

PREV CLASS NEXT CLASS  FRAMES NO FRAMES  
SUMMARY: NESTED  FIELD  CONSTR  METHOD  DETAIL: FIELD  CONSTR  METHOD 
Object common:Vector
class
Vector class.
The Vector class allows you to easily define a fourdimensional vector. These have a variety of uses in fractal generation, including use as a container for a 3D vector.
For performance reasons, none of the Vector methods return a vector. The last vector argument is the return value. For example,
Vector V1 = new Vector(....)
V1.Cross(V2,V3)
is equivalent to
V3 = V1 x V2
Also for performance reasons, you may access the vector elements directly, as m_x, m_y, m_z, and m_w.
Ron Barnett
class Vector { ; Vector class. ; ; <p> ; The Vector class allows you to easily define a fourdimensional vector. ; These have a variety of uses in fractal generation, including use as a ; container for a 3D vector. ; <p> ; For performance reasons, none of the Vector methods return a vector. ; The last vector argument is the return value. For example, ; <p> ; Vector V1 = new Vector(....)<br> ; V1.Cross(V2,V3) ; <p> ; is equivalent to ; <p> ; V3 = V1 x V2 ; <p> ; Also for performance reasons, you may access the vector elements ; directly, as m_x, m_y, m_z, and m_w. ; <p> ; Ron Barnett public: ; Constructor ; ; @param x x term of vector ; @param y y term of vector ; @param z z term of vector ; @param w w term of vector (use 1.0 if you are storing a 3D vector) func Vector(float x, float y, float z, float w) Init(x,y,z,w) endfunc ; Reinitialize a Vector. ; <p> ; If you need to completely change the value of a Vector, you can use this function rather than deleting the old Vector and creating a new one. (Reuse is faster.) ; ; @param x x term of vector ; @param y y term of vector ; @param z z term of vector ; @param w w term of vector (use 1.0 if you are storing a 3D vector) func Init(float x, float y, float z, float w) m_x = x m_y = y m_z = z m_w = w endfunc ; Copy a Vector to another Vector. ; <p> ; If you simply assign the value of one Vector to another, you actually create a reference in both variables to the same Vector object, and changes in one variable's vector will appear in the other. See the UF help file topic on "reference" ("Objects") for details. To make a true copy from one Vector to another Vector, use this function. ; ; @param T target vector that will receive a copy of the Vector's data func Copy(Vector T) T.m_x = m_x T.m_y = m_y T.m_z = m_z T.m_w = m_w endfunc ; Get a Vector element by index. ; <p> ; Sometimes you need to access a Vector's elements by index number (03) rather than by name. If you do, you may use this function. Note that this is slower than accessing the member variables directly. ; ; @param n element number (03) to retrieve ; @return the value of the element float func Get(int n) if (n == 0) return m_x elseif (n == 1) return m_y elseif (n == 2) return m_z elseif (n == 3) return m_w else return 0 endif endfunc ; Set a Vector element by index. ; <p> ; Sometimes you need to set a Vector's elements by index number (03) rather than by name. If you do, you may use this function. Note that this is slower than accessing the member variables directly. ; ; @param n element number (03) to set ; @param v the new value for the element func Set(int n, float v) if (n == 0) m_x = v elseif (n == 1) m_y = v elseif (n == 2) m_z = v elseif (n == 3) m_w = v endif endfunc ; Normalize a Vector. ; <p> ; Normalization gives a unit vector. The x, y, z and w values are ; direction cosines. ; ; @param V target vector that will receive the normalized vector func Normalize(Vector V) float vd = 1/sqrt(m_x^2+m_y^2+m_z^2+m_w^2) V.m_x = m_x*vd V.m_y = m_y*vd V.m_z = m_z*vd V.m_w = m_w*vd endfunc ; Determine a Vector's size. ; ; @return the size (or length) of the vector float func Size() return sqrt(m_x^2+m_y^2+m_z^2+m_w^2) endfunc ; Add two Vectors. ; ; @param V1 the second vector to add ; @param V2 the target vector for the added vectors to be stored in func Add(Vector V1, Vector V2) V2.m_x = m_x+V1.m_x V2.m_y = m_y+V1.m_y V2.m_z = m_z+V1.m_z V2.m_w = m_w+V1.m_w endfunc ; Subtract two Vectors. ; ; @param V1 the second vector to subtract ; @param V2 the target vector for the differenced vectors to be stored in func Sub(Vector V1, Vector V2) V2.m_x = m_xV1.m_x V2.m_y = m_yV1.m_y V2.m_z = m_zV1.m_z V2.m_w = m_wV1.m_w endfunc ; Multiply a vector by a constant. ; ; @param c the constant to multiply by ; @param V the target vector for the multiplied values to be stored in func MConst(float c, Vector V) V.m_x = m_x*c V.m_y = m_y*c V.m_z = m_z*c V.m_w = m_w*c endfunc ; Shift Vector elements. ; <p> ; This function shifts the vector elements so that x becomes y, y becomes z, z becomes w, and w becomes x. You may shift by any number of positions, although any multiple of four will return the elements to their starting positions. Negative values will be interpreted as shifts in reverse. ; ; @param shift number of places to shift (negative values shift in reverse) ; @param V the target vector to store the shifted vector in func Shift(int shift, Vector V) float x = m_x float y = m_y float z = m_z float w = m_w shift = shift % 4 if shift < 0 shift = shift + 4 endif if shift == 1 V.m_x = w V.m_y = x V.m_z = y V.m_w = z elseif shift == 2 V.m_x = z V.m_y = w V.m_z = x V.m_w = y elseif shift == 3 V.m_x = y V.m_y = z V.m_z = w V.m_w = x else V.m_x = x V.m_y = y V.m_z = z V.m_w = w endif endfunc ; Vector Dot Product ; <p> ; This gives the cosine of the angle between the vectors. ; ; @param V the second vector in the dot product ; @return the dot product float func Dot(Vector V) return V.m_x*m_x+V.m_y*m_y+V.m_z*m_z+V.m_w*m_w endfunc ; Vector Cross Product (3D) ; <p> ; This gives the vector cross product, which given two 3D vectors will produce a third vector which is at right angles to the plane containing the two vectors. Note that changing the order of the two vectors will generally result in the cross product pointing in the opposite direction: ; <p> ; V x V1 =  V1 x V ; <p> ; This version of the cross product assumes the Vector objects hold a 3D vector, and returns a 3D vector. ; ; @param V1 the second vector in the cross product ; @param V2 the target vector to store the cross product vector in func Cross(Vector V1, Vector V2) float x = m_y*V1.m_zm_z*V1.m_y float y = m_z*V1.m_xm_x*V1.m_z float z = m_x*V1.m_ym_y*V1.m_x V2.m_x = x V2.m_y = y V2.m_z = z V2.m_w = 1 endfunc ; Vector Cross Product (4D) ; <p> ; This gives the vector cross product, which given three 4D vectors will produce a fourth vector which is at right angles to the hyperplane containing the three vectors. Note that changing the order of the three vectors will generally result in a different orientation of the result. ; ; @param V1 the second vector in the cross product ; @param V2 the third vector in the cross product ; @param V3 the target vector to store the cross product vector in func Cross4D(Vector V1, Vector V2, Vector V3) float a = (V1.m_x * V2.m_y)  (V1.m_y * V2.m_x); float b = (V1.m_x * V2.m_z)  (V1.m_z * V2.m_x); float c = (V1.m_x * V2.m_w)  (V1.m_w * V2.m_x); float d = (V1.m_y * V2.m_z)  (V1.m_z * V2.m_y); float e = (V1.m_y * V2.m_w)  (V1.m_w * V2.m_y); float f = (V1.m_z * V2.m_w)  (V1.m_w * V2.m_z); float x = (m_y * f)  (m_z * e) + (m_w * d); float y =  (m_x * f) + (m_z * c)  (m_w * b); float z = (m_x * e)  (m_y * c) + (m_w * a); float w =  (m_x * d) + (m_y * b)  (m_z * a); V3.m_x = x V3.m_y = y V3.m_z = z V3.m_w = w endfunc ; Rotate Vector in the YZ plane. ; ; @param theta angle to rotate, in radians ; @param V target vector to store resulting rotated vector in func RotYZ(float theta, Vector V) theta = theta*#pi/180 float y = m_y*cos(theta)  m_z*sin(theta) float z = m_y*sin(theta) + m_z*cos(theta) V.m_y = y V.m_z = z V.m_x = m_x V.m_w = m_w endfunc ; Rotate Vector in the ZX plane. ; ; @param theta angle to rotate, in radians ; @param V target vector to store resulting rotated vector in func RotZX(float theta, Vector V) theta = theta*#pi/180 float z = m_z*cos(theta)  m_x*sin(theta) float x = m_z*sin(theta) + m_x*cos(theta) V.m_z = z V.m_x = x V.m_y = m_y V.m_w = m_w endfunc ; Rotate Vector in the XY plane. ; ; @param theta angle to rotate, in radians ; @param V target vector to store resulting rotated vector in func RotXY(float theta, Vector V) theta = theta*#pi/180 float x = m_x*cos(theta)  m_y*sin(theta) float y = m_x*sin(theta) + m_y*cos(theta) V.m_x = x V.m_y = y V.m_z = m_z V.m_w = m_w endfunc ; Rotate Vector in the XW plane. ; ; @param theta angle to rotate, in radians ; @param V target vector to store resulting rotated vector in func RotXW(float theta, Vector V) theta = theta*#pi/180 float x = m_x*cos(theta)  m_w*sin(theta) float w = m_x*sin(theta) + m_w*cos(theta) V.m_x = x V.m_w = w V.m_z = m_z V.m_y = m_y endfunc ; Rotate Vector in the YW plane. ; ; @param theta angle to rotate, in radians ; @param V target vector to store resulting rotated vector in func RotYW(float theta, Vector V) theta = theta*#pi/180 float w = m_w*cos(theta)  m_y*sin(theta) float y = m_w*sin(theta) + m_y*cos(theta) V.m_y = y V.m_w = w V.m_x = m_x V.m_z = m_z endfunc ; Rotate Vector in the ZW plane. ; ; @param theta angle to rotate, in radians ; @param V target vector to store resulting rotated vector in func RotZW(float theta, Vector V) theta = theta*#pi/180 float w = m_w*cos(theta)  m_z*sin(theta) float z = m_w*sin(theta) + m_z*cos(theta) V.m_w = w V.m_z = z V.m_x = m_x V.m_y = m_y endfunc float m_x float m_y float m_z float m_w default: }
Constructor Summary  

Vector()


Vector(float x,
float y,
float z,
float w)
Constructor 
Method Summary  

void 
Add(Vector V1,
Vector V2)
Add two Vectors. 
void 
Copy(Vector T)
Copy a Vector to another Vector. 
void 
Cross(Vector V1,
Vector V2)
Vector Cross Product (3D) 
void 
Cross4D(Vector V1,
Vector V2,
Vector V3)
Vector Cross Product (4D) 
float 
Dot(Vector V)
Vector Dot Product 
float 
Get(int n)
Get a Vector element by index. 
void 
Init(float x,
float y,
float z,
float w)
Reinitialize a Vector. 
void 
MConst(float c,
Vector V)
Multiply a vector by a constant. 
void 
Normalize(Vector V)
Normalize a Vector. 
void 
RotXW(float theta,
Vector V)
Rotate Vector in the XW plane. 
void 
RotXY(float theta,
Vector V)
Rotate Vector in the XY plane. 
void 
RotYW(float theta,
Vector V)
Rotate Vector in the YW plane. 
void 
RotYZ(float theta,
Vector V)
Rotate Vector in the YZ plane. 
void 
RotZW(float theta,
Vector V)
Rotate Vector in the ZW plane. 
void 
RotZX(float theta,
Vector V)
Rotate Vector in the ZX plane. 
void 
Set(int n,
float v)
Set a Vector element by index. 
void 
Shift(int shift,
Vector V)
Shift Vector elements. 
float 
Size()
Determine a Vector's size. 
void 
Sub(Vector V1,
Vector V2)
Subtract two Vectors. 
Methods inherited from class Object 


Constructor Detail 

public Vector(float x, float y, float z, float w)
x
 x term of vectory
 y term of vectorz
 z term of vectorw
 w term of vector (use 1.0 if you are storing a 3D vector)public Vector()
Method Detail 

public void Init(float x, float y, float z, float w)
If you need to completely change the value of a Vector, you can use this function rather than deleting the old Vector and creating a new one. (Reuse is faster.)
x
 x term of vectory
 y term of vectorz
 z term of vectorw
 w term of vector (use 1.0 if you are storing a 3D vector)public void Copy(Vector T)
If you simply assign the value of one Vector to another, you actually create a reference in both variables to the same Vector object, and changes in one variable's vector will appear in the other. See the UF help file topic on "reference" ("Objects") for details. To make a true copy from one Vector to another Vector, use this function.
T
 target vector that will receive a copy of the Vector's datapublic float Get(int n)
Sometimes you need to access a Vector's elements by index number (03) rather than by name. If you do, you may use this function. Note that this is slower than accessing the member variables directly.
n
 element number (03) to retrieve
public void Set(int n, float v)
Sometimes you need to set a Vector's elements by index number (03) rather than by name. If you do, you may use this function. Note that this is slower than accessing the member variables directly.
n
 element number (03) to setv
 the new value for the elementpublic void Normalize(Vector V)
Normalization gives a unit vector. The x, y, z and w values are direction cosines.
V
 target vector that will receive the normalized vectorpublic float Size()
public void Add(Vector V1, Vector V2)
V1
 the second vector to addV2
 the target vector for the added vectors to be stored inpublic void Sub(Vector V1, Vector V2)
V1
 the second vector to subtractV2
 the target vector for the differenced vectors to be stored inpublic void MConst(float c, Vector V)
c
 the constant to multiply byV
 the target vector for the multiplied values to be stored inpublic void Shift(int shift, Vector V)
This function shifts the vector elements so that x becomes y, y becomes z, z becomes w, and w becomes x. You may shift by any number of positions, although any multiple of four will return the elements to their starting positions. Negative values will be interpreted as shifts in reverse.
shift
 number of places to shift (negative values shift in reverse)V
 the target vector to store the shifted vector inpublic float Dot(Vector V)
This gives the cosine of the angle between the vectors.
V
 the second vector in the dot product
public void Cross(Vector V1, Vector V2)
This gives the vector cross product, which given two 3D vectors will produce a third vector which is at right angles to the plane containing the two vectors. Note that changing the order of the two vectors will generally result in the cross product pointing in the opposite direction:
V x V1 =  V1 x V
This version of the cross product assumes the Vector objects hold a 3D vector, and returns a 3D vector.
V1
 the second vector in the cross productV2
 the target vector to store the cross product vector inpublic void Cross4D(Vector V1, Vector V2, Vector V3)
This gives the vector cross product, which given three 4D vectors will produce a fourth vector which is at right angles to the hyperplane containing the three vectors. Note that changing the order of the three vectors will generally result in a different orientation of the result.
V1
 the second vector in the cross productV2
 the third vector in the cross productV3
 the target vector to store the cross product vector inpublic void RotYZ(float theta, Vector V)
theta
 angle to rotate, in radiansV
 target vector to store resulting rotated vector inpublic void RotZX(float theta, Vector V)
theta
 angle to rotate, in radiansV
 target vector to store resulting rotated vector inpublic void RotXY(float theta, Vector V)
theta
 angle to rotate, in radiansV
 target vector to store resulting rotated vector inpublic void RotXW(float theta, Vector V)
theta
 angle to rotate, in radiansV
 target vector to store resulting rotated vector inpublic void RotYW(float theta, Vector V)
theta
 angle to rotate, in radiansV
 target vector to store resulting rotated vector inpublic void RotZW(float theta, Vector V)
theta
 angle to rotate, in radiansV
 target vector to store resulting rotated vector in


PREV CLASS NEXT CLASS  FRAMES NO FRAMES  
SUMMARY: NESTED  FIELD  CONSTR  METHOD  DETAIL: FIELD  CONSTR  METHOD 