sj-1].fcen)-imag(ss.sph[sj].fcen)
ddr = ss.sph[sj-1].frad-ss.sph[sj].frad
c = 0
done = false
; Lines precede circles
if ss.sph[sj-1].frad <= 0 && ss.sph[sj].frad > 0
c = -1
done = true
elseif ss.sph[sj].frad <= 0 && ss.sph[sj-1].frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif ss.sph[sj-1].frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
sj = sj + 1
endif
endif
ddx = real(rra.fcen)-real(ss.sph[sj-1].fcen)
ddy = imag(rra.fcen)-imag(ss.sph[sj-1].fcen)
ddr = rra.frad-ss.sph[sj-1].frad
c = 0
done = false
; ; Lines precede circles
if rra.frad <= 0 && ss.sph[sj-1].frad > 0
c = -1
done = true
elseif ss.sph[sj-1].frad <= 0 && rra.frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif rra.frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
ss.sph[si-1] = ss.sph[sj-1]
si = sj
sj = sj + sj
else
sj = ir + 1
endif
endwhile
if (continue == true)
ss.sph[si-1] = rra
endif
until continue == false
; eliminate duplicates in place
; ir = oldj-iii+1
; l = oldj-iii
ir = j+1
l = j
while ir < j
ddx = real(ss.sph[ir].fcen)-real(ss.sph[ir-1].fcen)
ddy = imag(ss.sph[ir].fcen)-imag(ss.sph[ir-1].fcen)
ddr = ss.sph[ir].frad-ss.sph[ir-1].frad
c = 0
done = false
; Lines precede circles
if ss.sph[ir].frad <= 0 && ss.sph[ir-1].frad > 0
c = -1
done = true
elseif ss.sph[ir-1].frad <= 0 && ss.sph[ir].frad > 0
c = 1
done = true
elseif ddx < -thresh && !done
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif ss.sph[ir].frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c == 0
ir = ir + 1
else
ss.sph[l] = ss.sph[ir]
ir = ir +1
l = l + 1
endif
endwhile
j = j-(ir-l)+1
; move to final array, skipping dups
ifinal = 0
istack = 0
nold = nfinal
while ifinal < nold && istack < j && nfinal < flength
ddx = real(s.sph[ifinal].fcen)-real(ss.sph[istack].fcen)
ddy = imag(s.sph[ifinal].fcen)-imag(ss.sph[istack].fcen)
ddr = s.sph[ifinal].frad-ss.sph[istack].frad
c = 0
done = false
; Lines precede circles
if s.sph[ifinal].frad <= 0 && ss.sph[istack].frad > 0
c = -1
done = true
elseif ss.sph[istack].frad <= 0 && s.sph[ifinal].frad > 0
c = 1
done = true
elseif ddx < -thresh
c = -1
done = true
elseif ddx > thresh && !done
c = 1
done = true
elseif ddy < -thresh && !done
c = -1
done = true
elseif ddy > thresh && !done
c = 1
done = true
elseif s.sph[ifinal].frad <= 0 && !done ; Lines
if ddr < -PARAFUZZ && !done
c = -1
done = true
elseif ddr > PARAFUZZ && !done
c = 1
done = true
endif
elseif !done ; Circles
if ddr < -thresh && !done
c = -1
done = true
elseif ddr > thresh && !done
c = 1
done = true
endif
endif
if c < 0
ifinal = ifinal + 1
endif
if c == 0
istack = istack + 1
endif
if c > 0
s.sph[nfinal] = ss.sph[istack]
nfinal = nfinal + 1
istack = istack + 1
endif
endwhile
while istack < j && nfinal < flength
s.sph[nfinal] = ss.sph[istack]
nfinal = nfinal + 1
istack = istack + 1
endwhile
ir = nold
while ir
; Mathematical Curves
;
;
class REB_TrapShapeIkenaga(common.ulb:TrapShape) {
; Uses the Ikenaga fractal function as the trap
public:
import "common.ulb"
; Constructor
func REB_TrapShapeIkenaga(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
complex p = pz*@scale
p = @fn1(p)
int ike_iter = 0
complex c = #pixel
while ike_iter < @max_iterations
p = p*p*p +(c-1)*p - c
ike_iter = ike_iter + 1
endwhile
m_LastZ = @fn2(p)
float d = abs(|pz| - |m_LastZ|)
return d
endfunc
default:
title = "Ikenaga"
int param v_trapshapeikenaga
caption = "Version (Trap Shape Ikenaga)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeikenaga < 101
endparam
float param scale
caption = "Scale"
default = 1.0
endparam
param max_iterations
caption = "Ikenaga iterations"
hint = "This is the number of iterations for the Ikenaga formula."
default = 1
endparam
func fn1
caption = "Pre Function"
default = atan()
endfunc
func fn2
caption = "Post Function"
default = sinh()
endfunc
}
class REB_TrapShapePlatonicSolids(common.ulb:TrapShape) {
public:
import "common.ulb"
import "reb.ulb"
$define debug
; Constructor
func REB_TrapShapePlatonicSolids(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call before each iteration
func Init(complex pz)
TrapShape.Init(pz)
twopi = 2*#pi
mx = 0
my = 0
i = 0
x = 0.0
y = 0.0
out = false
rotx = @rotx+1e-10
roty = @roty+1e-10
rotz = @rotz+1e-10
if @polygontype == "Tetrahedron"
vertex = 4
side = 6
i = 0
vx[0] = 0.5
vy[0] = 0.5
vz[0] = 0.5
vx[1] = -0.5
vy[1] = -0.5
vz[1] = 0.5
vx[2] = 0.5
vy[2] = -0.5
vz[2] = 0.5
vx[3] = -0.5
vy[3] = 0.5
vz[3] = -0.5
repeat
rot.rotatex(vx[i],vy[i],vz[i],rotx)
rot.rotatey(vx[i],vy[i],vz[i],roty)
rot.rotatez(vx[i],vy[i],vz[i],rotz)
i = i + 1
until i == vertex
i = 0
repeat
v[i] = vx[i] + flip(vy[i])
i = i+1
until i == vertex
elseif @polygontype == "Cube"
vertex = 8
side = 12
i = 0
vx[0] = 0.5
vy[0] = 0.5
vz[0] = 0.5
vx[1] = 0.5
vy[1] = -0.5
vz[1] = 0.5
vx[2] = -0.5
vy[2] = -0.5
vz[2] = 0.5
vx[3] = -0.5
vy[3] = 0.5
vz[3] = 0.5
vx[4] = -0.5
vy[4] = 0.5
vz[4] = -0.5
vx[5] = 0.5
vy[5] = 0.5
vz[5] = -0.5
vx[6] = 0.5
vy[6] = -0.5
vz[6] = -0.5
vx[7] = -0.5
vy[7] = -0.5
vz[7] = -0.5
repeat
rot.rotatex(vx[i],vy[i],vz[i],rotx)
rot.rotatey(vx[i],vy[i],vz[i],roty)
rot.rotatez(vx[i],vy[i],vz[i],rotz)
i = i + 1
until i == vertex
i = 0
repeat
v[i] = vx[i] + flip(vy[i])
i = i+1
until i == vertex
elseif @polygontype == "Octahedron"
vertex = 6
side = 12
i = 0
vx[0] = 0.7071
vy[0] = 0
vz[0] = 0
vx[1] = 0
vy[1] = -0.7071
vz[1] = 0
vx[2] = 0
vy[2] = 0
vz[2] = 0.7071
vx[3] = 0
vy[3] = 1
vz[3] = 0
vx[4] = -0.7071
vy[4] = 0
vz[4] = 0
vx[5] = 0
vy[5] = 0
vz[5] = -0.7071
repeat
rot.rotatex(vx[i],vy[i],vz[i],rotx)
rot.rotatey(vx[i],vy[i],vz[i],roty)
rot.rotatez(vx[i],vy[i],vz[i],rotz)
i = i + 1
until i == vertex
i = 0
repeat
v[i] = vx[i] + flip(vy[i])
i = i+1
until i == vertex
elseif @polygontype == "Icosahedron"
vertex = 12
side = 30
i = 0
vx[0] = 0
vy[0] = 0
vz[0] = 1
vx[1] = 0.894
vy[1] = 0
vz[1] = 0.447
vx[2] = 0.276
vy[2] = 0.851
vz[2] = 0.447
vx[3] = -0.724
vy[3] = 0.526
vz[3] = 0.447
vx[4] = -0.724
vy[4] = -0.526
vz[4] = 0.447
vx[5] = 0.276
vy[5] = -0.851
vz[5] = 0.447
vx[6] = 0.724
vy[6] = 0.526
vz[6] = -0.447
vx[7] = -0.276
vy[7] = 0.851
vz[7] = -0.447
vx[8] = -0.894
vy[8] = 0
vz[8] = -0.447
vx[9] = -0.276
vy[9] = -0.851
vz[9] = -0.447
vx[10] = 0.724
vy[10] = -0.526
vz[10] = -0.447
vx[11] = 0
vy[11] = 0
vz[11] = -1
repeat
rot.rotatex(vx[i],vy[i],vz[i],rotx)
rot.rotatey(vx[i],vy[i],vz[i],roty)
rot.rotatez(vx[i],vy[i],vz[i],rotz)
i = i + 1
until i == vertex
i = 0
repeat
v[i] = vx[i] + flip(vy[i])
i = i+1
until i == vertex
elseif @polygontype == "Dodecahedron"
vertex = 20
side = 30
i = 0
vx[0] = 0.607
vy[0] = 0
vz[0] = 0.795
vx[1] = 0.188
vy[1] = 0.577
vz[1] = 0.795
vx[2] = -0.491
vy[2] = 0.357
vz[2] = 0.795
vx[3] = -0.491
vy[3] = -0.357
vz[3] = 0.795
vx[4] = 0.188
vy[4] = -0.577
vz[4] = 0.795
vx[5] = 0.982
vy[5] = 0
vz[5] = 0.188
vx[6] = 0.304
vy[6] = 0.934
vz[6] = 0.188
vx[7] = -0.795
vy[7] = 0.577
vz[7] = 0.188
vx[8] = -0.894
vy[8] = -0.577
vz[8] = 0.188
vx[9] = 0.304
vy[9] = -0.934
vz[9] = 0.188
vx[10] = 0.795
vy[10] = 0.577
vz[10] = -0.188
vx[11] = -0.304
vy[11] = 0.934
vz[11] = -0.188
vx[12] = -0.982
vy[12] = 0.000
vz[12] = -0.188
vx[13] = -0.304
vy[13] = -0.934
vz[13] = -0.188
vx[14] = 0.795
vy[14] = -0.577
vz[14] = -0.188
vx[15] = 0.491
vy[15] = 0.357
vz[15] = -0.795
vx[16] = -0.188
vy[16] = 0.577
vz[16] = -0.795
vx[17] = -0.607
vy[17] = 0
vz[17] = -0.795
vx[18] = -0.188
vy[18] = -0.577
vz[18] = -0.795
vx[19] = 0.491
vy[19] = -0.357
vz[19] = -0.795
repeat
rot.rotatex(vx[i],vy[i],vz[i],rotx)
rot.rotatey(vx[i],vy[i],vz[i],roty)
rot.rotatez(vx[i],vy[i],vz[i],rotz)
i = i + 1
until i == vertex
i = 0
repeat
v[i] = (vx[i] + flip(vy[i]))/0.713644
i = i+1
until i == vertex
endif
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
d = 1e10
size = @size
complex pzs = pz/size
i = 0
;
; calculate r[i] and t[i] for first n-1 sides
;
if @polygontype == "Tetrahedron"
;
; front face
repeat
t[i]=(pzs-v[i])/(v[i+1]-v[i])
x=real(t[i])
y=imag(t[i])
if y > 0
out = false
endif
if(x<0.0)
r[i]=sqr(x)+sqr(y)
elseif(x>1.0)
r[i]=sqr(x-1.0)+sqr(y)
else
r[i]=sqr(y)
endif
r[i]=sqrt(r[i])*cabs(v[i+1]-v[i])
i = i + 1
until i == 3
;
; calculate r[i] and t[i] for the last side of front face
;
t[2]=(pzs-v[2])/(v[0]-v[2])
x=real(t[2])
y=imag(t[2])
if y > 0
out = false
endif
if(x<0.0)
r[2]=sqr(x)+sqr(y)
elseif(x>1.0)
r[2]=sqr(x-1.0)+sqr(y)
else
r[2]=sqr(y)
endif
r[2]=sqrt(r[2])*cabs(v[0]-v[2])
;
; right side
;
t[3]=(pzs-v[3])/(v[0]-v[3])
x=real(t[3])
y=imag(t[3])
if y > 0
out = false
endif
if(x<0.0)
r[3]=sqr(x)+sqr(y)
elseif(x>1.0)
r[3]=sqr(x-1.0)+sqr(y)
else
r[3]=sqr(y)
endif
r[3]=sqrt(r[3])*cabs(v[0]-v[3])
t[4]=(pzs-v[3])/(v[1]-v[3])
x=real(t[4])
y=imag(t[4])
if y > 0
out = false
endif
if(x<0.0)
r[4]=sqr(x)+sqr(y)
elseif(x>1.0)
r[4]=sqr(x-1.0)+sqr(y)
else
r[4]=sqr(y)
endif
r[4]=sqrt(r[4])*cabs(v[1]-v[3])
;
; left side
;
t[5]=(pzs-v[3])/(v[2]-v[3])
x=real(t[5])
y=imag(t[5])
if y > 0
out = false
endif
if(x<0.0)
r[5]=sqr(x)+sqr(y)
elseif(x>1.0)
r[5]=sqr(x-1.0)+sqr(y)
else
r[5]=sqr(y)
endif
r[5]=sqrt(r[5])*cabs(v[2]-v[3])
elseif @polygontype == "Cube"
;
; front face
repeat
t[i]=(pzs-v[i])/(v[i+1]-v[i])
x=real(t[i])
y=imag(t[i])
if y > 0
out = false
endif
if(x<0.0)
r[i]=sqr(x)+sqr(y)
elseif(x>1.0)
r[i]=sqr(x-1.0)+sqr(y)
else
r[i]=sqr(y)
endif
r[i]=sqrt(r[i])*cabs(v[i+1]-v[i])
i = i + 1
until i == (vertex-5)
;
; calculate r[i] and t[i] for the last side of front face
;
t[vertex-5]=(pzs-v[vertex-5])/(v[0]-v[vertex-5])
x=real(t[vertex-5])
y=imag(t[vertex-5])
if y > 0
out = false
endif
if(x<0.0)
r[vertex-5]=sqr(x)+sqr(y)
elseif(x>1.0)
r[vertex-5]=sqr(x-1.0)+sqr(y)
else
r[vertex-5]=sqr(y)
endif
r[vertex-5]=sqrt(r[vertex-5])*cabs(v[0]-v[vertex-5])
;
; top face
;
t[4]=(pzs-v[4])/(v[3]-v[4])
x=real(t[4])
y=imag(t[4])
if y > 0
out = false
endif
if(x<0.0)
r[4]=sqr(x)+sqr(y)
elseif(x>1.0)
r[4]=sqr(x-1.0)+sqr(y)
else
r[4]=sqr(y)
endif
r[4]=sqrt(r[4])*cabs(v[3]-v[4])
t[5]=(pzs-v[5])/(v[4]-v[5])
x=real(t[5])
y=imag(t[5])
if y > 0
out = false
endif
if(x<0.0)
r[5]=sqr(x)+sqr(y)
elseif(x>1.0)
r[5]=sqr(x-1.0)+sqr(y)
else
r[5]=sqr(y)
endif
r[5]=sqrt(r[5])*cabs(v[4]-v[5])
t[6]=(pzs-v[5])/(v[0]-v[5])
x=real(t[6])
y=imag(t[6])
if y > 0
out = false
endif
if(x<0.0)
r[6]=sqr(x)+sqr(y)
elseif(x>1.0)
r[6]=sqr(x-1.0)+sqr(y)
else
r[6]=sqr(y)
endif
r[6]=sqrt(r[6])*cabs(v[0]-v[5])
;
; right face
;
t[7]=(pzs-v[6])/(v[1]-v[6])
x=real(t[7])
y=imag(t[7])
if y > 0
out = false
endif
if(x<0.0)
r[7]=sqr(x)+sqr(y)
elseif(x>1.0)
r[7]=sqr(x-1.0)+sqr(y)
else
r[7]=sqr(y)
endif
r[7]=sqrt(r[7])*cabs(v[1]-v[6])
t[8]=(pzs-v[6])/(v[5]-v[6])
x=real(t[8])
y=imag(t[8])
if y > 0
out = false
endif
if(x<0.0)
r[8]=sqr(x)+sqr(y)
elseif(x>1.0)
r[8]=sqr(x-1.0)+sqr(y)
else
r[8]=sqr(y)
endif
r[8]=sqrt(r[8])*cabs(v[5]-v[6])
;
; bottom face
;
t[9]=(pzs-v[7])/(v[2]-v[7])
x=real(t[9])
y=imag(t[9])
if y > 0
out = false
endif
if(x<0.0)
r[9]=sqr(x)+sqr(y)
elseif(x>1.0)
r[9]=sqr(x-1.0)+sqr(y)
else
r[9]=sqr(y)
endif
r[9]=sqrt(r[9])*cabs(v[2]-v[7])
t[10]=(pzs-v[7])/(v[6]-v[7])
x=real(t[10])
y=imag(t[10])
if y > 0
out = false
endif
if(x<0.0)
r[10]=sqr(x)+sqr(y)
elseif(x>1.0)
r[10]=sqr(x-1.0)+sqr(y)
else
r[10]=sqr(y)
endif
r[10]=sqrt(r[10])*cabs(v[6]-v[7])
;
; back face
;
t[11]=(pzs-v[7])/(v[4]-v[7])
x=real(t[11])
y=imag(t[11])
if y > 0
out = false
endif
if(x<0.0)
r[11]=sqr(x)+sqr(y)
elseif(x>1.0)
r[11]=sqr(x-1.0)+sqr(y)
else
r[11]=sqr(y)
endif
r[11]=sqrt(r[11])*cabs(v[4]-v[7])
elseif @polygontype == "Octahedron"
;
; lower right face
;
repeat
t[i]=(pzs-v[i])/(v[i+1]-v[i])
x=real(t[i])
y=imag(t[i])
if y > 0
out = false
endif
if(x<0.0)
r[i]=sqr(x)+sqr(y)
elseif(x>1.0)
r[i]=sqr(x-1.0)+sqr(y)
else
r[i]=sqr(y)
endif
r[i]=sqrt(r[i])*cabs(v[i+1]-v[i])
i = i + 1
until i == 3
; endif
t[2]=(pzs-v[2])/(v[0]-v[2])
x=real(t[2])
y=imag(t[2])
if y > 0
out = false
endif
if(x<0.0)
r[2]=sqr(x)+sqr(y)
elseif(x>1.0)
r[2]=sqr(x-1.0)+sqr(y)
else
r[2]=sqr(y)
endif
r[2]=sqrt(r[2])*cabs(v[0]-v[2])
;
; upper right face
;
t[3]=(pzs-v[3])/(v[0]-v[3])
x=real(t[3])
y=imag(t[3])
if y > 0
out = false
endif
if(x<0.0)
r[3]=sqr(x)+sqr(y)
elseif(x>1.0)
r[3]=sqr(x-1.0)+sqr(y)
else
r[3]=sqr(y)
endif
r[3]=sqrt(r[3])*cabs(v[0]-v[3])
t[7]=(pzs-v[3])/(v[2]-v[3])
x=real(t[7])
y=imag(t[7])
if y > 0
out = false
endif
if(x<0.0)
r[7]=sqr(x)+sqr(y)
elseif(x>1.0)
r[7]=sqr(x-1.0)+sqr(y)
else
r[7]=sqr(y)
endif
r[7]=sqrt(r[7])*cabs(v[2]-v[3])
;
; lower left face
;
t[4]=(pzs-v[4])/(v[1]-v[4])
x=real(t[4])
y=imag(t[4])
if y > 0
out = false
endif
if(x<0.0)
r[4]=sqr(x)+sqr(y)
elseif(x>1.0)
r[4]=sqr(x-1.0)+sqr(y)
else
r[4]=sqr(y)
endif
r[4]=sqrt(r[4])*cabs(v[1]-v[4])
t[6]=(pzs-v[4])/(v[2]-v[4])
x=real(t[6])
y=imag(t[6])
if y > 0
out = false
endif
if(x<0.0)
r[6]=sqr(x)+sqr(y)
elseif(x>1.0)
r[6]=sqr(x-1.0)+sqr(y)
else
r[6]=sqr(y)
endif
r[6]=sqrt(r[6])*cabs(v[2]-v[4])
;
; upper left face
;
t[7]=(pzs-v[3])/(v[2]-v[3])
x=real(t[7])
y=imag(t[7])
if y > 0
out = false
endif
if(x<0.0)
r[7]=sqr(x)+sqr(y)
elseif(x>1.0)
r[7]=sqr(x-1.0)+sqr(y)
else
r[7]=sqr(y)
endif
r[7]=sqrt(r[7])*cabs(v[2]-v[3])
t[5]=(pzs-v[4])/(v[3]-v[4])
x=real(t[5])
y=imag(t[5])
if y > 0
out = false
endif
if(x<0.0)
r[5]=sqr(x)+sqr(y)
elseif(x>1.0)
r[5]=sqr(x-1.0)+sqr(y)
else
r[5]=sqr(y)
endif
r[5]=sqrt(r[5])*cabs(v[3]-v[4])
;
; lower right face back
;
t[8]=(pzs-v[5])/(v[0]-v[5])
x=real(t[8])
y=imag(t[8])
if y > 0
out = false
endif
if(x<0.0)
r[8]=sqr(x)+sqr(y)
elseif(x>1.0)
r[8]=sqr(x-1.0)+sqr(y)
else
r[8]=sqr(y)
endif
r[8]=sqrt(r[8])*cabs(v[0]-v[5])
t[9]=(pzs-v[5])/(v[1]-v[5])
x=real(t[9])
y=imag(t[9])
if y > 0
out = false
endif
if(x<0.0)
r[9]=sqr(x)+sqr(y)
elseif(x>1.0)
r[9]=sqr(x-1.0)+sqr(y)
else
r[9]=sqr(y)
endif
r[9]=sqrt(r[9])*cabs(v[1]-v[5])
;
; upper right face back
;
t[10]=(pzs-v[5])/(v[3]-v[5])
x=real(t[10])
y=imag(t[10])
if y > 0
out = false
endif
if(x<0.0)
r[10]=sqr(x)+sqr(y)
elseif(x>1.0)
r[10]=sqr(x-1.0)+sqr(y)
else
r[10]=sqr(y)
endif
r[10]=sqrt(r[10])*cabs(v[3]-v[5])
;
; upper left face back
;
t[11]=(pzs-v[5])/(v[4]-v[5])
x=real(t[11])
y=imag(t[11])
if y > 0
out = false
endif
if(x<0.0)
r[11]=sqr(x)+sqr(y)
elseif(x>1.0)
r[11]=sqr(x-1.0)+sqr(y)
else
r[11]=sqr(y)
endif
r[11]=sqrt(r[11])*cabs(v[4]-v[5])
elseif @polygontype == "Icosahedron"
;
; 0,1,2
;
repeat
t[i]=(pzs-v[i])/(v[i+1]-v[i])
x=real(t[i])
y=imag(t[i])
if y > 0
out = false
endif
if(x<0.0)
r[i]=sqr(x)+sqr(y)
elseif(x>1.0)
r[i]=sqr(x-1.0)+sqr(y)
else
r[i]=sqr(y)
endif
r[i]=sqrt(r[i])*cabs(v[i+1]-v[i])
i = i + 1
until i == 3
; endif
t[2]=(pzs-v[2])/(v[0]-v[2])
x=real(t[2])
y=imag(t[2])
if y > 0
out = false
endif
if(x<0.0)
r[2]=sqr(x)+sqr(y)
elseif(x>1.0)
r[2]=sqr(x-1.0)+sqr(y)
else
r[2]=sqr(y)
endif
r[2]=sqrt(r[2])*cabs(v[0]-v[2])
;
; 0,2,3
;
t[3]=(pzs-v[3])/(v[0]-v[3])
x=real(t[3])
y=imag(t[3])
if y > 0
out = false
endif
if(x<0.0)
r[3]=sqr(x)+sqr(y)
elseif(x>1.0)
r[3]=sqr(x-1.0)+sqr(y)
else
r[3]=sqr(y)
endif
r[3]=sqrt(r[3])*cabs(v[0]-v[3])
t[4]=(pzs-v[3])/(v[2]-v[3])
x=real(t[4])
y=imag(t[4])
if y > 0
out = false
endif
if(x<0.0)
r[4]=sqr(x)+sqr(y)
elseif(x>1.0)
r[4]=sqr(x-1.0)+sqr(y)
else
r[4]=sqr(y)
endif
r[4]=sqrt(r[4])*cabs(v[2]-v[3])
;
; 0,3,4
;
t[5]=(pzs-v[3])/(v[4]-v[3])
x=real(t[5])
y=imag(t[5])
if y > 0
out = false
endif
if(x<0.0)
r[5]=sqr(x)+sqr(y)
elseif(x>1.0)
r[5]=sqr(x-1.0)+sqr(y)
else
r[5]=sqr(y)
endif
r[5]=sqrt(r[5])*cabs(v[4]-v[3])
t[6]=(pzs-v[4])/(v[0]-v[4])
x=real(t[6])
y=imag(t[6])
if y > 0
out = false
endif
if(x<0.0)
r[6]=sqr(x)+sqr(y)
elseif(x>1.0)
r[6]=sqr(x-1.0)+sqr(y)
else
r[6]=sqr(y)
endif
r[6]=sqrt(r[6])*cabs(v[0]-v[4])
;
; 0,4,5
;
t[7]=(pzs-v[5])/(v[4]-v[5])
x=real(t[7])
y=imag(t[7])
if y > 0
out = false
endif
if(x<0.0)
r[7]=sqr(x)+sqr(y)
elseif(x>1.0)
r[7]=sqr(x-1.0)+sqr(y)
else
r[7]=sqr(y)
endif
r[7]=sqrt(r[7])*cabs(v[4]-v[5])
t[8]=(pzs-v[0])/(v[5]-v[0])
x=real(t[8])
y=imag(t[8])
if y > 0
out = false
endif
if(x<0.0)
r[8]=sqr(x)+sqr(y)
elseif(x>1.0)
r[8]=sqr(x-1.0)+sqr(y)
else
r[8]=sqr(y)
endif
r[8]=sqrt(r[8])*cabs(v[5]-v[0])
;
; 0,5,1
;
t[9]=(pzs-v[5])/(v[1]-v[5])
x=real(t[9])
y=imag(t[9])
if y > 0
out = false
endif
if(x<0.0)
r[9]=sqr(x)+sqr(y)
elseif(x>1.0)
r[9]=sqr(x-1.0)+sqr(y)
else
r[9]=sqr(y)
endif
r[9]=sqrt(r[9])*cabs(v[1]-v[5])
;
; 1,2,6
;
t[10]=(pzs-v[6])/(v[1]-v[6])
x=real(t[10])
y=imag(t[10])
if y > 0
out = false
endif
if(x<0.0)
r[10]=sqr(x)+sqr(y)
elseif(x>1.0)
r[10]=sqr(x-1.0)+sqr(y)
else
r[10]=sqr(y)
endif
r[10]=sqrt(r[10])*cabs(v[1]-v[6])
t[11]=(pzs-v[6])/(v[2]-v[6])
x=real(t[11])
y=imag(t[11])
if y > 0
out = false
endif
if(x<0.0)
r[11]=sqr(x)+sqr(y)
elseif(x>1.0)
r[11]=sqr(x-1.0)+sqr(y)
else
r[11]=sqr(y)
endif
r[11]=sqrt(r[11])*cabs(v[2]-v[6])
;
; 2,3,7
;
t[12]=(pzs-v[7])/(v[2]-v[7])
x=real(t[12])
y=imag(t[12])
if y > 0
out = false
endif
if(x<0.0)
r[12]=sqr(x)+sqr(y)
elseif(x>1.0)
r[12]=sqr(x-1.0)+sqr(y)
else
r[12]=sqr(y)
endif
r[12]=sqrt(r[12])*cabs(v[2]-v[7])
t[13]=(pzs-v[7])/(v[3]-v[7])
x=real(t[13])
y=imag(t[13])
if y > 0
out = false
endif
if(x<0.0)
r[13]=sqr(x)+sqr(y)
elseif(x>1.0)
r[13]=sqr(x-1.0)+sqr(y)
else
r[13]=sqr(y)
endif
r[13]=sqrt(r[13])*cabs(v[3]-v[7])
;
; 3,4,8
;
t[14]=(pzs-v[8])/(v[3]-v[8])
x=real(t[14])
y=imag(t[14])
if y > 0
out = false
endif
if(x<0.0)
r[14]=sqr(x)+sqr(y)
elseif(x>1.0)
r[14]=sqr(x-1.0)+sqr(y)
else
r[14]=sqr(y)
endif
r[14]=sqrt(r[14])*cabs(v[3]-v[8])
t[15]=(pzs-v[8])/(v[4]-v[8])
x=real(t[15])
y=imag(t[15])
if y > 0
out = false
endif
if(x<0.0)
r[15]=sqr(x)+sqr(y)
elseif(x>1.0)
r[15]=sqr(x-1.0)+sqr(y)
else
r[15]=sqr(y)
endif
r[15]=sqrt(r[15])*cabs(v[4]-v[8])
;
; 4,5,9
;
t[16]=(pzs-v[9])/(v[4]-v[9])
x=real(t[16])
y=imag(t[16])
if y > 0
out = false
endif
if(x<0.0)
r[16]=sqr(x)+sqr(y)
elseif(x>1.0)
r[16]=sqr(x-1.0)+sqr(y)
else
r[16]=sqr(y)
endif
r[16]=sqrt(r[16])*cabs(v[4]-v[9])
t[17]=(pzs-v[9])/(v[5]-v[9])
x=real(t[17])
y=imag(t[17])
if y > 0
out = false
endif
if(x<0.0)
r[17]=sqr(x)+sqr(y)
elseif(x>1.0)
r[17]=sqr(x-1.0)+sqr(y)
else
r[17]=sqr(y)
endif
r[17]=sqrt(r[17])*cabs(v[5]-v[9])
;
; 5,1,10
;
t[18]=(pzs-v[10])/(v[1]-v[10])
x=real(t[18])
y=imag(t[18])
if y > 0
out = false
endif
if(x<0.0)
r[18]=sqr(x)+sqr(y)
elseif(x>1.0)
r[18]=sqr(x-1.0)+sqr(y)
else
r[18]=sqr(y)
endif
r[18]=sqrt(r[18])*cabs(v[1]-v[10])
t[19]=(pzs-v[10])/(v[5]-v[10])
x=real(t[19])
y=imag(t[19])
if y > 0
out = false
endif
if(x<0.0)
r[19]=sqr(x)+sqr(y)
elseif(x>1.0)
r[19]=sqr(x-1.0)+sqr(y)
else
r[19]=sqr(y)
endif
r[19]=sqrt(r[19])*cabs(v[5]-v[10])
;
; 6,7,2
;
t[20]=(pzs-v[7])/(v[6]-v[7])
x=real(t[20])
y=imag(t[20])
if y > 0
out = false
endif
if(x<0.0)
r[20]=sqr(x)+sqr(y)
elseif(x>1.0)
r[20]=sqr(x-1.0)+sqr(y)
else
r[20]=sqr(y)
endif
r[20]=sqrt(r[20])*cabs(v[6]-v[7])
;
; 7,8,3
;
t[21]=(pzs-v[8])/(v[7]-v[8])
x=real(t[21])
y=imag(t[21])
if y > 0
out = false
endif
if(x<0.0)
r[21]=sqr(x)+sqr(y)
elseif(x>1.0)
r[21]=sqr(x-1.0)+sqr(y)
else
r[21]=sqr(y)
endif
r[21]=sqrt(r[21])*cabs(v[7]-v[8])
;
; 8,9,4
;
t[22]=(pzs-v[9])/(v[8]-v[9])
x=real(t[22])
y=imag(t[22])
if y > 0
out = false
endif
if(x<0.0)
r[22]=sqr(x)+sqr(y)
elseif(x>1.0)
r[22]=sqr(x-1.0)+sqr(y)
else
r[22]=sqr(y)
endif
r[22]=sqrt(r[22])*cabs(v[8]-v[9])
;
; 9,10,5
;
t[23]=(pzs-v[9])/(v[10]-v[9])
x=real(t[23])
y=imag(t[23])
if y > 0
out = false
endif
if(x<0.0)
r[23]=sqr(x)+sqr(y)
elseif(x>1.0)
r[23]=sqr(x-1.0)+sqr(y)
else
r[23]=sqr(y)
endif
r[23]=sqrt(r[23])*cabs(v[10]-v[9])
;
; 10,6,1
;
t[24]=(pzs-v[6])/(v[10]-v[6])
x=real(t[24])
y=imag(t[24])
if y > 0
out = false
endif
if(x<0.0)
r[24]=sqr(x)+sqr(y)
elseif(x>1.0)
r[24]=sqr(x-1.0)+sqr(y)
else
r[24]=sqr(y)
endif
r[24]=sqrt(r[24])*cabs(v[10]-v[6])
;
; 11,6,7
;
t[25]=(pzs-v[11])/(v[6]-v[11])
x=real(t[25])
y=imag(t[25])
if y > 0
out = false
endif
if(x<0.0)
r[25]=sqr(x)+sqr(y)
elseif(x>1.0)
r[25]=sqr(x-1.0)+sqr(y)
else
r[25]=sqr(y)
endif
r[25]=sqrt(r[25])*cabs(v[6]-v[11])
t[26]=(pzs-v[11])/(v[7]-v[11])
x=real(t[26])
y=imag(t[26])
if y > 0
out = false
endif
if(x<0.0)
r[26]=sqr(x)+sqr(y)
elseif(x>1.0)
r[26]=sqr(x-1.0)+sqr(y)
else
r[26]=sqr(y)
endif
r[26]=sqrt(r[26])*cabs(v[7]-v[11])
;
; 11,7,8
;
t[27]=(pzs-v[11])/(v[8]-v[11])
x=real(t[27])
y=imag(t[27])
if y > 0
out = false
endif
if(x<0.0)
r[27]=sqr(x)+sqr(y)
elseif(x>1.0)
r[27]=sqr(x-1.0)+sqr(y)
else
r[27]=sqr(y)
endif
r[27]=sqrt(r[27])*cabs(v[8]-v[11])
;
; 11,8,9
;
t[28]=(pzs-v[11])/(v[9]-v[11])
x=real(t[28])
y=imag(t[28])
if y > 0
out = false
endif
if(x<0.0)
r[28]=sqr(x)+sqr(y)
elseif(x>1.0)
r[28]=sqr(x-1.0)+sqr(y)
else
r[28]=sqr(y)
endif
r[28]=sqrt(r[28])*cabs(v[9]-v[11])
;
; 11,9,10
;
t[29]=(pzs-v[11])/(v[10]-v[11])
x=real(t[29])
y=imag(t[29])
if y > 0
out = false
endif
if(x<0.0)
r[29]=sqr(x)+sqr(y)
elseif(x>1.0)
r[29]=sqr(x-1.0)+sqr(y)
else
r[29]=sqr(y)
endif
r[29]=sqrt(r[29])*cabs(v[10]-v[11])
elseif @polygontype == "Dodecahedron"
;
; 0,1,2,3,4
;
repeat
t[i]=(pzs-v[i])/(v[i+1]-v[i])
x=real(t[i])
y=imag(t[i])
if y > 0
out = false
endif
if(x<0.0)
r[i]=sqr(x)+sqr(y)
elseif(x>1.0)
r[i]=sqr(x-1.0)+sqr(y)
else
r[i]=sqr(y)
endif
r[i]=sqrt(r[i])*cabs(v[i+1]-v[i])
i = i + 1
until i == 5
t[4]=(pzs-v[4])/(v[0]-v[4])
x=real(t[4])
y=imag(t[4])
if y > 0
out = false
endif
if(x<0.0)
r[4]=sqr(x)+sqr(y)
elseif(x>1.0)
r[4]=sqr(x-1.0)+sqr(y)
else
r[4]=sqr(y)
endif
r[4]=sqrt(r[4])*cabs(v[0]-v[4])
;
; 0,1,6,10,5
;
t[5]=(pzs-v[5])/(v[0]-v[5])
x=real(t[5])
y=imag(t[5])
if y > 0
out = false
endif
if(x<0.0)
r[5]=sqr(x)+sqr(y)
elseif(x>1.0)
r[5]=sqr(x-1.0)+sqr(y)
else
r[5]=sqr(y)
endif
r[5]=sqrt(r[5])*cabs(v[0]-v[5])
t[6]=(pzs-v[5])/(v[10]-v[5])
x=real(t[6])
y=imag(t[6])
if y > 0
out = false
endif
if(x<0.0)
r[6]=sqr(x)+sqr(y)
elseif(x>1.0)
r[6]=sqr(x-1.0)+sqr(y)
else
r[6]=sqr(y)
endif
r[6]=sqrt(r[6])*cabs(v[10]-v[5])
t[7]=(pzs-v[6])/(v[10]-v[6])
x=real(t[7])
y=imag(t[7])
if y > 0
out = false
endif
if(x<0.0)
r[7]=sqr(x)+sqr(y)
elseif(x>1.0)
r[7]=sqr(x-1.0)+sqr(y)
else
r[7]=sqr(y)
endif
r[7]=sqrt(r[7])*cabs(v[10]-v[6])
t[8]=(pzs-v[6])/(v[1]-v[6])
x=real(t[8])
y=imag(t[8])
if y > 0
out = false
endif
if(x<0.0)
r[8]=sqr(x)+sqr(y)
elseif(x>1.0)
r[8]=sqr(x-1.0)+sqr(y)
else
r[8]=sqr(y)
endif
r[8]=sqrt(r[8])*cabs(v[1]-v[6])
;
; 1,2,7,11,6
;
t[9]=(pzs-v[7])/(v[2]-v[7])
x=real(t[9])
y=imag(t[9])
if y > 0
out = false
endif
if(x<0.0)
r[9]=sqr(x)+sqr(y)
elseif(x>1.0)
r[9]=sqr(x-1.0)+sqr(y)
else
r[9]=sqr(y)
endif
r[9]=sqrt(r[9])*cabs(v[2]-v[7])
;
t[10]=(pzs-v[11])/(v[7]-v[11])
x=real(t[10])
y=imag(t[10])
if y > 0
out = false
endif
if(x<0.0)
r[10]=sqr(x)+sqr(y)
elseif(x>1.0)
r[10]=sqr(x-1.0)+sqr(y)
else
r[10]=sqr(y)
endif
r[10]=sqrt(r[10])*cabs(v[7]-v[11])
t[11]=(pzs-v[11])/(v[6]-v[11])
x=real(t[11])
y=imag(t[11])
if y > 0
out = false
endif
if(x<0.0)
r[11]=sqr(x)+sqr(y)
elseif(x>1.0)
r[11]=sqr(x-1.0)+sqr(y)
else
r[11]=sqr(y)
endif
r[11]=sqrt(r[11])*cabs(v[6]-v[11])
;
; 2,3,8,12,7
;
t[12]=(pzs-v[8])/(v[3]-v[8])
x=real(t[12])
y=imag(t[12])
if y > 0
out = false
endif
if(x<0.0)
r[12]=sqr(x)+sqr(y)
elseif(x>1.0)
r[12]=sqr(x-1.0)+sqr(y)
else
r[12]=sqr(y)
endif
r[12]=sqrt(r[12])*cabs(v[3]-v[8])
t[13]=(pzs-v[12])/(v[8]-v[12])
x=real(t[13])
y=imag(t[13])
if y > 0
out = false
endif
if(x<0.0)
r[13]=sqr(x)+sqr(y)
elseif(x>1.0)
r[13]=sqr(x-1.0)+sqr(y)
else
r[13]=sqr(y)
endif
r[13]=sqrt(r[13])*cabs(v[8]-v[12])
t[14]=(pzs-v[12])/(v[7]-v[12])
x=real(t[14])
y=imag(t[14])
if y > 0
out = false
endif
if(x<0.0)
r[14]=sqr(x)+sqr(y)
elseif(x>1.0)
r[14]=sqr(x-1.0)+sqr(y)
else
r[14]=sqr(y)
endif
r[14]=sqrt(r[14])*cabs(v[7]-v[12])
;
; 3,4,9,13,8
;
t[15]=(pzs-v[9])/(v[4]-v[9])
x=real(t[15])
y=imag(t[15])
if y > 0
out = false
endif
if(x<0.0)
r[15]=sqr(x)+sqr(y)
elseif(x>1.0)
r[15]=sqr(x-1.0)+sqr(y)
else
r[15]=sqr(y)
endif
r[15]=sqrt(r[15])*cabs(v[4]-v[9])
t[16]=(pzs-v[13])/(v[9]-v[13])
x=real(t[16])
y=imag(t[16])
if y > 0
out = false
endif
if(x<0.0)
r[16]=sqr(x)+sqr(y)
elseif(x>1.0)
r[16]=sqr(x-1.0)+sqr(y)
else
r[16]=sqr(y)
endif
r[16]=sqrt(r[16])*cabs(v[9]-v[13])
t[17]=(pzs-v[8])/(v[13]-v[8])
x=real(t[17])
y=imag(t[17])
if y > 0
out = false
endif
if(x<0.0)
r[17]=sqr(x)+sqr(y)
elseif(x>1.0)
r[17]=sqr(x-1.0)+sqr(y)
else
r[17]=sqr(y)
endif
r[17]=sqrt(r[17])*cabs(v[13]-v[8])
;
; 4,0,5,14,9
;
t[18]=(pzs-v[5])/(v[14]-v[5])
x=real(t[18])
y=imag(t[18])
if y > 0
out = false
endif
if(x<0.0)
r[18]=sqr(x)+sqr(y)
elseif(x>1.0)
r[18]=sqr(x-1.0)+sqr(y)
else
r[18]=sqr(y)
endif
r[18]=sqrt(r[18])*cabs(v[14]-v[5])
t[19]=(pzs-v[9])/(v[14]-v[9])
x=real(t[19])
y=imag(t[19])
if y > 0
out = false
endif
if(x<0.0)
r[19]=sqr(x)+sqr(y)
elseif(x>1.0)
r[19]=sqr(x-1.0)+sqr(y)
else
r[19]=sqr(y)
endif
r[19]=sqrt(r[19])*cabs(v[14]-v[9])
;
; 15,16,11,6,10
;
t[20]=(pzs-v[16])/(v[11]-v[16])
x=real(t[20])
y=imag(t[20])
if y > 0
out = false
endif
if(x<0.0)
r[20]=sqr(x)+sqr(y)
elseif(x>1.0)
r[20]=sqr(x-1.0)+sqr(y)
else
r[20]=sqr(y)
endif
r[20]=sqrt(r[20])*cabs(v[11]-v[16])
t[21]=(pzs-v[15])/(v[16]-v[15])
x=real(t[21])
y=imag(t[21])
if y > 0
out = false
endif
if(x<0.0)
r[21]=sqr(x)+sqr(y)
elseif(x>1.0)
r[21]=sqr(x-1.0)+sqr(y)
else
r[21]=sqr(y)
endif
r[21]=sqrt(r[21])*cabs(v[16]-v[15])
t[22]=(pzs-v[10])/(v[15]-v[10])
x=real(t[22])
y=imag(t[22])
if y > 0
out = false
endif
if(x<0.0)
r[22]=sqr(x)+sqr(y)
elseif(x>1.0)
r[22]=sqr(x-1.0)+sqr(y)
else
r[22]=sqr(y)
endif
r[22]=sqrt(r[22])*cabs(v[15]-v[10])
;
; 16,17,12,7,11
;
t[23]=(pzs-v[17])/(v[12]-v[17])
x=real(t[23])
y=imag(t[23])
if y > 0
out = false
endif
if(x<0.0)
r[23]=sqr(x)+sqr(y)
elseif(x>1.0)
r[23]=sqr(x-1.0)+sqr(y)
else
r[23]=sqr(y)
endif
r[23]=sqrt(r[23])*cabs(v[12]-v[17])
t[24]=(pzs-v[16])/(v[17]-v[16])
x=real(t[24])
y=imag(t[24])
if y > 0
out = false
endif
if(x<0.0)
r[24]=sqr(x)+sqr(y)
elseif(x>1.0)
r[24]=sqr(x-1.0)+sqr(y)
else
r[24]=sqr(y)
endif
r[24]=sqrt(r[24])*cabs(v[17]-v[16])
;
; 17,18,13,8,12
;
t[25]=(pzs-v[18])/(v[13]-v[18])
x=real(t[25])
y=imag(t[25])
if y > 0
out = false
endif
if(x<0.0)
r[25]=sqr(x)+sqr(y)
elseif(x>1.0)
r[25]=sqr(x-1.0)+sqr(y)
else
r[25]=sqr(y)
endif
r[25]=sqrt(r[25])*cabs(v[13]-v[18])
t[26]=(pzs-v[17])/(v[18]-v[17])
x=real(t[26])
y=imag(t[26])
if y > 0
out = false
endif
if(x<0.0)
r[26]=sqr(x)+sqr(y)
elseif(x>1.0)
r[26]=sqr(x-1.0)+sqr(y)
else
r[26]=sqr(y)
endif
r[26]=sqrt(r[26])*cabs(v[18]-v[17])
;
; 18,19,14,9,13
;
t[27]=(pzs-v[19])/(v[14]-v[19])
x=real(t[27])
y=imag(t[27])
if y > 0
out = false
endif
if(x<0.0)
r[27]=sqr(x)+sqr(y)
elseif(x>1.0)
r[27]=sqr(x-1.0)+sqr(y)
else
r[27]=sqr(y)
endif
r[27]=sqrt(r[27])*cabs(v[14]-v[19])
t[28]=(pzs-v[18])/(v[19]-v[18])
x=real(t[28])
y=imag(t[28])
if y > 0
out = false
endif
if(x<0.0)
r[28]=sqr(x)+sqr(y)
elseif(x>1.0)
r[28]=sqr(x-1.0)+sqr(y)
else
r[28]=sqr(y)
endif
r[28]=sqrt(r[28])*cabs(v[19]-v[18])
;
; 19,15,10,5,14
;
t[29]=(pzs-v[15])/(v[19]-v[15])
x=real(t[29])
y=imag(t[29])
if y > 0
out = false
endif
if(x<0.0)
r[29]=sqr(x)+sqr(y)
elseif(x>1.0)
r[29]=sqr(x-1.0)+sqr(y)
else
r[29]=sqr(y)
endif
r[29]=sqrt(r[29])*cabs(v[19]-v[15])
endif
i = 0
repeat
if r[i] < @thick
if r[i] != 0
d = r[i]
endif
m_LastZ = m_LastZ + t[i]
endif
i = i + 1
until i == side
m_lastZ = m_lastZ/(side)^2
return d
endfunc
protected:
float r[30]
float vx[20]
float vy[20]
float vz[20]
complex v[30]
complex t[30]
float twopi
int seed
float mx
float my
int i
float x
float y
bool out
int vertex
int side
float d
float rotx
float roty
float rotz
default:
title = "Platonic Solids"
int param v_trapshapeplatonicsolids
caption = "Version (Trap Shape Platonic Solids)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeplatonicsolids < 100
endparam
heading
text = "This is a TrapShape that is still under development. I will try to \
maintain backwards compatibility, but I cannot guarantee it. The \
Trapshape creates solid and outline regular polygons from 3 sides \
to 10 sides."
endheading
param polygontype
caption = "Polygon Type"
default = 1
enum = "Tetrahedron" "Cube" "Octahedron" "Icosahedron" "Dodecahedron"
endparam
heading
text = "Rotations around the X, Y and Z axes."
endheading
float param rotx
caption = "X axis"
default = 20
endparam
float param roty
caption = "Y axis"
default = 20
endparam
float param rotz
caption = "Z axis"
default = 0
endparam
float param size
caption = "Polygon size"
default = 0.2
endparam
float param thick
caption = "Line thickness"
default = 0.02
endparam
}
class REB_TrapShapeSolid_OutlinePolygons(common.ulb:TrapShape) {
public:
import "common.ulb"
import "reb.ulb"
$define debug
; Constructor
func REB_TrapShapeSolid_OutlinePolygons(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call before each iteration
func Init(complex pz)
TrapShape.Init(pz)
twopi = 2*#pi
seed = @mseed
mx = 0
my = 0
i = 0
x = 0.0
y = 0.0
out = false
repeat
if @morph
seed = random (seed)
mx = 0.1*seed/#randomrange
seed = random(seed)
my = 0.1*seed/#randomrange
endif
if @inside
vx[i] = sin(i*twopi/@sides)*(1+10*mx/@sides)
vy[i] = cos(i*twopi/@sides)*(1+10*my/@sides)
else
vx[i] = cos(i*twopi/@sides)*(1+10*mx/@sides)
vy[i] = sin(i*twopi/@sides)*(1+10*my/@sides)
endif
v[i] = vx[i] + flip(vy[i])
i = i + 1
until i == @sides
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
complex lim = (100,0)
if !@inside
d = 1e10
else
d = 0
endif
size = @size
if @inside
if @sides == 3
size = size/350.877
elseif @sides == 4
size = size/200.000
elseif @sides == 5
size = size/145.985
elseif @sides == 6
size = size/115.607
elseif @sides == 7
size = size/96.618
elseif @sides == 8
size = size/82.987
elseif @sides == 9
size = size/72.993
elseif @sides == 10
size = size/65.146
endif
endif
complex pzs = pz/size
i = 0
;
; calculate r[i] and t[i] for first n-1 sides
;
repeat
t[i]=(pzs-v[i])/(v[i+1]-v[i])
x=real(t[i])
y=imag(t[i])
if y > 0
out = false
endif
if(x<0.0)
r[i]=sqr(x)+sqr(y)
elseif(x>1.0)
r[i]=sqr(x-1.0)+sqr(y)
else
r[i]=sqr(y)
endif
r[i]=sqrt(r[i])*cabs(v[i+1]-v[i])
i = i + 1
until i == (@sides-1)
;
; calculate r[i] and t[i] for the last side
;
t[@sides-1]=(pzs-v[@sides-1])/(v[0]-v[@sides-1])
x=real(t[@sides-1])
y=imag(t[@sides-1])
if y > 0
out = false
endif
if(x<0.0)
r[@sides-1]=sqr(x)+sqr(y)
elseif(x>1.0)
r[@sides-1]=sqr(x-1.0)+sqr(y)
else
r[@sides-1]=sqr(y)
endif
r[@sides-1]=sqrt(r[@sides-1])*cabs(v[0]-v[@sides-1])
i = 0
repeat
if ((r[i] < @thick)&&!@inside) || (!out && t[i] > lim)
d = r[i]
m_LastZ = m_LastZ + t[i]
endif
i = i + 1
until i == @sides
m_lastZ = m_lastZ/@sides^2
return d
endfunc
protected:
complex v[10]
complex t[10]
float r[10]
float vx[10]
float vy[10]
float twopi
int seed
float mx
float my
int i
float x
float y
bool out
float d
default:
title = "Polygons"
int param v_trapshapesolidpolygon
caption = "Version (Trap Shape Solid and Outlined Polygons)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesolidpolygon < 100
endparam
heading
text = "This is a TrapShape that is still under development. I will try to \
maintain backwards compatibility, but I cannot guarantee it. The \
Trapshape creates solid and outline regular polygons from 3 sides \
to 10 sides."
endheading
int param sides
caption="# of sides"
default = 5
min = 3
max = 10
endparam
float param size
caption = "Polygon size"
default = 0.2
endparam
float param thick
caption = "Line thickness"
default = 0.02
visible = !@inside
endparam
bool param morph
caption="Morph the polygon"
default=false
endparam
int param mseed
caption = "Morph seed"
default = 123456789
visible = @morph
endparam
bool param inside
caption = "Solid Polygon"
default = false
endparam
}
class REB_RangeColoringWrapper(common.ulb:TrapShape) {
; Based upone JLB_Range Coloring.
public:
import "common.ulb"
; Constructor
func REB_RangeColoringWrapper(Generic pparent)
TrapShape.TrapShape(pparent)
m_TrapShape = new @f_TrapShape(this)
endfunc
func Init(complex pz)
m_TrapShape.Init(pz)
m_RangeLow = @p_scale*(1.0-0.5*@p_width)
m_RangeHigh = @p_scale*(1.0+0.5*@p_width)
ang = -@p_rot*#pi/180
m_Rotate = cos(ang) + flip(sin(ang))
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
pz = pz * m_Rotate
dist = m_TrapShape.Iterate(pz)
m_LastZ = m_TrapShape.m_LastZ
dmin = dist*m_RangeLow
dmax = dist*m_RangeHigh
dist = cabs(pz - @p_Center)
if((dist >= dmin) && (dist <= dmax)) ; in the range
dist = (dist-dmin)/(dmax-dmin) ; 0 <= dist <= 1
else
dist = 1e100
endif
return dist
endfunc
trapshape m_trapshape
float m_RangeLow
float m_RangeHigh
complex m_Rotate
float dist
float dmin
float dmax
float ang
default:
title = "Range Coloring Wrapper"
int param v_RangeColoringWrapper
caption = "Version (Range Coloring Wrapper)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_RangeColoringWrapper < 100
endparam
TrapShape param f_TrapShape
caption = "TrapShape"
default = REB_TrapShapeBifolium
endparam
param p_scale
caption = "Range scale"
default = 0.9
endparam
param p_width
caption = "Range width"
default = 0.1
endparam
complex param p_Center
caption = "Curve center"
default = (0.0,0.0)
endparam
float param p_rot
caption = "Rotation angle"
default = 0.0
hint = "degrees"
endparam
}
class TrapShapeDoodads(common.ulb:TrapShape) {
; transcribed from the Doodads traps of Dennis Magar.
; I have been unable to contact Dennis. If he objects I will remove
; the trapshape.
public:
import "common.ulb"
func TrapShapeDoodads(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call before each iteration
func Init(complex pz)
TrapShape.Init(pz)
x = 0
y = 0
zr = 0
zi = 0
zz = 0
z1 = 0
a2 = 0
s1 = 0
g1 = 0
ff = 0
gc = 0
zc = 0
fc = 0
zr1 = 0
zi1 = 0
fmr = real(@fm)
fmi = imag(@fm)
sn = 1
if @m % 2 == 1
sn = -1
endif
vsa = sn*@sa/10
vsb = abs(@sb/10)
endfunc
; call for each iterated point
float func Iterate(complex pz)
TrapShape.Iterate(pz)
z1 = pz
zc = @fn4(z1)
zr = real(zc)
zi = imag(zc)
if (@m > 3 && @m < 26) || @mr == 5 || @mr == 8 \
|| @mr == 9 || @mr == 12
gc = @fn3(@fn1(@fn2(z1)))
g1 = cabs(gc)
endif
if @m == 7 || @mr == 5
a2 = atan2(gc)
endif
if @m == 8 || @m == 9 || @m == 12 || @m == 13 \
|| @m > 19 || @mr == 9 || @mr == 11
s1 = cabs(zc)
endif
if @m == 12 || @m == 13 || @m == 22 || @m == 23 \
|| @m == 26 || @m == 27 || @mr == 10 || @mr == 12
ff = cabs(@fn3(@fn1(real(z1))+@fn2(imag(z1))))
endif
if @m >27
fc = @fn3(@fn1(real(z1))+flip(@fn2(imag(z1))))
endif
if @mr < 5 || @mr >= 13
zr1 = real(@fn1(zr*fmr))
zi1 = real(@fn2(zi*fmi))
endif
if @mrf
zr1 = abs(zr1)
zi1 = abs(zi1)
endif
if @mr == 0
zz = real(@fn3(zr1*zi1))
elseif @mr == 1
zz = real(@fn3(zr1+zi1))
elseif @mr == 2
zz = real(@fn3(zr1/zi1))
elseif @mr == 3
zz = real(@fn3(zi1^zr1))
elseif @mr == 4
zz = real(@fn3(zr1^zi1))
elseif @mr == 5
zz = real(@fn4(@fn3(abs(@fn1(g1*fmr)-@fn2(a2*fmi)))))
elseif @mr == 6
if !@mrf
zz = real(atan(@fn3(@fn1(zr*fmr)) \
/(@fn3(@fn2(zi^2*fmi)))))
else
zz = real(atan(@fn3(abs(@fn1(zr*fmr)) \
/(@fn3(abs(@fn2(zi^2*fmi)))))))
endif
elseif @mr == 7
zz = cabs(recip(@fn3(@fn2(@fn1(zc*fmr*2)))))
elseif @mr == 8
zz = real(@fn3(@fn1(abs((g1-zr)*fmr/(g1-zi)*fmi))))^.1
elseif @mr == 9
float temp = abs((g1-zr)*fmr/(g1+1e-20))
zz = real(@fn3(abs(@fn1(temp)-@fn2(s1*fmi))))
elseif @mr == 10
zz = cabs(@fn4(ff*fmr-gc*fmi))^2
elseif @mr == 11
zz = cabs(@fn4(s1-1)*fmr/(s1+1)*fmi)
elseif @mr == 12
zz = cabs(@fn4(g1)*fmr/(ff)*fmi)
elseif @mr == 13
zz = real(@fn3(zi1/zr1))
elseif @mr == 14
zz = real(@fn3((zi1*zr1)/(zi1+zr1)))
elseif @mr == 15
zz = real(@fn3((zi1-zr1)/(zi1+zr1)))
endif
if @m < 2
y = zr
elseif @m == 2 || @m == 3
y = zr*3-zi
elseif @m == 4
y = abs(g1^3/(zr-g1))
elseif @m == 5
y = zr/2+g1
elseif @m == 6
y = g1^3
elseif @m == 7
y = g1^2/a2
elseif @m == 8 || @m == 9
y = zr*s1/zi
elseif @m == 10 || @m == 11
y = g1^2
elseif @m == 12 || @m == 13
y = g1-abs((ff-g1)/s1)
elseif @m == 14 || @m == 15
y = g1-zr/g1
elseif @m == 16 || @m == 17
y = g1-abs(zr/g1)
elseif @m == 18 || @m == 19
y = g1
elseif @m == 20 || @m == 21
y = s1*.1/g1^2
elseif @m == 22 || @m == 23
y = g1^2-abs((ff-g1)/s1)
elseif @m == 24 || @m == 25
y = g1^2-s1
elseif @m == 26 || @m == 27
y = ff
else
y = imag(fc)
endif
y = real(@fn9(y - @tad/10))
if @sa < 0 && sn == -1
y = y * (-@sa+5)/5
vsa = sn*@sa/20
endif
if @sb > 0
y = y % vsb
endif
if @m % 2 == 0
x = zz - @mul*(real(abs(@fn1(y - abs(@fn2(y))))))
else
x = zz - @mul*y
endif
if @sb < 0
x = x % vsb
endif
x = x + vsa
xb = (@fn8(x + flip(y)))^@pwr
zz = cabs(z1 - xb)
m_lastz = xb
return zz
endfunc
protected:
float x
float y
float zr
float zi
float zz
float a2
float s1
float g1
float ff
complex gc
complex zc
complex fc
complex z1
float zr1
float zi1
float fmr
float fmi
int sn
float vsa
float vsb
default:
title = "Doodad Traps"
int param v_doodad
caption = "Version (Doodad Traps)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_doodad < 100
endparam
param trp
caption = "More Trap Parameters"
hint = "Additional parameters less frequently used."
default = true
endparam
param m
caption = " Trap Mode"
enum = "1" "2" "3" "4" "5" "6" "7" "8" \
"9" "A" "B" "C" "D" "E" "F" "G" \
"H" "I" "J" "K" "L" "M" "N" "O" \
"P" "Q" "R" "S" "T" "U"
default = 0
endparam
param mr
caption = "Flavor"
enum = "A" "B" "C" "D" "E" "F" "G" \
"H" "I" "J" "K" "L" "M" "N" \
"O" "P"
default = 0
endparam
param mrf
caption = "Apply ABS to Flavor"
default = false
visible = @mr < 5 && @trp
endparam
param tad
caption = "Trap Addend"
default = 0.0
visible = @trp
endparam
param fm
caption = "Flavor Multiplier"
default = (1,1)
visible = @trp
endparam
param pwr
caption = "`Trap Power'"
default = 3.0
visible = @trp
endparam
param mul
caption = " Trap Multiplier"
default = 3.0
visible = @trp
endparam
param sb
caption = "'Ripple' Control"
hint = "A few Trap Modes are unaffected by this \
parameter. Useful Range is -50 to 50"
default = 0.0
visible = @trp
endparam
param sa
caption = "Expand+|-Contract"
hint = "Useful Range is around -10 to 10"
default = 0.0
visible = @trp
endparam
heading
caption = "Functions"
endheading
func fn4
caption = "Initial function"
default = ident()
endfunc
func fn1
caption = "Real function"
default = ident()
endfunc
func fn2
caption = "Imag function"
default = ident()
endfunc
func fn3
caption = "Overall function"
default = ident()
endfunc
func fn9
caption = "First Trap function"
default = ident()
visible = @trp
endfunc
func fn8
caption = "Final Trap function"
default = ident()
endfunc
}
class REB_ShapeTextureMerge(common.ulb:TrapShape) {
; This is a wrappoer transform which allows you to use 2-3
; trap shapes an trap shape textures in a trap shape slot.
; If you need more than three trap shapes, put a TrapShapeTextureMerge
; object in one or more of the slots.
$define debug
public:
import "common.ulb"
import "dmj5.ulb"
func REB_ShapeTextureMerge(Generic pparent)
TrapShape.TrapShape(pparent)
int a = 0
int b = 1
int c = 2
if @trapno == "2"
if @merge_order2 == "2 1"
a = 1
b = 0
endif
endif
if @trapno == "2"
m_Enables[a] = true
m_Enables[b] = true
m_Enables[c] = false
m_tmax = 2
else
m_Enables[a] = true
m_Enables[b] = true
m_Enables[c] = true
m_tmax = 3
endif
m_Elements[a] = new @f_trapshape1(this)
m_Elements[b] = new @f_trapshape2(this)
m_Elements[c] = new @f_trapshape3(this)
weightF[a] = @weightf1
weightF[b] = @weightf2
weightF[c] = @weightf3
endfunc
func Init(complex pz)
TrapShape.Init(pz)
m_TextureValue = 0
int j = 0
while (j < m_tmax)
if (m_Enables[j])
m_Elements[j].Init(pz)
distance[j] = 0
distance3[j] = 0
endif
j = j + 1
endwhile
dist = 0
endfunc
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if m_Enables[0]
distance[0] = m_Elements[0].Iterate(pz)*weightf[0]
LastZ[0] = m_Elements[0].GetTransformedPoint()
if @v_REB_ShapeTextureMerge < 101
if @tamode == "-A"
distance[0] = - distance[0]
elseif @tamode == "|A|"
distance[0] = abs(distance[0])
elseif @tamode == "A*A"
distance[0] = distance[0]*distance[0]
elseif @tamode == "-A*A"
distance[0] = -distance[0]*distance[0]
elseif @tamode == "A*A*A"
distance[0] = distance[0]*distance[0]*distance[0]
elseif @tamode == "-A*A*A"
distance[0] = -distance[0]*distance[0]*distance[0]
elseif @tamode == "|A*A*A|"
distance[0] = abs(distance[0]*distance[0]*distance[0])
elseif @tamode == "log(A)"
distance[0] = log(distance[0])
elseif @tamode == "exp(A)"
distance[0] = exp(distance[0])
endif
else
if @tamode2 == "-A"
distance[0] = - distance[0]
elseif @tamode2 == "|A|"
distance[0] = abs(distance[0])
elseif @tamode2 == "A*A"
distance[0] = distance[0]*distance[0]
elseif @tamode2 == "-A*A"
distance[0] = -distance[0]*distance[0]
elseif @tamode2 == "A*A*A"
distance[0] = distance[0]*distance[0]*distance[0]
elseif @tamode2 == "-A*A*A"
distance[0] = -distance[0]*distance[0]*distance[0]
elseif @tamode2 == "|A*A*A|"
distance[0] = abs(distance[0]*distance[0]*distance[0])
endif
distance[0] = real(@mFuncA(distance[0]))
endif
endif
if m_Enables[1]
distance[1] = m_Elements[1].Iterate(pz)*weightf[1]
LastZ[1] = m_Elements[1].GetTransformedPoint()
if @v_REB_ShapeTextureMerge < 101
if @tbmode == "-B"
distance[1] = - distance[1]
elseif @tbmode == "|B|"
distance[1] = abs(distance[1])
elseif @tbmode == "B*B"
distance[1] = distance[1]*distance[1]
elseif @tbmode == "-B*B"
distance[1] = -distance[1]*distance[1]
elseif @tbmode == "B*B*B"
distance[1] = distance[1]*distance[1]*distance[1]
elseif @tbmode == "-B*B*B"
distance[1] = -distance[1]*distance[1]*distance[1]
elseif @tbmode == "|B*B*B|"
distance[1] = abs(distance[1]*distance[1]*distance[1])
elseif @tbmode == "log(B)"
distance[1] = log(distance[1])
elseif @tbmode == "exp(B)"
distance[1] = exp(distance[1])
endif
else
if @tbmode2 == "-B"
distance[1] = - distance[1]
elseif @tbmode2 == "|B|"
distance[1] = abs(distance[1])
elseif @tbmode2 == "B*B"
distance[1] = distance[1]*distance[1]
elseif @tbmode2 == "-B*B"
distance[1] = -distance[1]*distance[1]
elseif @tbmode2 == "B*B*B"
distance[1] = distance[1]*distance[1]*distance[1]
elseif @tbmode2 == "-B*B*B"
distance[1] = -distance[1]*distance[1]*distance[1]
elseif @tbmode2 == "|B*B*B|"
distance[1] = abs(distance[1]*distance[1]*distance[1])
endif
distance[1] = real(@mFuncB(distance[1]))
endif
endif
if m_Enables[2]
distance[2] = m_Elements[2].Iterate(pz)*weightf[2]
LastZ[2] = m_Elements[2].GetTransformedPoint()
if @v_REB_ShapeTextureMerge < 101
if @tcmode == "-C"
distance[2] = - distance[2]
elseif @tcmode == "|C|"
distance[2] = abs(distance[2])
elseif @tcmode == "C*C"
distance[2] = distance[2]*distance[2]
elseif @tcmode == "-C*C"
distance[2] = -distance[2]*distance[2]
elseif @tcmode == "C*C*C"
distance[2] = distance[2]*distance[2]*distance[2]
elseif @tcmode == "-C*C*C"
distance[2] = -distance[2]*distance[2]*distance[2]
elseif @tcmode == "|C*C*C|"
distance[2] = abs(distance[2]*distance[2]*distance[2])
elseif @tcmode == "log(C)"
distance[2] = log(distance[2])
elseif @tcmode == "exp(C)"
distance[2] = exp(distance[2])
endif
else
if @tcmode2 == "-C"
distance[2] = - distance[2]
elseif @tcmode2 == "|C|"
distance[2] = abs(distance[2])
elseif @tcmode2 == "C*C"
distance[2] = distance[2]*distance[2]
elseif @tcmode2 == "-C*C"
distance[2] = -distance[2]*distance[2]
elseif @tcmode2 == "C*C*C"
distance[2] = distance[2]*distance[2]*distance[2]
elseif @tcmode2 == "-C*C*C"
distance[2] = -distance[2]*distance[2]*distance[2]
elseif @tcmode2 == "|C*C*C|"
distance[2] = abs(distance[2]*distance[2]*distance[2])
endif
distance[2] = real(@mFuncC(distance[2]))
endif
endif
if @trapno == "3"
if @tterm31 == "A"
distance3[0] = distance[0]
elseif @tterm31 == "1/A"
distance3[0] = 1/distance[0]
elseif @tterm31 == "B"
distance3[0] = distance[1]
elseif @tterm31 == "1/B"
distance3[0] = 1/distance[1]
elseif @tterm31 == "C"
distance3[0] = distance[2]
elseif @tterm31 == "1/C"
distance3[0] = 1/distance[2]
endif
if @tterm32 == "A"
distance3[1] = distance[0]
elseif @tterm32 == "1/A"
distance3[1] = 1/distance[0]
elseif @tterm32 == "B"
distance3[1] = distance[1]
elseif @tterm32 == "1/B"
distance3[1] = 1/distance[1]
elseif @tterm32 == "C"
distance3[1] = distance[2]
elseif @tterm32 == "1/C"
distance3[1] = 1/distance[2]
endif
if @tterm33 == "A"
distance3[2] = distance[0]
elseif @tterm33 == "1/A"
distance3[2] = 1/distance[0]
elseif @tterm33 == "B"
distance3[2] = distance[1]
elseif @tterm33 == "1/B"
distance3[2] = 1/distance[1]
elseif @tterm33 == "C"
distance3[2] = distance[2]
elseif @tterm33 == "1/C"
distance3[2] = 1/distance[2]
endif
endif
if @trapno == "2"
if @p_mergemode == "minimum"
float dmin = 1e100
if distance[0] < distance[1]
dmin = distance[0]
m_lastz = lastz[0]
else
dmin = distance[1]
m_lastz = lastz[1]
endif
return dmin
elseif @p_mergemode == "maximum"
float dmax = -1e100
if distance[0] > distance[1]
dmax = distance[0]
m_lastz = lastz[0]
else
dmax = distance[1]
m_lastz = lastz[1]
endif
return dmax
elseif @p_mergemode == "add"
m_lastZ = lastz[0] + lastz[1]
return distance[0]+distance[1]
elseif @p_mergemode == "|A-B|"
m_LastZ = abs(lastz[0] - lastz[1])
return abs(distance[0]-distance[1])
elseif @p_mergemode == "multiply"
m_LastZ = lastz[0]*lastz[1]
return distance[0]*distance[1]
elseif @p_mergemode == "divide"
m_LastZ = lastz[0]/lastz[1]
if distance[1] == 0
distance[1] = 1e-10
endif
return distance[0]/distance[1]
elseif @p_mergemode == "1/(A*B)"
m_lastZ = 1/(lastz[0]*lastz[1])
return 1/(distance[0]*distance[1])
elseif @p_mergemode == "exponentiate"
m_lastZ = lastz[0]^lastz[1]
return distance[0]^distance[1]
elseif @p_mergemode == "A"
m_lastZ = lastz[0]
return distance[0]
elseif @p_mergemode == "B"
m_lastZ = lastz[1]
return distance[1]
elseif @p_mergemode == "and"
if distance[0] < @width && distance[1] < @width
dist = distance[0]
m_lastZ = lastz[0]
else
dist = @width
m_lastZ = @width
endif
return dist
elseif @p_mergemode == "or"
if distance[0] < @width
dist = distance[0]
m_lastZ = lastz[0]
elseif distance[1] < @width
dist = distance[1]
m_lastZ = lastz[1]
else
dist = @width
m_lastz = @width
endif
return dist
elseif @p_mergemode == "xor"
if distance[0] < @width && distance[1] >= @width
dist = distance[0]
m_lastZ = lastz[0]
elseif distance[1] < @width && distance[0] >= @width
dist = distance[1]
m_lastZ = lastz[1]
else
dist = @width
m_lastz = @width
endif
return dist
endif
elseif @trapno == "3"
if @tmerge1 == "+"
dist = distance3[0]+distance3[1]
m_lastZ = lastz[0] + lastz[1]
elseif @tmerge1 == "*"
dist = distance3[0]*distance3[1]
m_lastZ = lastz[0] * lastz[1]
elseif @tmerge1 == "^"
dist = distance3[0]^distance3[1]
m_lastZ = lastz[0] ^ lastz[1]
elseif @tmerge1 == "min"
if distance3[0] < distance3[1]
dist = distance3[0]
m_lastZ = lastz[0]
else
dist = distance3[1]
m_lastZ = lastz[1]
endif
elseif @tmerge1 == "max"
if distance3[0] > distance3[1]
dist = distance3[0]
m_lastZ = lastz[0]
else
dist = distance3[1]
m_lastZ = lastz[1]
endif
elseif @tmerge1 == "and"
if distance3[0] < @width && distance3[1] < @width
dist = distance3[0]
m_lastZ = lastz[0]
else
dist = @width
m_lastZ = @width
endif
elseif @tmerge1 == "or"
if distance3[0] < @width
dist = distance3[0]
m_lastZ = lastz[0]
elseif distance3[1] < @width
dist = distance3[1]
m_lastZ = lastz[1]
else
dist = @width
m_lastZ = @width
endif
elseif @tmerge1 == "xor"
if distance3[0] < @width && distance3[1] >= @width
dist = distance3[0]
m_lastZ = lastz[0]
elseif distance3[1] < @width && distance3[0] >= @width
dist = distance3[1]
m_lastZ = lastz[1]
else
dist = @width
m_lastZ = @width
endif
endif
if @tmerge2 == "+"
dist = dist+distance3[2]
m_lastZ = m_lastz + lastz[2]
elseif @tmerge2 == "*"
dist = dist*distance3[2]
m_lastZ = m_lastz * lastz[2]
elseif @tmerge2 == "^"
dist = dist^distance3[2]
m_lastZ = m_lastz ^ lastz[2]
elseif @tmerge2 == "min"
if dist < distance3[2]
;
else
dist = distance3[2]
m_lastZ = lastz[2]
endif
elseif @tmerge2 == "max"
if dist > distance3[2]
;
else
dist = distance3[2]
m_lastZ = lastz[2]
endif
elseif @tmerge2 == "and"
if dist < @width && distance3[2] < @width
;
else
dist = @width
m_lastZ = @width
endif
elseif @tmerge2 == "or"
if dist < @width
;
elseif distance3[2] < @width
dist = distance3[2]
m_lastZ = lastz[2]
else
dist = @width
m_lastZ = @width
endif
elseif @tmerge2 == "xor"
if dist < @width && distance3[2] >= @width
;
elseif distance3[2] < @width && dist >= @width
dist = distance3[2]
m_lastZ = lastz[2]
else
dist = @width
m_lastZ = @width
endif
endif
return dist
endif
return 0
endfunc
func SetThreshold(float pthreshold)
int j = 0
while (j < 3)
if (m_Enables[j])
m_Elements[j].SetThreshold(pthreshold)
endif
j = j + 1
endwhile
endfunc
complex func GetTransformedPoint()
return m_LastZ
endfunc
protected:
bool m_Enables[3]
float distance[3]
float distance3[3]
TrapShape m_Elements[3]
float weightF[3]
float m_TextureValue
int m_tmax
complex lastz[3]
float dist
default:
title = "Trap Shape/Texture Merge"
int param v_REB_ShapeTextureMerge
caption = "Version (Trap Shape/Texture Merge)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_REB_ShapeTextureMerge < 101
endparam
param tamode
caption = "Trap A Mode"
default = 0
enum = "A" "-A" "|A|" "A*A" "-A*A" "A*A*A" "-A*A*A" "|A*A*A|" "log(A)" "exp(A)"
visible = @v_REB_ShapeTextureMerge < 101
endparam
param tamode2
caption = "Trap A Mode"
default = 0
enum = "A" "-A" "|A|" "A*A" "-A*A" "A*A*A" "-A*A*A" "|A*A*A|"
visible = @v_REB_ShapeTextureMerge >= 101
endparam
param tbmode
caption = "Trap B Mode"
default = 0
enum = "B" "-B" "|B|" "B*B" "-B*B" "B*B*B" "-B*B*B" "|B*B*B|" "log(B)" "exp(B)"
visible = @v_REB_ShapeTextureMerge < 101
endparam
param tcmode
caption = "Trap C Mode"
default = 0
enum = "C" "-C" "|C|" "C*C" "-C*C" "C*C*C" "-C*C*C" "|C*C*C|" "log(C)" "exp(C)"
visible = @trapno == 1 && @v_REB_ShapeTextureMerge < 101
endparam
param tbmode2
caption = "Trap B Mode"
default = 0
enum = "B" "-B" "|B|" "B*B" "-B*B" "B*B*B" "-B*B*B" "|B*B*B|"
visible = @v_REB_ShapeTextureMerge >= 101
endparam
param tcmode2
caption = "Trap C Mode"
default = 0
enum = "C" "-C" "|C|" "C*C" "-C*C" "C*C*C" "-C*C*C" "|C*C*C|"
visible = @trapno == 1 && @v_REB_ShapeTextureMerge >= 101
endparam
param tterm31
caption = "Merge Term 1"
default = 0
enum = "A" "1/A" "B" "1/B" "C" "1/C"
visible = @trapno == 1
endparam
param tmerge1
caption = " Merge Operator 1"
default = 0
enum = "min" "max" "+" "*" "^" "and" "or" "xor"
visible = @trapno == 1
endparam
param tterm32
caption = "Merge Term 2"
default = 2
enum = "A" "1/A" "B" "1/B" "C" "1/C"
visible = @trapno == 1
endparam
param tmerge2
caption = " Merge Operator 2"
default = 0
enum = "min" "max" "+" "*" "^" "and" "or" "xor"
visible = @trapno == 1
endparam
param tterm33
caption = "Merge Term 3"
default = 4
enum = "A" "1/A" "B" "1/B" "C" "1/C"
visible = @trapno == 1
endparam
int param p_mergemode
caption = "Merge Mode"
enum = "minimum" "maximum" "add" "|A-B|" "multiply" "divide" "1/(A*B)" \
"exponentiate" "A" "B" "and" "or" "xor"
default = 0
visible = @trapno == 0
endparam
heading
text = "Set the 'Thrshold' equal to the value of the 'Trap Threshold' for the \
Trap Mode. Other values may give interesting effects but will not give \
a true 'and', 'or' or 'xor' merge."
visible = @p_mergemode == "AND" ||@p_mergemode == "OR" ||@p_mergemode == "xor" \
|| @tmerge1 == "and" || @tmerge1 == "or" || @tmerge1 == "xor" \
|| @tmerge2 == "and" || @tmerge2 == "or" || @tmerge2 == "xor"
endheading
float param @width
caption = "Threshold"
default = 0.25
visible = @p_mergemode == "AND"||@p_mergemode == "OR" ||@p_mergemode == "xor" \
|| @tmerge1 == "and" || @tmerge1 == "or" || @tmerge1 == "xor" \
|| @tmerge2 == "and" || @tmerge2 == "or" || @tmerge2 == "xor"
endparam
param trapno
caption = "# of shapes"
enum = "2" "3"
endparam
param merge_order2
caption = "Merge Order"
enum = "1 2" "2 1"
visible = @trapno == "2" && (@p_mergemode == "exponentiate" || @p_mergemode == "divide" \
|| @p_mergemode == "and" ||@p_mergemode == "or" ||@p_mergemode == "xor" )
endparam
func mfuncA
caption = "Merge func A"
default = ident()
visible = @v_REB_ShapeTextureMerge >= 101
endfunc
func mfuncB
caption = "Merge func B"
default = ident()
visible = @v_REB_ShapeTextureMerge >= 101
endfunc
func mfuncC
caption = "Merge func C"
default = ident()
visible = @trapno == "3" && @v_REB_ShapeTextureMerge >= 101
endfunc
TrapShape param f_trapshape1
caption = "Trap Shape"
default = REB_TrapShapeBifolium
hint = "Sets the trap shape for this slot. Using a TrapShapeBlock in this slot is recommended so that each trap shape can have its own position and transfer settings. If you do xor need these, you may load a TrapShape directly into this slot to reduce clutter."
endparam
float param weightF1
caption = "Weight factor"
default = 1
endparam
TrapShape param f_trapshape2
caption = "Trap Shape"
default = DMJ_TrapShapeAstroid
hint = "Sets the trap shape for this slot. Using a TrapShapeBlock in this slot is recommended so that each trap shape can have its own position and transfer settings. If you do xor need these, you may load a TrapShape directly into this slot to reduce clutter."
endparam
float param weightF2
caption = "Weight factor"
default = 1
endparam
TrapShape param f_trapshape3
caption = "Trap Shape"
default = REB_TrapShapeAmpersand
hint = "Sets the trap shape for this slot. Using a TrapShapeBlock in this slot is recommended so that each trap shape can have its own position and transfer settings. If you do need these, you may load a TrapShape directly into this slot to reduce clutter."
visible = @trapno == "3"
endparam
float param weightF3
caption = "Weight factor"
default = 1
visible = @trapno == "3"
endparam
}
class REB_TrapShapeGaussianInteger(common.ulb:TrapShape) {
; Modified from the Gaussian Integer code of Kerry Mitchell
public:
func Init(complex pz)
trapshape.Init(pz)
r=0.0
rmin=1.0e12
rmax=0.0
rave=0.0
total=0.0
t=0.0
iter=0
itermin=0
itermax=0
zmin=(0.0,0.0)
zmax=(0.0,0.0)
if(@norm==1) ; pixel normalization
normfac=#pixel
elseif(@norm==2) ; factor normalization
normfac=@fac
elseif(@norm==3) ; f(z) normalization
normfac=@normfunc(pz)
else ; no normalization
normfac=(1.0,0.0)
endif
logfac=@logseed
endfunc
float func Iterate(complex pz)
TrapShape.Iterate(pz)
iter = iter + 1
complex temp2=pz/@scale
float return_val = 0
if @randomize
logfac=4*logfac*(1-logfac)
temp2=temp2*(1-@randomsize*logfac)
endif
if(@inttype==1) ; trunc
temp=trunc(temp2/normfac)
elseif(@inttype==2) ; floor
temp=floor(temp2/normfac)
elseif(@inttype==3) ; ceil
temp=ceil(temp2/normfac)
else ; round
temp=round(temp2/normfac)
endif
remain=temp2-temp*normfac
r=cabs(remain)
total=total+r
rave=total/iter
if(r
;
; Used with his permission.
public:
import "common.ulb"
func Monnier_SFBM_II_Texture(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call before each iteration
func Init(complex pz)
TrapShape.Init(pz)
if @v_monniersfbm < 102 || (!@init && @v_monniersfbm >= 102)
z = 0
zc1 = 0
zc2 = 0
zc3 = 0
zc4 = 0
i = 0
j = 0
jmax = 0
niter = 0
a = 0
sum = 0
x = 0
y = 0
d1 = 0
d2 = 0
d3 = 0
d4 = 0
nindex = 0
sindex = 0
scale = 1
cr1r = 0
cr1i = 0
cr2r = 0
cr2i = 0
cr3r = 0
cr3i = 0
cr4r = 0
cr4i = 0
crp1 = 0
crp2 = 0
crp3 = 0
crp4 = 0
norm = 1
if @interp == 0
niter = ceil(real(log(real(@fmm)-imag(@fmm))/log(1+@mstep)))
else
niter = ceil((real(@fmm)-imag(@fmm))/@mstep)
endif
if @mode == 0
jmax = 1
else
jmax = 5
endif
endif
endfunc
; call for each iterated point
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @v_monniersfbm >= 102 && @init
z = 0
zc1 = 0
zc2 = 0
zc3 = 0
zc4 = 0
i = 0
j = 0
jmax = 0
niter = 0
a = 0
sum = 0
x = 0
y = 0
d1 = 0
d2 = 0
d3 = 0
d4 = 0
nindex = 0
sindex = 0
scale = 1
cr1r = 0
cr1i = 0
cr2r = 0
cr2i = 0
cr3r = 0
cr3i = 0
cr4r = 0
cr4i = 0
crp1 = 0
crp2 = 0
crp3 = 0
crp4 = 0
norm = 1
if @interp == 0
niter = ceil(real(log(real(@fmm)-imag(@fmm))/log(1+@mstep)))
else
niter = ceil((real(@fmm)-imag(@fmm))/@mstep)
endif
if @mode == 0
jmax = 1
else
jmax = 5
endif
endif
while j < jmax
z = pz/@size
if @mode == 1 || @mode == 2
if j == 0
a = @cbl + @ctl + @cbr + @ctr + @cc;/20
elseif j == 1
z = z + @eps*(-1,-1)
a = -@cbl
elseif j == 2
z = z + @eps*(-1,1)
a = -@ctl
elseif j == 3
z = z + @eps*(1,-1)
a = -@cbr
elseif j == 4
z = z + @eps*(1,1)
a = -@ctr
endif
else
a = 1
endif
j = j + 1
i = 0
while i < niter + 2
if i == 2
if @pptype == 0
z = (real(@pp)*(1/sqrt(imag(@ppp))*x + 1i*sqrt(imag(@ppp))*y)^real(@ppp)+(1-real(@pp))*z)*imag(@pp)
else
z = (real(@pp)*x^real(@ppp)*exp(imag(@ppp)*1i*y)+(1-real(@pp))*z)*imag(@pp)
endif
elseif i == 0
z = z/imag(@pp)
endif
z = z*exp(1i*pi/180*@rot) + 1 - 2i
if i > 1
if @interp == 0
scale = (1+@mstep)^(i-2)*imag(@fmm)
else
scale = real(@fmm)-(i-1)*(@mstep+.001)
endif
endif
i = i + 1
zc = round(scale*z)/scale
zc1 = zc + (.5,.5)/scale
zc2 = zc + (-.5,.5)/scale
zc3 = zc + (.5,-.5)/scale
zc4 = zc + (-.5,-.5)/scale
cr1r = ((real(zc1)-859-i)^5 % (132+i) - (imag(zc1)+328+i)^3 % (113+i))^2 %2 - 1
if @noise != 6 && @noise != 8 && @noise != 10 && @noise != 12 && @noise != 14
cr2r = ((real(zc2)-859-i)^5 % (132+i) - (imag(zc2)+328+i)^3 % (113+i))^2 %2 - 1
cr3r = ((real(zc3)-859-i)^5 % (132+i) - (imag(zc3)+328+i)^3 % (113+i))^2 %2 - 1
cr4r = ((real(zc4)-859-i)^5 % (132+i) - (imag(zc4)+328+i)^3 % (113+i))^2 %2 - 1
endif
if @noise == 0 || @noise == 5
cr1i = ((real(zc1)-465+i)^3 % (120+i) - (imag(zc1)-756+i)^2 % (107+i))^2 %2 - 1
cr2i = ((real(zc2)-465+i)^3 % (120+i) - (imag(zc2)-756+i)^2 % (107+i))^2 %2 - 1
cr3i = ((real(zc3)-465+i)^3 % (120+i) - (imag(zc3)-756+i)^2 % (107+i))^2 %2 - 1
cr4i = ((real(zc4)-465+i)^3 % (120+i) - (imag(zc4)-756+i)^2 % (107+i))^2 %2 - 1
endif
if @noise == 0
v1 = (z - zc1)*scale
v2 = (z - zc2)*scale
v3 = (z - zc3)*scale
v4 = (z - zc4)*scale
crp1 = cr1r*real(v1) + cr1i*imag(v1)
crp2 = cr2r*real(v2) + cr2i*imag(v2)
crp3 = cr3r*real(v3) + cr3i*imag(v3)
crp4 = cr4r*real(v4) + cr4i*imag(v4)
elseif @noise == 1
crp1 = cr1r
crp2 = cr1r
crp3 = cr1r
crp4 = cr1r
norm = .5
elseif @noise == 2
crp1 = cr1r
crp2 = cr2r
crp3 = cr1r
crp4 = cr2r
norm = .5
elseif @noise == 3
crp1 = cr1r
crp2 = cr2r
crp3 = cr3r
crp4 = cr2r
norm = .5
elseif @noise == 4
crp1 = -cr1r
crp2 = cr2r
crp3 = cr3r
crp4 = -cr4r
norm = .5
elseif @noise == 5
crp1 = cr1r*abs(real(z-zc)*scale)^real(@noisep) + cr1i*abs(imag(z-zc)*scale)^imag(@noisep)
crp2 = cr2r*abs(real(z-zc)*scale)^real(@noisep) + cr2i*abs(imag(z-zc)*scale)^imag(@noisep)
crp3 = cr3r*abs(real(z-zc)*scale)^real(@noisep) + cr3i*abs(imag(z-zc)*scale)^imag(@noisep)
crp4 = cr4r*abs(real(z-zc)*scale)^real(@noisep) + cr4i*abs(imag(z-zc)*scale)^imag(@noisep)
norm = .2
elseif @noise == 6
crp1 = (cabs(z-zc)*scale-imag(@noisep))^real(@noisep)
norm = .4
elseif @noise == 7
crp1 = cr1r*(cabs(z-zc)*scale-imag(@noisep))^real(@noisep)
crp2 = cr2r*(cabs(z-zc)*scale-imag(@noisep))^real(@noisep)
crp3 = cr3r*(cabs(z-zc)*scale-imag(@noisep))^real(@noisep)
crp4 = cr4r*(cabs(z-zc)*scale-imag(@noisep))^real(@noisep)
norm = .4
elseif @noise == 8
arg = atan2(z-zc)
arg = -round(arg/(2*pi)*4)/4*(2*pi)
ztest = (z-zc)*exp(1i*arg)
crp1 = (real(ztest)*scale-imag(@noisep))^real(@noisep)
norm = .4
elseif @noise == 9
arg = atan2(z-zc)
arg = -round(arg/(2*pi)*4)/4*(2*pi)
ztest = (z-zc)*exp(1i*arg)
crp1 = cr1r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
crp2 = cr2r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
crp3 = cr3r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
crp4 = cr4r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
norm = .4
elseif @noise == 10
arg = atan2(z-zc)
arg = -round(arg/(2*pi)*8)/8*(2*pi)
ztest = (z-zc)*exp(1i*arg)
crp1 = (real(ztest)*scale-imag(@noisep))^real(@noisep)
norm = .4
elseif @noise == 11
arg = atan2(z-zc)
arg = -round(arg/(2*pi)*8)/8*(2*pi)
ztest = (z-zc)*exp(1i*arg)
crp1 = cr1r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
crp2 = cr2r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
crp3 = cr3r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
crp4 = cr4r*(real(ztest)*scale-imag(@noisep))^real(@noisep)
norm = .4
elseif @noise == 12
ztest = z - zc
if real(cr1r) > 0
d1 = abs(cabs(ztest*scale+(.5,.5))-.5)
d2 = abs(cabs(ztest*scale-(.5,.5))-.5)
if d2 < d1
d1 = d2
endif
else
d1 = abs(cabs(ztest*scale+(.5,-.5))-.5)
d2 = abs(cabs(ztest*scale-(.5,-.5))-.5)
if d2 < d1
d1 = d2
endif
endif
crp1 = d1^real(@noisep)
norm = .4
elseif @noise == 13
ztest = z - zc
if real(cr1r) > 0
d1 = abs(cabs(ztest*scale+(.5,.5))-.5)
d2 = abs(cabs(ztest*scale-(.5,.5))-.5)
if d2 < d1
d1 = d2
endif
else
d1 = abs(cabs(ztest*scale+(.5,-.5))-.5)
d2 = abs(cabs(ztest*scale-(.5,-.5))-.5)
if d2 < d1
d1 = d2
endif
endif
crp1 = cr1r*(d1^real(@noisep)-imag(@noisep))
crp2 = cr2r*(d1^real(@noisep)-imag(@noisep))
crp3 = cr3r*(d1^real(@noisep)-imag(@noisep))
crp4 = cr4r*(d1^real(@noisep)-imag(@noisep))
norm = .4
elseif @noise == 14
ztest = (z - zc)*scale
if real(cr1r) > 0
d1 = abs(real(ztest) - imag(ztest) -.5)
d2 = abs(real(ztest) - imag(ztest) +.5)
if d2 < d1
d1 = d2
endif
else
d1 = abs(real(ztest) + imag(ztest) -.5)
d2 = abs(real(ztest) + imag(ztest) +.5)
if d2 < d1
d1 = d2
endif
endif
crp1 = d1^real(@noisep)
norm = .4
elseif @noise == 15
ztest = (z - zc)*scale
if real(cr1r) > 0
d1 = abs(real(ztest) - imag(ztest) -.5)
d2 = abs(real(ztest) - imag(ztest) +.5)
if d2 < d1
d1 = d2
endif
else
d1 = abs(real(ztest) + imag(ztest) -.5)
d2 = abs(real(ztest) + imag(ztest) +.5)
if d2 < d1
d1 = d2
endif
endif
crp1 = cr1r*(d1^real(@noisep)-imag(@noisep))
crp2 = cr2r*(d1^real(@noisep)-imag(@noisep))
crp3 = cr3r*(d1^real(@noisep)-imag(@noisep))
crp4 = cr4r*(d1^real(@noisep)-imag(@noisep))
norm = .4
elseif @noise == 16
endif
if @noise == 6 || @noise == 8 || @noise == 10 || @noise == 12 || @noise == 14
nindex = crp1
else
d1 = real(z - zc)*scale + 0.5
d2 = (1 - d1)
d3 = imag(z - zc)*scale + 0.5
d4 = (1 - d3)
d1 = (.5 + .5*sin(pi*d1-pi/2))^@power
d2 = (.5 + .5*sin(pi*d2-pi/2))^@power
d3 = (.5 + .5*sin(pi*d3-pi/2))^@power
d4 = (.5 + .5*sin(pi*d4-pi/2))^@power
nindex = crp1*d1*d3 + crp3*d1*d4 + crp2*d2*d3 + crp4*d2*d4
endif
if @f1 == 1
nindex = real(sin(100*real(@fp1)*nindex+imag(@fp1)))/10
elseif @f1 == 2
nindex = real(@fp1)*10*nindex+2+imag(@fp1)
if abs(nindex) > 1
nindex = 1
endif
nindex = real(asin(nindex))/4
elseif @f1 == 3
nindex = 20*real(@fp1)*nindex+1+imag(@fp1)
if abs(nindex) > 1
nindex = 1
endif
nindex = real(acos(nindex))/4
elseif @f1 == 4
nindex = real(atanh(20*real(@fp1)*nindex+imag(@fp1)))/8
elseif @f1 == 5
nindex = (20*nindex+imag(@fp1))^(2+real(@fp1))/160
elseif @f1 == 6
nindex = real((15*nindex+imag(@fp1))^(.1*real(@fp1)))
elseif @f1 == 7
nindex = real(exp(10*real(@fp1)*nindex+imag(@fp1)-.5))/8
elseif @f1 == 8
nindex = real(round(5*real(@fp1)*nindex+imag(@fp1)/5))/4
elseif @f1 == 9
nindex = real(round(15*real(@fp1)*nindex+imag(@fp1)/5)^.1)/3
elseif @f1 == 10
if real(@fp1)<0.0
nindex = (sin(-(real(z)+(4+imag(@fp1))*nindex))+cos(-(imag(z)+(4+imag(@fp1))*nindex)))/15
else
nindex = (sin(5*sqrt(real(@fp1))*(real(z)+(4+imag(@fp1))*nindex))+cos(5*1/sqrt(real(@fp1))*(imag(z)+(4+imag(@fp1))*nindex)))/15
endif
endif
if @f2 == 1
nindex = real(sin(100*real(@fp2)*nindex+imag(@fp2)))/10
elseif @f2 == 2
nindex = real(@fp2)*10*nindex+2+imag(@fp2)
if abs(nindex) > 1
nindex = 1
endif
nindex = real(asin(nindex))/4
elseif @f2 == 3
nindex = 20*real(@fp2)*nindex+1+imag(@fp2)
if abs(nindex) > 1
nindex = 1
endif
nindex = real(acos(nindex))/4
elseif @f2 == 4
nindex = real(atanh(20*real(@fp2)*nindex+imag(@fp2)))/8
elseif @f2 == 5
nindex = (20*nindex+imag(@fp2))^(2+real(@fp2))/160
elseif @f2 == 6
nindex = real((15*nindex+imag(@fp2))^(.1*real(@fp2)))
elseif @f2 == 7
nindex = real(exp(10*real(@fp2)*nindex+imag(@fp2)-.5))/8
elseif @f2 == 8
nindex = real(round(5*real(@fp2)*nindex+imag(@fp2)/5))/4
elseif @f2 == 9
nindex = real(round(15*real(@fp2)*nindex+imag(@fp2)/5)^.1)/3
elseif @f2 == 10
if real(@fp2)<0.0
nindex = (sin(-(real(z)+(4+imag(@fp2))*nindex))+cos(-(imag(z)+(4+imag(@fp2))*nindex)))/15
else
nindex = (sin(5*sqrt(real(@fp2))*(real(z)+(4+imag(@fp2))*nindex))+cos(5*1/sqrt(real(@fp2))*(imag(z)+(4+imag(@fp2))*nindex)))/15
endif
endif
nindex = real(nindex^@power2)
if i == 1
x = nindex
elseif i == 2
y = nindex
else
sindex = sindex + nindex/scale^@beta
endif
endwhile
if @mode != 2
sum = sum + a*sindex
else
sum = sum + a*abs(sindex)
endif
sindex = 0
scale = 1
endwhile
if @mode == 2
sum = 3*abs(sum)
endif
if @mode == 1
sindex = sum/(10*@eps*(abs(@cbl + @ctl + @cbr + @ctr)+1))
else
sindex = sum
endif
if @interp == 0
d = 2*norm*sindex/(niter)^.5
else
d = .4*norm*sindex
endif
if @v_monniersfbm >= 104
z = exp(flip(2 * #pi * sqrt(2) * d))
endif
m_lastz = z
return d
endfunc
protected:
complex z
complex zc1
complex zc2
complex zc3
complex zc4
int i
int j
int jmax
int niter
float a
float sum
float x
float y
float d1
float d2
float d3
float d4
float nindex
float sindex
float scale
float cr1r
float cr1i
float cr2r
float cr2i
float cr3r
float cr3i
float cr4r
float cr4i
float crp1
float crp2
float crp3
float crp4
float norm
float d
default:
title = "Monnier's S.F.B.M. II Texture"
int param v_monniersfbm
caption = "Version (Monnier's S.F.B.M. II Texture)"
default = 104
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_monniersfbm < 104
endparam
param init
caption = "Init with each iter"
default = true
visible = @v_monniersfbm >= 102
endparam
param size
caption = "Pattern Size"
default = 0.1
endparam
param noise
caption = "Noise Function"
default = 0
enum = "Perlin" "Raw Gird" "Strips" "Corners" "Checkerboard" \
"Soft Gird" "Circles" "Soft Circles" "Squares" "Soft Squares" \
"Octogons" "Soft Octogons" "Roundy Truchet" "Soft Roundy Truchet" \
"Squarry Truchet" "Soft Squarry Truchet"
endparam
param noisep
caption = "Noise F. Parameters"
default = (.2,.5)
hint = "Noise Function Parameters"
endparam
param f1
caption = "flavor 1"
default = 0
enum = "Original" "Wavy" "Blobs" "Cut" "Messy" "Soft I" "Strings" "Soft II" "Sharp" "String-Sharp" "Random Phase"
endparam
param fp1
caption = "flavor 1 Parameters"
default = (1,0)
hint = "flavor 1 Parameters"
endparam
param f2
caption = "flavor 2"
default = 0
enum = "Original" "Wavy" "Blobs" "Cut" "Messy" "Soft I" "Strings" "Soft II" "Sharp" "String-Sharp" "Random Phase"
endparam
param fp2
caption = "flavor 2 Parameters"
default = (1,0)
hint = "flavor 2 Parameters"
endparam
param mode
caption = "Mode"
default = 0
enum = "Normal" "Convolution" "Absolute Convolution"
endparam
param beta
caption = "Beta (Spectral Density Parameter)"
default = 1.0
hint = "Spectral Density Exponent"
endparam
param power
caption = "Power"
default = 2.0
endparam
param power2
caption = "Post-Power"
default = 1.0
endparam
param pp
caption = "Pre-Processing"
default = (0,1)
endparam
param pptype
caption = "Pre-Processing Type"
default = 0
enum = "Cartesian" "Polar"
hint = "Pre-Processing Type"
endparam
param ppp
caption = "Pre-P. Power and Aspect"
default = (1,1)
hint = "Pre-Processing Power and Aspect"
endparam
param rot
caption = "Rotation Step"
default = 28.0
endparam
param mstep
caption = "Frequency Separation"
default = 1.0
hint = "Frequency Separation"
endparam
param fmm
caption = "Inv. of max/min Frequency"
default = (40,1)
hint = "Inverse of max/min Frequency"
endparam
param interp
caption = "Frequency Interpolation"
default = 0
enum = "Logarithmic" "Linear"
hint = "Frequency Interpolation"
endparam
param cc
caption = "Center Extra Weight"
default = 0.0
endparam
param cbl
caption = "Bottom Left Weight"
default = 1.0
endparam
param ctl
caption = "Top Left Weight"
default = 0.0
endparam
param cbr
caption = "Bottom Right Weight"
default = 0.0
endparam
param ctr
caption = "Top Right Weight"
default = 0.0
endparam
param eps
caption = "Epsilon"
default = 0.006
endparam
}
class REB_TrapShapeSlopeBasic(common.ulb:TrapShape) {
; Provides the basic trap shapes for Slope with Shapes.
public:
import "common.ulb"
; constructor
func REB_TrapShapeSlopeBasic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call for each iterated point
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float m_d = 0
if @zmode == 0
m_d = -10000
elseif @zmode == 1
m_d = |pz|; get current distance from origin
elseif @zmode == 2
m_d = abs(real(pz)); get current distances from i axis
elseif @zmode == 3
m_d = abs(imag(pz)); get current distances from r axis
elseif @zmode == 4
m_d = abs(real(pz))+abs(imag(pz)); get current distances from i axis
elseif @zmode == 5
m_d = abs(atan2(pz)); get current angles
elseif @zmode == 6
m_d = -20000
endif
m_lastZ = pz
return m_d
endfunc
default:
title = "Slope Basics"
int param v_slopebasics
caption = "Version (Slope Basics)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_slopebasics < 101
endparam
heading
text = "This plugin provides the basic slope height values."
endheading
param zmode
caption = "Basic heights"
default = 0
enum = "smoothed iteration" "smallest |z|" "smallest |real(z)|" \
"smallest |imag(z)|" "smallest summ(z)" "smallest |atan(z)|"
endparam
}
class REB_ImageTileTexture(common.ulb:TrapShape) {
;
; Uses an image to create a texture.
;
public:
import "common.ulb"
; Constructor
func REB_TrapShapeChip(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
if x != 0
x = y - x/abs(x)*cos(sqr(log(abs(@h2*x-@h3))))*atan(sqr(log(abs(@h3*x-@h2))))
else
x = y - cos(sqr(log(abs(@h2*x-@h3))))*atan(sqr(log(abs(@h3*x-@h2))))
endif
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Chip"
heading
text="Chip Attractor"
endheading
heading
text="x -> y - sign(x)*cos(sqr(log(abs(b*x - c)))) \
* atan(sqr(log(abs(c*x - b))))"
endheading
heading
text="y -> a - x"
endheading
int param v_trapshapechip
caption = "Version (Trap Shape Chip)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapechip < 101
endparam
float param h1
caption = "Chip param 1"
default = -15
endparam
float param h2
caption = "Chip param 2"
default = -3
endparam
float param h3
caption = "Chip param 3"
default = 1
endparam
float param distscale
caption = "Distance scale"
default = 0.01
endparam
float param s
caption = "Attractor scale"
default = 40
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 5
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeChip2(common.ulb:TrapShape) {
; Based upon the Chip strange attractor. Can also be used as a texture.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeChip2(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float scale = sqrt(@h1*@h1+@h2*@h2+@h3*@h3)
scale = @scaleadj*scale
int sgn = 1
if @sgn
sgn = -1
endif
complex p = pz
p = @fn1(p)
float x = real(p)*scale
float y = imag(p)*scale
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
if x != 0
x = y - x/abs(x)*cos(sqr(log(abs(@h2*x-@h3))))*atan(sqr(log(abs(@h3*x-@h2))))
else
x = y - cos(sqr(log(abs(@h2*x-@h3))))*atan(sqr(log(abs(@h3*x-@h2))))
endif
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = @fn2(x + sgn*flip(y))
float d = abs(|pz| - |m_LastZ|)
if @v_trapshapechip2 >= 102
d = d*@dscale
endif
return d
endfunc
default:
title = "Chip 2"
heading
caption="Chip Attractor"
endheading
heading
text="x -> y - sign(x)*cos(sqr(log(abs(b*x - c)))) \
* atan(sqr(log(abs(c*x - b))))"
endheading
heading
text="y -> a - x"
endheading
int param v_trapshapechip2
caption = "Version (Trap Shape Chip 2)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapechip2 < 102
endparam
float param h1
caption = "Chip param 1"
default = -15
endparam
float param h2
caption = "Chip param 2"
default = -3
endparam
float param h3
caption = "Chip param 3"
default = 1
endparam
float param dscale
caption = "Distance scale"
default = 1
visible = @v_trapshapechip2 >= 102
endparam
float param scaleadj
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 1
endparam
func fn1
caption = "Pre Function"
default = atan()
endfunc
func fn2
caption = "Post Function"
default = sinh()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeHenon2(common.ulb:TrapShape) {
; Uses the Henon strange attractor as the trap shape.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHenon2(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float scale = sqrt(@h1*@h1+@h2*@h2)
scale = @scaleadj*scale
int sgn = 1
if @sgn
sgn = -1
endif
complex p = pz
p = @fn1(p)
float x = real(p)*scale
float y = imag(p)*scale
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = 1 + y - @h1*x*x
y = @h2*pxx
att_iter = att_iter + 1
endwhile
m_LastZ = @fn2(x + sgn*flip(y))
float d = abs(|pz| - |m_LastZ|)
if @v_trapshapehenon2 >= 102
d = d*@dscale
endif
return d
endfunc
default:
title = "Henon 2"
heading
text = "Henon attractor"
endheading
heading
text = "x -> 1 + y - h1*x^2"
endheading
heading
text = "y -> h2*x"
endheading
int param v_trapshapehenon2
caption = "Version (Trap Shape Henon 2)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapehenon2 < 102
endparam
float param h1
caption = "Henon param 1"
default = 1.4
endparam
float param h2
caption = "Henon param 2"
default = 0.3
endparam
float param dscale
caption = "Distance scale"
default = 1
visible = @v_trapshapehenon2 >= 102
endparam
float param scaleadj
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 5
endparam
func fn1
caption = "Pre Function"
default = atan()
endfunc
func fn2
caption = "Post Function"
default = sinh()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeHopalong2(common.ulb:TrapShape) {
; Uses the Hopalong strange attractor as the trap shape. Can also be used as a texture.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHopalong2(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float scale = sqrt(@h1*@h1+@h2*@h2+@h3*@h3)
scale = @scaleadj*scale
int sgn = 1
if @sgn
sgn = -1
endif
complex p = pz
p = @fn1(p)
float x = real(p)*scale
float y = imag(p)*scale
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations
pxx = x
if x != 0
x = y - x/abs(x)*sqrt(abs(@h2*x-@h3))
else
x = y - sqrt(abs(@h2*x-3))
endif
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = @fn2(x + sgn*flip(y))
float d = abs(|pz| - |m_LastZ|)
if @v_trapshapehopalong2 >= 102
d = d*@dscale
endif
return d
endfunc
default:
title = "Hopalong 2"
heading
text="Hopalong Attractor"
endheading
heading
text="x -> y - sign(x)*sqrt(abs(b*x-c))"
endheading
heading
text="y -> a - x"
endheading
int param v_trapshapehopalong2
caption = "Version (Trap Shape Hopalong 2)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapehopalong2 < 102
endparam
float param h1
caption = "Hopalong param 1"
default = 0.4
endparam
float param h2
caption = "Hopalong param 2"
default = 1
endparam
float param h3
caption = "Hopalong param 3"
default = 0
endparam
float param dscale
caption = "Distance scale"
default = 1
visible = @v_trapshapehopalong2 >= 102
endparam
float param scaleadj
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 1
endparam
func fn1
caption = "Pre Function"
default = atan()
endfunc
func fn2
caption = "Post Function"
default = sinh()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShape4DOrbit(common.ulb:TrapShape) {
; Based upon the 4D fractal formula approach of Gordon Lamb.
;
; CosMartin is the cosine variant of the Martin strange attractor.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCosMartin(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = y - cos(x)
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "CosMartin"
heading
text="CosMartin Attractor"
endheading
heading
text="x -> y - cos(x)"
endheading
heading
text="y -> a - x"
endheading
int param v_trapshapecosmartin
caption = "Version (Trap Shape CosMartin)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecosmartin < 101
endparam
float param h1
caption = "CosMartin param"
default = 6.28
endparam
float param distscale
caption = "Distance scale"
default = 0.01
endparam
float param s
caption = "Attractor scale"
default = 15
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 5
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeCosMartin2(common.ulb:TrapShape) {
; Uses the CosMartin strange attractor as the trap shape. Can also be used as a texture.
; CosMartin is the cosine variant of the Martin strange attractor.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCosMartin2(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float scale = @h1
scale = @scaleadj*scale
int sgn = 1
if @sgn
sgn = -1
endif
complex p = pz
p = @fn1(p)
float x = real(p)*scale
float y = imag(p)*scale
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = y - cos(x)
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = @fn2(x + sgn*flip(y))
float d = abs(|pz| - |m_LastZ|)
if @v_trapshapecosmartin2 >= 102
d = d*@dscale
endif
return d
endfunc
default:
title = "CosMartin 2"
heading
text="CosMartin Attractor"
endheading
heading
text="x -> y - cos(x)"
endheading
heading
text="y -> a - x"
endheading
int param v_trapshapecosmartin2
caption = "Version (Trap Shape CosMartin 2)"
default = 102
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecosmartin2 < 102
endparam
float param h1
caption = "CosMartin param"
default = 6.28
endparam
float param dscale
caption = "Distance scale"
default = 1
visible = @v_trapshapecosmartin2 >= 102
endparam
float param scaleadj
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 1
endparam
func fn1
caption = "Pre Function"
default = atan()
endfunc
func fn2
caption = "Post Function"
default = sinh()
endfunc
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeHenon(common.ulb:TrapShape) {
; This shape uses the Henon strange attractor
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHenon(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = 1 + y - @h1*x*x
y = @h2*pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Henon"
heading
text = "Henon attractor"
endheading
heading
text = "x -> 1 + y - h1*x^2"
endheading
heading
text = "y -> h2*x"
endheading
int param v_trapshapehenon
caption = "Version (Trap Shape Henon)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapehenon < 101
endparam
float param h1
caption = "Henon param 1"
default = 1.4
endparam
float param h2
caption = "Henon param 2"
default = 0.3
endparam
float param distscale
caption = "Distance scale"
default = 1.0
endparam
float param s
caption = "Attractor scale"
default = 1.0
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 5
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeGingerbread(common.ulb:TrapShape) {
; This shape uses the Gingerbread strange attractor.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeGingerbread(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = 1 - y + abs(x)
y = pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Gingerbread"
heading
text = "Gingerbread attractor"
endheading
heading
text = "x -> y + abs(x)"
endheading
heading
text = "y -> x"
endheading
int param v_trapshapegingerbread
caption = "Version (Trap Shape Gingerbread)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapegingerbread < 101
endparam
float param distscale
caption = "Distance scale"
default = 0.07
endparam
float param s
caption = "Attractor scale"
default = 10
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 10
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeDampedSine(common.ulb:TrapShape) {
; This shape uses the Damped sine equation.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeDampedSine(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b
float x = 5*@a*t
float y = 5*@a*sin(t)/t
m_lastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Damped Sine"
int param v_DampedSine
caption = "Version (Damped Sine)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_DampedSine < 100
endparam
float param a
caption = "Polar Parameter"
default = 0.2
endparam
float param b
caption = "2nd polar Parameter"
default = 1.0
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
}
class REB_TrapShapeHopalong(common.ulb:TrapShape) {
; This shape uses the Hopalong strange attractor. It can also be used as a texture.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHopalong(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
if x != 0
x = y - x/abs(x)*sqrt(abs(@h2*x-@h3))
else
x = y - sqrt(abs(@h2*x-3))
endif
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Hopalong"
heading
text="Hopalong attractor"
endheading
heading
text="x -> y - sign(x)*sqrt(abs(b*x-c))"
endheading
heading
text="y -> a - x"
endheading
int param v_trapshapehopalong
caption = "Version (Trap Shape Hopalong)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapehopalong < 101
endparam
float param h1
caption = "Hopalong param 1"
default = 0.4
endparam
float param h2
caption = "Hopalong param 2"
default = 1
endparam
float param h3
caption = "Hopalong param 3"
default = 0
endparam
float param distscale
caption = "Distance scale"
default = 0.06
endparam
float param s
caption = "Attractor scale"
default = 3
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 5
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeKam_Torus(common.ulb:TrapShape) {
; This shape uses the Hopalong strange attractor. It can also be used as a texture.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKam_Torus(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s+@sorbit
float y = imag(pz)*@s+@sorbit
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = x*cos(@a) - (y - x^2)*sin(@a)
y = pxx*sin(@a) + (y - pxx^2)*cos(@a)
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Kam Torus"
heading
text = "Kam Torus attractor"
endheading
heading
text = "Kam Torus is the phase map for the Henon attractor"
endheading
heading
text = "x -> x*cos(a) - (y-x^2)*sin(a)"
endheading
heading
text = "y -> x*sin(a) + (y-x^2)*cos(a)"
endheading
heading
text = "The full phase map is determined by progressing through a continuum of \
starting points for x and y."
endheading
int param v_trapshapeKamTorus
caption = "Version (Trap Shape Kam Torus)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeKamTorus < 101
endparam
float param a
caption = "Kam Torus param"
default = 1.57
endparam
float param sorbit
caption = "Start orbit"
default = 0.0
endparam
float param distscale
caption = "Distance scale"
default = 1
endparam
float param s
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 100
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeLatoocarfian(common.ulb:TrapShape) {
; This shape uses the Latoocarfian strange attractor
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLatoocarfian(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = sin(y*@h2) + @h3*sin(x*@h2)
y = sin(pxx*@h1) + @h4*sin(y*@h1)
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Latoocarfian"
heading
text = "Latoocarfian attractor"
endheading
heading
text = "x -> sin(h2*y) + h3*sin(h2*x)"
endheading
heading
text = "y -> sin(h1*x) + h4*sin(h1*y)"
endheading
int param v_trapshapelatoocarfian
caption = "Version (Trap Shape Latoocarfian)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapelatoocarfian < 101
endparam
float param h1
caption = "Latoocarfian 1"
default = --0.960918
endparam
float param h2
caption = "Latoocarfian 2"
default = 2.879879
endparam
float param h3
caption = "Latoocarfian 3"
default = 0.765145
endparam
float param h4
caption = "Latoocarfian 4"
default = 0.744728
endparam
float param distscale
caption = "Distance scale"
default = 1
endparam
float param s
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 5
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeKaneko(common.ulb:TrapShape) {
; This shape uses the Kaneko strange attractor
; Suggested values to try:
; a b
;-----------------
; 0.1 1.67
; 0.5 4.0
; 0.17 1.3
; 0.562 2.76
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKaneko(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
if @kantype == "I"
x = @a*x + (1-@a)*(1-@b*y^2)
else
x = @a*x + (1-@a)*(1-@b*abs(y))
endif
y = pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Kaneko"
heading
text = "Kaneko attractor"
endheading
heading
text = "There are two forms of the Kaneko attractor"
endheading
heading
text = " Form I"
endheading
heading
text = "x -> a*x + (1-a)*(1-b*y^2)"
endheading
heading
text = "y -> x"
endheading
heading
text = " Form II"
endheading
heading
text = "x -> a*x + (1-a)*(1-b*abs(y))"
endheading
heading
text = "y -> x"
endheading
int param v_trapshapeKaneko
caption = "Version (Trap Shape Kaneko)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeKaneko < 100
endparam
param kantype
caption = "Kaneko type"
default = 0
enum = "I" "II"
endparam
param a
caption = "parameter a"
default = 0.4
endparam
param b
caption = "parameter b"
default = 2.76
endparam
float param distscale
caption = "Distance scale"
default = 0.5
endparam
float param s
caption = "Attractor scale"
default = 2.5
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 10
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeMira(common.ulb:TrapShape) {
; This shape uses the Mira strange attractor
; Suggested values to try:
; a b
;-----------------
; 0.29 1.0005
; -0.48 0.93
; -0.4 0.9999
; -0.2 1.000
public:
import "common.ulb"
; Constructor
func REB_TrapShapeMira(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = @b*y + @a*x - (1-@a)*2*x^2/(1+x^2)^2
y = -pxx + @a*pxx - (1-@a)*2*pxx^2/(1+pxx^2)^2
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Mira"
heading
text = "Mira attractor"
endheading
heading
text = "x -> b*y + a*x - (1-a)*2*x^2/(1+x^2)^2"
endheading
heading
text = "y -> -x + a*x - (1-a)*2*x^2/(1+x^2)^2"
endheading
int param v_trapshapeMira
caption = "Version (Trap Shape Mira)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeMira < 100
endparam
param a
caption = "parameter a"
default = -.399000001
endparam
param b
caption = "parameter b"
default = 1.000001
endparam
float param distscale
caption = "Distance scale"
default = 0.5
endparam
float param s
caption = "Attractor scale"
default = 2.5
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 10
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeTinkerbell(common.ulb:TrapShape) {
; This shape uses the Tinkerbell strange attractor
public:
import "common.ulb"
; Constructor
func REB_TrapShapeTinkerbell(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s + @xoff
float y = imag(pz)*@s + @yoff
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
x = x^2 - y^2 + @a*x + @b*y
y = 2*pxx*y + @c*pxx + @d*y
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Tinkerbell"
heading
text = "Tinkerbell attractor"
endheading
heading
text = "x -> x^2 - y^2 + a*x + b*y"
endheading
heading
text = "y -> 2*x*y + c*x + d*y"
endheading
int param v_trapshapeTinkerbell
caption = "Version (Trap Shape Tinkerbell)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeTinkerbell < 100
endparam
float param a
caption = "parameter a"
default = 0.9
endparam
float param b
caption = "parameter b"
default = -0.6103
endparam
float param c
caption = "parameter c"
default = 2.0
endparam
float param d
caption = "parameter d"
default = 0.5
endparam
float param xoff
caption = "x offset"
default = -0.72
endparam
float param yoff
caption = "y offset"
default = -0.64
endparam
float param distscale
caption = "Distance scale"
default = 0.5
endparam
float param s
caption = "Attractor scale"
default = -0.5
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 15
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeLiar(common.ulb:TrapShape) {
; This shape uses the Liar formula of Chuck Ebbert. It is a texture shape.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLiar(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations
pxx = x
if @liartype == 0
if real(x + flip(pz)) < (@h1)
x = @h2 - abs(y-x)
y = abs(@h3 - pxx - y)
endif
elseif @liartype == 1
if imag(x + flip(pz)) < (@h1)
x = @h2 - abs(y-x)
y = abs(@h3 - pxx - y)
endif
else
if cabs(x + flip(pz)) < (@h1)
x = @h2 - abs(y-x)
y = abs(@h3 - pxx - y)
endif
endif
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Liar"
heading
text = "Liar attractor"
endheading
heading
text = "There are three Liar types which depend upon the value of x + flip(z) \
where the real, the imaginary or the cabs value is compared to the \
parameter h1. If the quantity is less than h1 then new values of x \
and y are calculated, otherwise they are left the same. z is the complex \
value passed from the fractal function."
endheading
heading
text = "x -> h2 - abs(y-x)"
endheading
heading
text = "y -> abs(h3-x-y)"
endheading
int param v_trapshapeliar
caption = "Version (Trap Shape Liar)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapeliar < 101
endparam
param liartype
caption = "Liar type"
default = 0
enum = "real" "imag" "abs"
endparam
float param h1
caption = "Liar 1"
default = 2.0
endparam
float param h2
caption = "Liar 2"
default = 0.5
endparam
float param h3
caption = "Liar 3"
default = 0.5
endparam
float param distscale
caption = "Distance scale"
default = 0.5
endparam
float param s
caption = "Attractor scale"
default = 0.1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 20
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapePickover(common.ulb:TrapShape) {
; This shape uses the Pickover strange attractor
public:
import "common.ulb"
; Constructor
func REB_TrapShapePickover(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float ppz = @ppz
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations
pxx = x
x = real(@pfun1(y*@h1) - ppz*@pfun2(x*@h2))
y = real(ppz*@pfun3(pxx*@h3) - @pfun4(y*@h4))
ppz = real(@h5*@pfun5(pxx))
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y)+ppz*@pw)
float d = @distscale*|pz-(x + sgn*flip(y) + ppz*@pw)|
return d
endfunc
default:
title = "Pickover"
heading
text = "Pickover attractor"
endheading
heading
text = "This attractor has been generalized to allow the use of multiple function \
settings."
endheading
heading
text = "x -> fun1(y*h1) - z*fun2(x*h2)"
endheading
heading
text = "y -> z*fun3(x*h3) - fun4(y*h4)"
endheading
heading
text = "z -> h5*fun5(x)"
endheading
int param v_trapshapepickover
caption = "Version (Trap Shape Pickover)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapepickover < 101
endparam
heading
text = "'Initialize Height' sets the starting z value for the attractor."
endheading
float param ppz
caption = "Initialize Height"
default = 0.5
endparam
heading
text = "'Height weight' determines the weight of the final z value which is added \
to the trap distance."
endheading
complex param pw
caption = "Height weight"
default = (0.5,0)
endparam
float param h1
caption = "Pickover 1"
default = 2.24
endparam
float param h2
caption = "Pickover 2"
default = 0.43
endparam
float param h3
caption = "Pickover 3"
default = -0.65
endparam
float param h4
caption = "Pickover 4"
default = -2.43
endparam
float param h5
caption = "Pickover 5"
default = 1
endparam
func pfun1
caption = "Pickover Fn 1"
default = sin()
endfunc
func pfun2
caption = "Pickover Fn 2"
default = cos()
endfunc
func pfun3
caption = "Pickover Fn 3"
endfunc
func pfun4
caption = "Pickover Fn 4"
default = cos()
endfunc
func pfun5
caption = "Pickover Fn 5"
default = sin()
endfunc
float param distscale
caption = "Distance scale"
default = 0.5
endparam
float param s
caption = "Attractor scale"
default = 1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 5
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeQuadruptwo(common.ulb:TrapShape) {
; This shape uses the Quadruptwo strange attractor.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeQuadruptwo(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
int sgn = 1
if @sgn
sgn = -1
endif
float x = real(pz)*@s
float y = imag(pz)*@s
float pxx = 0
int att_iter = 0
while att_iter < @max_att_iterations && x < 1e100 && x > -1e100
pxx = x
if x != 0
x = y - x/abs(x)*sin(log(abs(@h2*x-@h3))) \
*atan(sqr(log(abs(@h3*x-@h2))))
else
x = y - sin(log(abs(@h2*x-@h3))) \
*atan(sqr(log(abs(@h3*x-@h2))))
endif
y = @h1 - pxx
att_iter = att_iter + 1
endwhile
m_LastZ = (x + sgn*flip(y))
float d = @distscale*|pz-(x + sgn*flip(y))|
return d
endfunc
default:
title = "Quadruptwo"
int param v_trapshapequadruptwo
caption = "Version (Trap Shape Quadruptwo)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapequadruptwo < 101
endparam
float param h1
caption = "Quadruptwo param 1"
default = 34
endparam
float param h2
caption = "Quadruptwo param 2"
default = 1
endparam
float param h3
caption = "Quadruptwo param 3"
default = 5
endparam
float param distscale
caption = "Distance scale"
default = 0.0001
endparam
float param s
caption = "Attractor scale"
default = 30
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 50
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSierpinski(common.ulb:TrapShape) {
; This shape uses the Sierpinski strange attractor.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeSierpinski(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
complex pp = pz*@s
int att_iter = 0
while att_iter < @max_att_iterations
if (imag(pp) > @h3)
pp = @h1*real(pp) + flip(@h1*imag(pp) -@h2)
elseif (real(pp) > @h4)
pp = @h1*real(pp) -@h2 + flip(@h1*imag(pp))
else
pp = @h1*real(pp) + flip(@h1*imag(pp))
endif
att_iter = att_iter + 1
endwhile
if !@sgn
m_LastZ = pp
else
m_LastZ = conj(pp)
endif
float d = @distscale*|pz-pp|
return d
endfunc
default:
title = "Sierpinski"
heading
text = "Sierpinski atractor"
endheading
int param v_trapshapesierpinski
caption = "Version (Trap Shape Sierpinski)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapesierpinski < 101
endparam
float param h1
caption = "Sierpinski 1"
default = 2
endparam
float param h2
caption = "Sierpinski 2"
default = 1
endparam
float param h3
caption = "Sierpinski 3"
default = 0.5
endparam
float param h4
caption = "Sierpinski 4"
default = 0.5
endparam
float param distscale
caption = "Distance scale"
default = 1
endparam
float param s
caption = "Attractor scale"
default = 0.1
endparam
int param max_att_iterations
caption = "Attractor iterations"
default = 10
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
}
class REB_TrapShapeSprott3D(common.ulb:TrapShape) {
; This shape uses a Sprott strange attractor.
;
;
;
;
;
;
;
; It can also be used as a texture
;
public:
import "common.ulb"
; constructor
func REB_SpokesNRings(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call for each iterated point
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float dist = cabs(pz)
float theta = atan2(pz)
if theta < 0
theta = theta + 2*#pi
endif
if theta > 2*#pi
theta = 2*#pi
endif
float wedge = 2*#pi/@spokes
float swidth = @swidth
if swidth >= wedge
swidth = wedge
endif
if @type == "Spokes"
if @spiralize
if (theta+@twist*dist) % wedge < (theta+@twist*dist+swidth) % wedge
dist = 1e20
pz = (1e20,1e20)
endif
else
if theta % wedge < (theta+swidth) % wedge
dist = 1e20
pz = (1e20,1e20)
endif
endif
elseif @type == "Rings"
if dist % (1/@dens) < (dist+0.5*@rwidth/@dens) % (1/@dens)
dist = 1e20
pz = (1e20,1e20)
endif
endif
m_lastZ = pz
return dist
endfunc
protected:
default:
title = "Spokes N Rings"
int param v_spokesnrings
caption = "Version (Trap Shape Spokes N Rings)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_spokesnrings < 100
endparam
param type
caption = "Trap Type"
default = 0
enum = "Spokes" "Rings"
endparam
int param spokes
caption = "# of Spokes"
default = 5
visible = @type == "Spokes"
endparam
float param swidth
caption = "Spoke thickness"
default = 1
visible = @type == "Spokes"
endparam
bool param spiralize
caption = "Spiral spokes"
default = false
visible = @type == "Spokes"
endparam
float param twist
caption = "Amount of twist"
default = 1
visible = @type == "Spokes" && @spiralize
endparam
float param dens
caption = "Ring density"
default = 20
visible = @type == "Rings"
endparam
float param rwidth
caption = "Ring thickness"
default = 1
visible = @type == "Rings"
endparam
}
class REB_TrapShapeAmpersand(common.ulb:TrapShape) {
; This shape uses the ampersand function.
;
;
;
;
;
;
;
;
;
;
;
;
;
$define debug
public:
import "common.ulb"
; Constructor
func REB_TrapShapeConvexPolygons(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call before each iteration
func Init(complex pz)
TrapShape.Init(pz)
twopi = 2*#pi
i = 0
x=0.0
y=0.0
; create the vertex aray
repeat
vx[i] = sin(i*twopi/@sides)
vy[i] = cos(i*twopi/@sides)
v[i] = vx[i] + flip(vy[i])
i = i + 1
until i == @sides
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
i = 0
if @flavor == "flavor 1"
d = 1e10
else
d = 0
endif
; calculate r[i] and t[i] for first n-1 sides
repeat
t[i]=(5*pz/@scale-v[i])/(v[i+1]-v[i])
x=real(t[i])
y=imag(t[i])
if @extend && @flavor == "flavor 1"
r[i]=abs(y)
else
if(x<0.0)
r[i]=cabs(t[i])
elseif(x>1.0)
r[i]=cabs(t[i]-1)
else
r[i]=abs(y)
endif
endif
r[i]=r[i]*cabs(v[i+1]-v[i])
i = i + 1
until i == (@sides-1)
; calculate r[i] and t[i] for the last side
t[@sides-1]=(5*pz/@scale-v[@sides-1])/(v[0]-v[@sides-1])
x=real(t[@sides-1])
y=imag(t[@sides-1])
if @extend && @flavor == "flavor 1"
r[@sides-1]=abs(y)
else
if(x<0.0)
r[@sides-1]=cabs(t[@sides-1])
elseif(x>1.0)
r[@sides-1]=cabs(t[@sides-1]-1)
else
r[@sides-1]=abs(y)
endif
endif
r[@sides-1]=r[@sides-1]*cabs(v[0]-v[@sides-1])
i = 0
repeat
if r[i] < d
if @flavor == "flavor 1"
d = r[i]
endif
endif
m_LastZ = m_LastZ + t[i]
if @flavor == "flavor 2"
d = d + cabs(r[i])
elseif @flavor == "flavor 3"
d = d + cabs(t[i])
endif
i = i + 1
until i == @sides
m_LastZ = m_LastZ/@sides^2
if @flavor != "flavor 1"
d = d/@sides^2
else
d = d/@sscale
endif
return d
endfunc
private:
complex v[10]
complex t[10]
float r[10]
float vx[10]
float vy[10]
float twopi
int i
float x
float y
float d
default:
title = "Convex Polygons"
int param v_ConvexPolygons
caption = "Version (ConvexPolygons)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_ConvexPolygons < 100
endparam
int param sides
caption="# of sides"
default = 5
min = 3
max = 10
endparam
float param scale
caption = "Polygon scale"
default = 1.0
endparam
bool param extend
caption = "Extend the sides"
default = false
visible = @flavor == "flavor 1"
endparam
param flavor
caption = "Poly Shape flavor"
default = 0
enum = "flavor 1" "flavor 2" "flavor 3"
endparam
float param sscale
caption = "Poly Shape scale"
default = 1.0
visible = @flavor == "flavor 1"
endparam
}
class REB_TrapShapeStars(common.ulb:TrapShape) {
; This shape uses the Convex Polygons.
$define debug
public:
import "common.ulb"
; Constructor
func REB_TrapShapeStars(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; call before each iteration
func Init(complex pz)
TrapShape.Init(pz)
twopi = 2*#pi
i = 0
x=0.0
y=0.0
; create the vertex aray
repeat
vx[i] = sin(i*twopi/@sides)
vy[i] = cos(i*twopi/@sides)
v[i] = vx[i] + flip(vy[i])
i = i + 1
until i == @sides
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
i = 0
if @flavor == "flavor 1"
d = 1e10
else
d = 0
endif
; calculate r[i] and t[i] for first n-2 sides
repeat
t[i]=(5*pz/@scale-v[i])/(v[i+2]-v[i])
x=real(t[i])
y=imag(t[i])
if @extend && @flavor == "flavor 1"
r[i]=abs(y)
else
if(x<0.0)
r[i]=cabs(t[i])
elseif(x>1.0)
r[i]=cabs(t[i]-1)
else
r[i]=abs(y)
endif
endif
r[i]=r[i]*cabs(v[i+2]-v[i])
i = i + 1
until i == (@sides-2)
; calculate r[i] and t[i] for the last two sides
t[@sides-2]=(5*pz/@scale-v[@sides-2])/(v[0]-v[@sides-2])
x=real(t[@sides-2])
y=imag(t[@sides-2])
if @extend && @flavor == "flavor 1"
r[@sides-2]=abs(y)
else
if(x<0.0)
r[@sides-2]=cabs(t[@sides-2])
elseif(x>1.0)
r[@sides-2]=cabs(t[@sides-2]-1)
else
r[@sides-2]=abs(y)
endif
endif
r[@sides-2]=r[@sides-2]*cabs(v[0]-v[@sides-2])
t[@sides-1]=(5*pz/@scale-v[@sides-1])/(v[1]-v[@sides-1])
x=real(t[@sides-1])
y=imag(t[@sides-1])
if @extend && @flavor == "flavor 1"
r[@sides-1]=abs(y)
else
if(x<0.0)
r[@sides-1]=cabs(t[@sides-1])
elseif(x>1.0)
r[@sides-1]=cabs(t[@sides-1]-1)
else
r[@sides-1]=abs(y)
endif
endif
r[@sides-1]=r[@sides-1]*cabs(v[1]-v[@sides-1])
i = 0
repeat
if r[i] < d
if @flavor == "flavor 1"
d = r[i]
endif
endif
m_LastZ = m_LastZ + t[i]
if @flavor == "flavor 2"
d = d + cabs(r[i])
elseif @flavor == "flavor 3"
d = d + cabs(t[i])
endif
i = i + 1
until i == @sides
m_LastZ = m_LastZ/@sides^2
if @flavor != "flavor 1"
d = d/@sides^2
else
d = d/@sscale
endif
return d
endfunc
private:
complex v[10]
complex t[10]
float r[10]
float vx[10]
float vy[10]
float twopi
int i
float x
float y
float d
default:
title = "Stars"
int param v_Stars
caption = "Version (Stars)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Stars < 100
endparam
int param sides
caption="# of sides"
default = 5
min = 5
max = 10
endparam
float param scale
caption = "Star scale"
default = 1.0
endparam
bool param extend
caption = "Extend the sides"
default = false
visible = @flavor == "flavor 1"
endparam
param flavor
caption = "Star Shape flavor"
default = 0
enum = "flavor 1" "flavor 2" "flavor 3"
endparam
float param sscale
caption = "Star Shape scale"
default = 1.0
visible = @flavor == "flavor 1"
endparam
}
class REB_TrapShapeCircleCatacaustic(common.ulb:TrapShape) {
; This shape uses the circle catacaustic function.
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
;
public:
import "common.ulb"
; Constructor
func REB_TrapShapeEpitrochoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@scale
float x = (@a*2.5+@b*0.6)*cos(t) - 1.3*@c*cos((2.5*@a/(@b*0.6)+1)*t)
float y = (@a*2.5+@b*0.6)*sin(t) - 1.3*@c*sin((2.5*@a/(@b*0.6)+1)*t)
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Epitrochoid"
int param v_Epitrochoid
caption = "Version (Epitrochoid)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Epitrochoid < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param scale
caption = "Scale"
default = 1.0
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
}
class REB_TrapShapeCornoid(common.ulb:TrapShape) {
; This shape uses the Cornoid function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCornoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave && @partype == "angle"
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b*10
float x = @a*cos(t)*(1-2*sin(t)^2)
float y = @a*sin(t)*(1+2*cos(t)^2)
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Cornoid"
int param v_Cornoid
caption = "Version (Cornoid)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Cornoid < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = @partype == "angle"
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && @partype == "angle"
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && @partype == "angle"
endparam
}
class REB_TrapShapeResonanceCurve(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_ResonanceCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave && @partype == "angle"
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b*10
float x = @a*tan(t)
float y = @a*cos(t)^2
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Resonance Curve"
int param v_ResonanceCurve
caption = "Version (Resonance Curve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_ResonanceCurve < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = @partype == "angle"
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && @partype == "angle"
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && @partype == "angle"
endparam
}
class REB_TrapShapeInfiniteQuadrifolium(common.ulb:TrapShape) {
; This shape uses the InfiniteQuadrifolium function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeInfiniteQuadrifolium(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b*6.28
float x = 2*@a*(t^3-t)*(t-1)/(t^3+1)^2
float y = 2*@a*(t^3-t)*(t+1)/(t^3+1)^2
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Infinite Quadrifolium"
int param v_InfiniteQuadrifolium
caption = "Version (Infinite Quadrifolium)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_InfiniteQuadrifolium < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
}
class REB_TrapShapeLegendre(common.ulb:TrapShape) {
; This shape uses the Legendre function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLegendre(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave && @partype == "angle"
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float d = 0
float t = 0
float x = 0
float y = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b
if @n == "2"
y = 5*@a*(3*sin(t)^2 - 1)/2
x = 5*@a*(3*cos(t)^2 - 1)/2
elseif @n == "3"
y = 5*@a*(5*sin(t)^3 - 3*sin(t))/2
x = 5*@a*(5*cos(t)^3 - 3*cos(t))/2
elseif @n == "4"
y = 5*@a*(35*sin(t)^4 - 30*sin(t)^2 + 3)/8
x = 5*@a*(35*cos(t)^4 - 30*cos(t)^2 + 3)/8
elseif @n == "5"
y = 5*@a*(63*sin(t)^5 - 70*sin(t)^3 + 15*sin(t))/8
x = 5*@a*(63*cos(t)^5 - 70*cos(t)^3 + 15*cos(t))/8
elseif @n == "6"
y = 5*@a*(231*sin(t)^6 - 315*sin(t)^4 + 105*sin(t)^2 -5)/16
x = 5*@a*(231*cos(t)^6 - 315*cos(t)^4 + 105*cos(t)^2 -5)/16
endif
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Legendre"
int param v_Legendre
caption = "Version (Legendre)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Legendre < 100
endparam
param n
caption = "Legendre number"
default = 0
enum = "2" "3" "4" "5" "6"
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = @partype == "angle"
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && @partype == "angle"
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && @partype == "angle"
endparam
}
class REB_TrapShapeLaguerre(common.ulb:TrapShape) {
; This shape uses the Laguerre function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLaguerre(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave && @partype == "angle"
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float d = 0
float t = 0
float x = 0
float y = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b*5
if @n == "2"
y = @a*(Sin(t)^2 - 4*sin(t) + 2)/2
x = @a*(cos(t)^2 - 4*cos(t) + 2)/2
elseif @n == "3"
y = @a*(-sin(t)^3 + 9*sin(t)^2 - 18*sin(t) + 6)/6
x = @a*(-cos(t)^3 + 9*cos(t)^2 - 18*cos(t) + 6)/6
elseif @n == "4"
y = @a*(sin(t)^4 - 16*sin(t)^3 + 72*sin(t)^2 - 96*sin(t) + 24)/24
x = @a*(cos(t)^4 - 16*cos(t)^3 + 72*cos(t)^2 - 96*cos(t) + 24)/24
elseif @n == "5"
y = @a*(-sin(t)^5 + 25*sin(t)^4 - 200*sin(t)^3 + 600*sin(t)^2 - 600*sin(t) + 120)/120
x = @a*(-cos(t)^5 + 25*cos(t)^4 - 200*cos(t)^3 + 600*cos(t)^2 - 600*cos(t) + 120)/120
elseif @n == "6"
y = @a*(sin(t)^6 - 36*sin(t)^5 + 450*sin(t)^4 - 2400*sin(t)^3 + 5400*sin(t)^2 \
-4320*sin(t) + 720)/720
x = @a*(cos(t)^6 - 36*cos(t)^5 + 450*cos(t)^4 - 2400*cos(t)^3 + 5400*cos(t)^2 \
-4320*cos(t) + 720)/720
endif
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Laguerre"
int param v_Laguerre
caption = "Version (Laguerre)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Laguerre < 100
endparam
param n
caption = "Laguerre number"
default = 0
enum = "2" "3" "4" "5" "6"
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = @partype == "angle"
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && @partype == "angle"
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && @partype == "angle"
endparam
}
class REB_TrapShapeHermite(common.ulb:TrapShape) {
; This shape uses the Hermite function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHermite(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave && @partype == "angle"
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float d = 0
float t = 0
float x = 0
float y = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b
if @htype == 0
if @n == "2"
x = @a*(cos(t)^2 - 1)
y = @a*(sin(t)^2 - 1)
elseif @n == "3"
x = @a*(cos(t)^3 - 3*cos(t))/3
y = @a*(sin(t)^3 - 3*sin(t))/3
elseif @n == "4"
x = @a*(cos(t)^4 - 6*cos(t)^2 + 3)/3
y = @a*(sin(t)^4 - 6*sin(t)^2 + 3)/3
elseif @n == "5"
x = @a*(cos(t)^5 - 10*cos(t)^3 + 15*cos(t))/15
y = @a*(sin(t)^5 - 10*sin(t)^3 + 15*sin(t))/15
elseif @n == "6"
x = @a*(cos(t)^6 - 15*cos(t)^4 + 45*cos(t)^2 - 15)/15
y = @a*(sin(t)^6 - 15*sin(t)^4 + 45*sin(t)^2 - 15)/15
elseif @n == "7"
x = @a*(cos(t)^7 - 21*cos(t)^5 + 105*cos(t)^3 - 105*cos(t))/105
y = @a*(sin(t)^7 - 21*sin(t)^5 + 105*sin(t)^3 - 105*sin(t))/105
elseif @n == "8"
x = @a*(cos(t)^8 - 28*cos(t)^6 + 210*cos(t)^4 - 420*cos(t)^2 + 105)/105
y = @a*(sin(t)^8 - 28*sin(t)^6 + 210*sin(t)^4 - 420*sin(t)^2 + 105)/105
elseif @n == "9"
x = @a*(cos(t)^9 - 36*cos(t)^7 + 378*cos(t)^5 - 1260*cos(t)^3 + 945*cos(t))/945
y = @a*(sin(t)^9 - 36*sin(t)^7 + 378*sin(t)^5 - 1260*sin(t)^3 + 945*sin(t))/945
elseif @n == "10"
x = @a*(cos(t)^10 - 45*cos(t)^8 + 630*cos(t)^6 - 3150*cos(t)^4 + 4275*cos(t)^2 - 945)/945
y = @a*(sin(t)^10 - 45*sin(t)^8 + 630*sin(t)^6 - 3150*sin(t)^4 + 4275*sin(t)^2 - 945)/945
endif
else
if @n == "2"
x = @a*4*(cos(t)^2 - 2)/2
y = @a*4*(sin(t)^2 - 2)/2
elseif @n == "3"
x = @a*8*(cos(t)^3 - 12*cos(t))/144
y = @a*8*(sin(t)^3 - 12*sin(t))/144
elseif @n == "4"
x = @a*16*(cos(t)^4 - 48*cos(t)^2 + 12)/288
y = @a*16*(sin(t)^4 - 48*sin(t)^2 + 12)/288
elseif @n == "5"
x = @a*32*(cos(t)^5 - 160*cos(t)^3 + 120*cos(t))/2880
y = @a*32*(sin(t)^5 - 160*sin(t)^3 + 120*sin(t))/2880
elseif @n == "6"
x = @a*64*(cos(t)^6 - 480*cos(t)^4 + 720*cos(t)^2 - 120)/14400
y = @a*64*(sin(t)^6 - 480*sin(t)^4 + 720*sin(t)^2 - 120)/14400
elseif @n == "7"
x = @a*128*(cos(t)^7 - 1344*cos(t)^5 + 3360*cos(t)^3 - 1680*cos(t))/113000
y = @a*128*(sin(t)^7 - 1344*sin(t)^5 + 3360*sin(t)^3 - 1680*sin(t))/113000
elseif @n == "8"
x = @a*256*(cos(t)^8 - 3584*cos(t)^6 + 13440*cos(t)^4 - 13440*cos(t)^2 + 1680)/564480
y = @a*256*(sin(t)^8 - 3584*sin(t)^6 + 13440*sin(t)^4 - 13440*sin(t)^2 + 1680)/564480
elseif @n == "9"
x = @a*512*(cos(t)^9 - 9216*cos(t)^7 + 48384*cos(t)^5 - 80640*cos(t)^3 + 30240*cos(t))/1e7
y = @a*512*(sin(t)^9 - 9216*sin(t)^7 + 48384*sin(t)^5 - 80640*sin(t)^3 + 30240*sin(t))/1e7
elseif @n == "10"
x = @a*1024*(cos(t)^10 - 23040*cos(t)^8 + 161280*cos(t)^6 - 403200*cos(t)^4 + 302400*cos(t)^2 - 20340)/1e8
y = @a*1024*(sin(t)^10 - 23040*sin(t)^8 + 161280*sin(t)^6 - 403200*sin(t)^4 + 302400*sin(t)^2 - 20340)/1e8
endif
endif
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Hermite"
int param v_Hermite
caption = "Version (Hermite)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Hermite < 100
endparam
param n
caption = "Hermite number"
default = 0
enum = "2" "3" "4" "5" "6" "7" "8" "9" "10"
endparam
param htype
caption = "Hermite type"
default = 0
enum = "probabilist" "physicist"
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = @partype == "angle"
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && @partype == "angle"
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && @partype == "angle"
endparam
}
class REB_TrapShapeChebychev(common.ulb:TrapShape) {
; This shape uses the Chebychev function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeChebychev(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 0
float x = 0
float y = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@b*5
y = @a*cos(@n*acos(sin(t)))
x = @a*cos(@n*acos(cos(t)))
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Chebychev"
int param v_Chebychev
caption = "Version (Chebychev)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Chebychev < 100
endparam
int param n
caption = "Chebychev number"
default = 2
min = 2
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
}
class REB_TrapShapeLissajous(common.ulb:TrapShape) {
; This shape uses the Lissajous function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeLissajous(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = @scale*t
float x = 2.5*@a*sin(t)
float y = 2.5*@a*sin(10*@b*t+@c)
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Lissajous"
int param v_Lissajous
caption = "Version (Lissajous)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Lissajous < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param scale
caption = "Param scale"
default = 1.0
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
}
class REB_TrapShapeHypotrochoid(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHypotrochoid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t *@scale
float x = (@a*6-@b*0.3)*cos(t) + 1.3*@c*cos((6*@a/(@b*0.3)-1)*t)
float y = (@a*6-@b*0.3)*sin(t) - 1.3*@c*sin((6*@a/(@b*0.3)-1)*t)
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Hypotrochoid"
int param v_Hypotrochoid
caption = "Version (Hypotrochoid)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Hypotrochoid < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param scale
caption = "Scale"
default = 1.0
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
}
class REB_TrapShapeHypocycloid(common.ulb:TrapShape) {
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHypocycloid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
if @wave && @partype == "angle"
float r = cabs(pz)
float wtheta = atan2(pz)
if wtheta < 0
wtheta = wtheta + 2 * #pi
endif
int iter = 0
while iter < 2
wtheta = wtheta + @wamp * cos(@wfreq * r)
iter = iter + 1
endwhile
float x = r * cos(wtheta)
float y = r * sin(wtheta)
pz = x + flip(y)
endif
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t *@scale
float x = @a*((1-@b*3)*cos(3*@b*t)+3*@b*@c*cos((1-3*@b)*t))
float y = @a*((1-@b*3)*sin(3*@b*t)-3*@b*@c*sin((1-3*@b)*t))
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Hypocycloid"
int param v_Hypocycloid
caption = "Version (v)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Hypocycloid < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param c
caption = "3rd Polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param scale
caption = "Scale"
default = 1.0
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
bool param wave
caption = "Add petal wave"
default = false
visible = @partype == "angle"
endparam
float param wamp
caption = "Wave amplitude"
default = 0.05
visible = @wave && @partype == "angle"
endparam
float param wfreq
caption = "Wave frequency"
default = 20
visible = @wave && @partype == "angle"
endparam
}
class REB_TrapShapePlateauCurve(common.ulb:TrapShape) {
; This shape uses the Plateau Curve function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapePlateauCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = 0
if @partype == "cabs(z)"
t = cabs(pz)
elseif @partype == "real(z)"
t = real(pz)
elseif @partype == "imag(z)"
t = imag(pz)
elseif @partype == "real(z) + imag(z)"
t = real(pz) + imag(pz)
elseif @partype == "real(z) * imag(z)"
t = real(pz) * imag(pz)
elseif @partype == "angle"
t = atan2(pz)
endif
t = t*@scale
float x = @a*sin((1+@b*1.2)*t)/sin((1-@b*1.2)*t)
float y = @a*sin(t)*sin(@b*1.2*t)/sin((1-@b*1.2)*t)
m_LastZ = x + flip(y)
d = cabs(pz-m_LastZ)
return d
endfunc
default:
title = "Plateau Curve"
int param v_PlateauCurve
caption = "Version (PlateauCurve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_PlateauCurve < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1
hint = "Affects spread and scale of trap"
endparam
float param scale
caption = "Scale"
default = 1.0
endparam
param partype
caption = "Param Type"
default = 0
enum = "cabs(z)" "real(z)" "imag(z)" "real(z) + imag(z)" "real(z) * imag(z)" \
"angle"
endparam
}
class REB_TrapShapeEquiangularSpiral(common.ulb:TrapShape) {
; This shape uses the Equiangular Spiral function.
;
;
;
;
;
;
;
;
;
;
;
;
;
public:
import "common.ulb"
; Constructor
func REB_TrapShapeHeartCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float t = (7.5*@a*atan2(pz))%1
float x = 0.33*@b*sin(t)*cos(t)*log(abs(t))
float y = 0.33*@b*abs(t)^0.3*cos(t)^0.5
m_lastZ = x + flip(y)
d = cabs(pz-m_lastZ)
return d
endfunc
default:
title = "Heart Curve"
int param v_HeartCurve
caption = "Version (HeartCurve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_HeartCurve < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
}
class REB_TrapShapeAtriphtaloid(common.ulb:TrapShape) {
; This shape uses the Atriphtaloid function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeAtriphtaloid(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = x^4*(x^2+y^2)-(@ps*@aa*x^2-@ps*@ab)^2+cabs(pz)*@offset
else
d = x^4*(x^2+y^2)-(@ps*@aa*x^2-@ps*@ab)^2+@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
x = real(pz)
y = (-x^2+(100*@b)^2-100*@b*@c/x^2+ (0.5*@c)^2/x^4)^0.5
m_lastZ = 0.005*@a*(x + flip(y))
d = cabs(pz-m_lastZ)
endif
return d
endfunc
default:
title = "Atriphtaloid"
int param v_Atriphtaloid
caption = "Version (Atriphtaloid)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_Atriphtaloid < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.2
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param aa
caption = "parameter a"
default = 5
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
float param ab
caption = "parameter b"
default = 1.0
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
float param ps
caption = "param scaler"
default = 0.4
hint = "Affects spread and scale of trap"
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
float param c
caption = "3rd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
}
class REB_TrapShapeBurnsideCurve(common.ulb:TrapShape) {
; This shape uses the Burnside Curve function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeBurnsideCurve(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float d = 0
float x = 0
float y = 0
if @altformula
pz = pz/@scale
; pz = pz*(cos(rotangle)+flip(sin(rotangle)))
x = real(@fn1(pz))
y = imag(@fn2(pz))
if @ref == "pz"
d = y^2-x*(x^4-@a1)-cabs(pz)*@offset
else
d = y^2-x*(x^4-@a1)-@offset
endif
if abs(d) < @width
d =abs(d)
else
d = 1e20
endif
else
x = real(pz)
y = (x^5 - x)^0.5
m_lastZ = 2*@a*(x + flip(y))
d = cabs(pz-m_lastZ)
endif
return d
endfunc
default:
title = "Burnside Curve"
int param v_BurnsideCurve
caption = "Version (BurnsideCurve)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_BurnsideCurve < 100
endparam
heading
text = "The 'Alternate formula' is a polynomial form which may give a more \
accurate rendering of the trap shape."
endheading
bool param altformula
caption = "Alternate formula"
default = false
endparam
float param scale
caption = "scale"
default = 0.25
visible = @altformula
endparam
float param width
caption = "width"
default = 1
visible = @altformula
endparam
float param a1
caption = "parameter a"
default = 1
visible = @altformula
endparam
param ref
caption = "offset reference"
default = 0
enum = "zero" "pz"
visible = @altformula
endparam
float param offset
caption = "Offset"
default = 0.0
hint = "Trap offset"
visible = @altformula
endparam
func fn1
caption = "Function 1"
default = ident()
visible = @altformula
endfunc
func fn2
caption = "Function 2"
default = ident()
visible = @altformula
endfunc
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
visible = !@altformula
endparam
}
class REB_TrapShapeKleinQuartic(common.ulb:TrapShape) {
; This shape uses the KleinQuartic function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeKleinQuartic(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float x = real(pz)
float y = (-x/2+(x^2/4+x^9/27)^0.5)^(1/3)+(-x/2-(x^2/4+x^9/27)^0.5)^(1/3)
m_lastZ = @a*(x + flip(y))
float d = cabs(pz-m_lastZ)
return d
endfunc
default:
title = "Klein Quartic"
int param v_KleinQuartic
caption = "Version (Klein Quartic)"
default = 100
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_KleinQuartic < 100
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
}
class REB_TrapShapeTrochoid(common.ulb:TrapShape) {
; This shape uses the Trochoid function.
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