Gielis_plus { 
; 
; based on the 'super formula' of Johan Gielis,
; Kerry Mitchell's 'polar-curves' 15nov98, 
; and some curves from the web and from textbooks on analytic geometry.
;
; The use of those three sources (gielis, single and extra) is
; optional and there are several ways of combining them available.
;
; Acknowledgements
;
; Thanks to Mr. Gielis for his consent to use his patented 
; 'super formula' for non-commercial use in Ultra Fractal, and
; also to Kerry Mitchell, who allowed me to use his routines as found
; in 'Polar Curves' in his lkm.ucl,
; and thanks for Kerry's valuable lessons in the courses of
; 'Writing UF Calculation Formualas', and
; 'Writing UF Coloring and Transformation Formulas'
;
;
; Copyright Ed Algra - july 22 2007
; algra275@planet.nl
; 
;
global:
  float twopi=2.0*pi
  float halfpi=0.5*pi
;
init:
  bool flag=true
  int iter=0
  int itermin=0
  int incount=0
  float err=0.0
  float errmin=1.0e12
  float r=0.0   ; radius of composition
  float rs=0.0  ; single
  float rg=0.0  ; gielis
  float re=0.0  ; extra
  float t=0.0
  float term1=0.0
  float term2=0.0
  float temp=0.0
  float hk=0.0
  complex z1=(0,0)
  complex z2=(0,0)
  complex zmin=(0,0)
  complex first_in=(0,0)
  complex last_in=(0,0)
  complex tmp=(0,0)
;
loop:
  iter=iter+1
  if (iter%@skip==0) && (iter>@threshold) && (iter<@end)
     z1=#z-@r_center
;  
; calculation angle t from z1 with Euler formula
     t=imag(log(z1))+@rot ; total pre-rotation
     while t>twopi
        t=t-twopi
     endwhile
     while t<0.0
        t=t+twopi
     endwhile
;
; Gielis (based on the 'superformula' of Johan Gielis)
     if @gielis==true
        hk=0.25*@m*(t+@rot_g)
        while hk>twopi
           hk=hk-twopi
        endwhile
        while hk<0.0
           hk=hk+twopi
        endwhile
        if @hf==false
          term1=abs(cos(hk)/real(@g))^real(@ng)
          term2=abs(sin(hk)/imag(@g))^imag(@ng)
        else
          term1=abs(cosh(hk)/real(@g))^real(@ng)
          term2=abs(sinh(hk)/imag(@g))^imag(@ng)
        endif
        if @hyper==false
           temp=term1+term2
        else
           temp=term1-term2
        endif
        if temp==0
           temp=1e-30
        endif
        if @ge==true ; enhanced
           rg=@rg0+real(@fg_sub(@fg_main(@gc*hk)*@gs/(temp^(1/@n1))))
        else ; gielis 'original'
           rg=@rg0+real(@fg_sub(@gs/(temp^(1/@n1))))
        endif        
     endif
;   
; single functions (based on 'polar curves' of Kerry Mitchell)
     if @single==true
        hk=@b*(t+@rot_s) 
        while hk>twopi
           hk=hk-twopi
        endwhile
        while hk<0.0
           hk=hk+twopi
        endwhile
        rs=@a*real(@fs_main(hk))
        if rs>=0.0
           rs=rs^@n
        else
           rs=-((-rs)^@n)
        endif
        rs=@rs0+real(@fs_sub(rs))
     endif
;       
; extra functions (standard polar functions, mostly composed)
     if @extra==true
        hk=@be*(t+@rot_e) ; be=freq. rot_e=pre-rotation extra
        while hk>twopi
           hk=hk-twopi
        endwhile
        while hk<0.0
           hk=hk+twopi
        endwhile
        if @functiontype==0 ; lemniscate
           re=real(@p)*sqr(2*cos(2*hk))+imag(@p)*sqr(2*sin(2*hk))
        elseif @functiontype==1 ; rose
           re=real(@p)*cos(real(@q)*hk)+imag(@p)*sin(imag(@q)*hk)
        elseif @functiontype==2 ; conchoid
           re=real(@p)/cos((hk)+imag(@p))
        elseif @functiontype==3 ; limaçon
           re=real(@p)*cos(hk)+imag(@p)
        elseif @functiontype==4 ; cissoid
           re=@pp*cos(2*hk)/cos(hk)
        elseif @functiontype==5 ; trifolium
           re=real(@p)*cos(hk)*cos(2*hk)+imag(@p) 
        elseif @functiontype==6 ; cassinoid 1
           re=sqr(real(@p))*(cos(2*hk)+sqrt((imag(@p)/real(@p))^4-sqr(sin(2*hk))))
        elseif @functiontype==7 ; cassinoid 2
           re=sqr(real(@p))*(cos(2*hk)-sqrt((imag(@p)/real(@p))^4-sqr(sin(2*hk))))
        elseif @functiontype==8 ; ellips
           re=real(@p)+imag(@p)*cos(hk)
        elseif @functiontype==9 ; astroid generalized
           re=sqrt(real(@p)*(cos(hk)^(real(@q)))+imag(@p)*(sin(hk)^(imag(@q))))
        elseif @functiontype==10 ; rectangle
           if hk==halfpi || hk==3*halfpi
              re=imag(@p) ; vertical
           elseif hk==0 || hk==pi || hk==twopi
              re=real(@p) ; horizontal
           else
              if hk>halfpi && hk<pi ; NW
                 temp=pi-hk
              elseif hk>pi && hk<3*halfpi ; SW
                 temp=hk-pi
              elseif hk>3*halfpi && hk<twopi ; SE
                 temp=twopi-hk
              else ; NE
                 temp=hk
              endif
              if temp<=atan(imag(@p)/real(@p))
                 re=real(@p)/cos(temp)
              else
                 re=imag(@p)/sin(temp)
              endif
           endif
        elseif @functiontype==11 ; flower
           re=cos(@pp*hk)
        endif
        re=@re0+@es*real(@fe_sub(re))
     endif
;
; combinations (calculation of r)
;   
     if @gielis==true && @single==false && @extra==false
        r=rg
     elseif @gielis==false && @single==true && @extra==false
        r=rs
     elseif @gielis==false && @single==false && @extra==true
        r=re
     elseif @gielis==true && @single==true && @extra==false
        if @combi1=="g+s"
           r=rg+rs
        elseif @combi1=="g-s"
           r=rg-rs
        elseif @combi1=="g*s"
           r=rg*rs
        elseif @combi1=="g/s"
           if rs==0
              r=1e30
           else
              r=rg/rs
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi1=="s/g"
           if rg==0
              r=1e30
           else
              r=rs/rg
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi1=="harm.mean g,s"
           r=2*(rg*rs)/(rg+rs)
        elseif @combi1=="contraharm.mean g,s"
           r=(sqr(rg)+sqr(rs))/(rg+rs)
        elseif @combi1=="quadratic mean g,s"
           r=sqrt(0.5*sqr(rg)+sqr(rs))
        elseif @combi1=="root mean g,s"
           r=sqr(0.5*(sqrt(rg)+sqrt(rs)))
        elseif @combi1=="fantasy g,s"
           r=(sqrt(rg)+sqrt(rs))/(rg+rs)
        elseif @combi1=="recipr.fantasy g,s"
           r=(rg+rs)/(sqrt(rg)+sqrt(rs))
        endif    
     elseif @gielis==true && @single==false && @extra==true
        if @combi2=="g+e"
           r=rg+re
        elseif @combi2=="g-e"
           r=rg-re
        elseif @combi2=="g*e"
           r=rg*re
        elseif @combi2=="g/e"
           if re==0
              r=1e30
           else
              r=rg/re
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi2=="e/g"
           if rg==0
              r=1e30
           else
              r=re/rg
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi2=="harm.mean g,e"
           r=2*(rg*re)/(rg+re)
        elseif @combi2=="contraharm.mean g,e"
           r=(sqr(rg)+sqr(re))/(rg+re)
        elseif @combi2=="quadratic mean g,e"
           r=sqrt(0.5*sqr(rg)+sqr(re))
        elseif @combi2=="root mean g,e"
           r=sqr(0.5*(sqrt(rg)+sqrt(re)))
        elseif @combi2=="fantasy g,e"
           r=(sqrt(rg)+sqrt(re))/(rg+re)
        elseif @combi2=="recipr.fantasy g,e"
           r=(rg+re)/(sqrt(rg)+sqrt(re))
        endif
     elseif @gielis==false && @single==true && @extra==true
        if @combi3=="s+e"
           r=rs+re
        elseif @combi3=="s-e"
           r=rs-re
        elseif @combi3=="s*e"
           r=rs*re
        elseif @combi3=="s/e"
           if re==0
              r=1e30
           else
              r=rs/re
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi3=="e/s"
           if rs==0
              r=1e30
           else
              r=re/rs
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi3=="harm.mean s,e"
           r=2*(rs*re)/(rs+re)
        elseif @combi3=="contraharm.mean s,e"
           r=(sqr(rs)+sqr(re))/(rs+re)
        elseif @combi3=="quadratic mean s,e"
           r=sqrt(0.5*sqr(rs)+sqr(re))
        elseif @combi3=="root mean s,e"
           r=sqr(0.5*(sqrt(rs)+sqrt(re)))
        elseif @combi3=="fantasy s,e"
           r=(sqrt(rs)+sqrt(re))/(rs+re)
        elseif @combi3=="recipr.fantasy s,e"
           r=(rs+re)/(sqrt(rs)+sqrt(re))
        endif     
     elseif @gielis==true && @single==true && @extra==true
        if @combi4=="g+s+e" ; 0
           r=rg+rs+re
        elseif @combi4=="g+s-e" ; 1
           r=rg+rs-re
        elseif @combi4=="g-s+e" ; 2
           r=rg-rs+re
        elseif @combi4=="g-s-e" ; 3
           r=rg-rs-re
        elseif @combi4=="g*s+e" ; 4
           r=rg*rs+re
        elseif @combi4=="g*e+s" ; 5
           r=rg*re+rs
        elseif @combi4=="s*e+g" ; 6
           r=rs*re+rg
        elseif @combi4=="g*s-e" ; 7
           r=rg*rs-re
        elseif @combi4=="g*e-s" ; 8
           r=rg*re-rs
        elseif @combi4=="s*e-g" ; 9
           r=rs*re-rg
        elseif @combi4=="(g+s)e" ; 10
           r=(rg+rs)*re
        elseif @combi4=="(g+e)s" ; 11
           r=(rg+re)*rs
        elseif @combi4=="(s+e)g" ; 12
           r=(rs+re)*rg
        elseif @combi4=="(g-s)e" ; 13
           r=(rg-rs)*re
        elseif @combi4=="(g-e)s" ; 14
           r=(rg-re)*rs
        elseif @combi4=="(s-e)g" ; 15
           r=(rs-re)*rg
        elseif @combi4=="g*s*e"  ; 16
           r=rg*rs*re
        elseif @combi4=="g*s/e"  ; 17
           if re==0
              r=1e30
           else
              r=rg*rs/re
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="g*e/s" ; 18
           if rs==0
              r=1e30
           else
              r=rg*re/rs
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="s*e/g" ; 19
           if rg==0
             r=1e30
           else
              r=rs*re/rg
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="e/(g*s)" ; 20
           if rg+rs==0
              r=1e30
           else
              r=re/(rg*rs)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="s/(g*e)" ; 21
           if rg+re==0
              r=1e30
           else
              r=rs/(rg*re)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="g/(s*e)" ; 22 
           if rs*re==0
              r=1e30
           else
              r=rg/(rs*re)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="(g+s)/e" ; 23
           if re==0
              r=1e30
           else
              r=(rg+rs)/re
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="(g+e)/s" ; 24
            if rs==0
              r=1e30
           else
              r=(rg+re)/rs
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="(s+e)/g" ; 25
           if rg==0
              r=1e30
           else
              r=(rs+re)/rg
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="e/(g+s)" ; 26
            if rg+rs==0
              r=1e30
           else
              r=re/(rg+rs)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="s/(g+e)" ; 27
           if rg+re==0
              r=1e30
           else
              r=rs/(rg+re)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="g/(s+e)" ; 28
           if rs+re==0
              r=1e30
           else
              r=rg/(rs+re)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="(g-s)/e" ; 29
           if re==0
              r=1e30
           else
              r=(rg-rs)/re
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="(g-e)/s" ; 30
           if rs==0
              r=1e30
           else
              r=(rg-re)/rs
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="(s-e)/g" ; 31
           if rg==0
              r=1e30
           else
              r=(rs-re)/rg
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="e/(g-s)" ; 32
           if rg-rs==0
              r=1e30
           else
              r=re/(rg-rs)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="s/(g-e)" ; 33
           if rg-re==0
              r=1e30
           else
              r=rs/(rg-re)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="g/(s-e)" ; 34
           if rs-re==0
              r=1e30
           else
              r=rg/(rs-re)
              if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                 r=@rc/r
              endif
           endif
        elseif @combi4=="harm.mean g,s,e" ; 35
           r=3*rg*rs*re/(rg*rs+rg*re+rs*re)
        elseif @combi4=="contraharm.mean g,s,e" ; 36
           r=(sqr(rg)+sqr(rs)+sqr(re))/(rg+rs+re) 
        elseif @combi4=="quadratic mean g,s,e" ;37
           r=sqrt(0.5*(sqr(rg)+sqr(rs)+sqr(re)))
        elseif @combi4=="root mean g,s,e" ;38
           r=sqr(0.5*(sqrt(rg)+sqrt(rs)+sqrt(re)))
        elseif @combi4=="fantasy g,s,e" ; 39
           r=(sqrt(rg)+sqrt(rs)+sqrt(re))/(rg+rs+re)
        elseif @combi4=="recipr.fantasy g,s,e" ;40
           r=(rg+rs+re)/(sqrt(rg)+sqrt(rs)+sqrt(re))
        endif
     endif ; calculation of r
            
; totaal 3+10+10+10+40=73 stuks
;
; overall parameters (scale & baseline) applied to r
;
     r=@scale*(@r0+r)
;
     if @rneg==true 
        err=r-cabs(z1) ; ignore r<0
     else              ; @rneg=false, 
        err=|r|-|z1|   ; treat as positive
     endif
     if err<0.0
        incount=incount+1
        err=-err ; positive again
        last_in=z1
        if flag==true
           first_in=z1
           flag=false
        endif
; tmp will be used in 'final'
        if @coloring_mode=="mean1"
           tmp=tmp+z1
        elseif @coloring_mode=="mean2"
           tmp=tmp+abs(real(z1))+abs(imag(z1))
        elseif @coloring_mode=="mean3"
           tmp=tmp+abs(real(z1))
        elseif @coloring_mode=="mean4"
           tmp=tmp+abs(imag(z1))
        endif
     endif
     if(err<errmin)
        errmin=err ; nearest distance pixel to curve
        zmin=z1
        itermin=iter
     endif
  endif
;
final:
  if @coloring_mode==0 ; from 'polar curves' of KM, only solid added
     if(@colorby_1==0)               ; minimum distance
        if err>@width
           #solid=true
        else
           #index=abs(log(errmin)) ; original cabs (why? log(errmin) is a float)
        endif
     elseif(@colorby_1==1)           ; iteration @ min
        if err>@width
           #solid=true
        else
           #index=0.01*itermin
        endif
     elseif(@colorby_1==2)           ; angle @ min
        if err>@width
           #solid=true
        else
           t=atan2(zmin)
           t=t/pi
           if(t<0.0)
              t=t+2.0
           endif
           #index=0.5*t
        endif
     elseif(@colorby_1==3)           ; in fraction
        if incount==0
           #solid=true
        else  
           #index=incount/iter
        endif
     elseif(@colorby_1==4)           ; draw curves
        if err>@width
           #solid=true
        else
           z2=#pixel-@r_center
           t=imag(log(z2))+@rot
           while t>twopi
              t=t-twopi
           endwhile
           while t<0.0
              t=t+twopi
           endwhile                      
; Gielis
           if @gielis==true
              hk=0.25*@m*(t+@rot_g) ; m=freq. rot_g=pre-rotation Gielis
              term1=abs(cos(hk)/real(@g))^real(@ng)
              term2=abs(sin(hk)/imag(@g))^imag(@ng)
              while hk>twopi
                 hk=hk-twopi
              endwhile
              while hk<0.0
                 hk=hk+twopi
              endwhile
              if @hf==false
                 term1=abs(cos(hk)/real(@g))^real(@ng)
                 term2=abs(sin(hk)/imag(@g))^imag(@ng)
              else
                 term1=abs(cosh(hk)/real(@g))^real(@ng)
                 term2=abs(sinh(hk)/imag(@g))^imag(@ng)
              endif

              if @hyper==false
                 temp=term1+term2
              else
                 temp=term1-term2
              endif
              if temp==0
                 temp=1e-30
              endif
              if @ge==true ; enhanced
                 rg=@rg0+real(@fg_sub(@fg_main(@gc*hk)*@gs/(temp^(1/@n1))))
              else ; gielis 'original'
                 rg=@rg0+real(@fg_sub(@gs/(temp^(1/@n1))))
              endif
           endif
;
; single functions 
           if @single==true
              hk=@b*(t+@rot_s)   ; b=freq. rot_s=pre-rotation single
              while hk>twopi
                 hk=hk-twopi
              endwhile
              while hk<0.0
                 hk=hk+twopi
              endwhile
              rs=@a*real(@fs_main(hk))
              if rs>=0.0
                 rs=rs^@n
              else
                 rs=-((-rs)^@n)
              endif
              rs=@rs0+real(@fs_sub(rs)) ; a=scale single rs0=preset single
           endif
;
; extra functions 
           if @extra==true
              hk=@be*(t+@rot_e) ; be=freq. rot_e=pre-rotation extra
              while hk>twopi
                 hk=hk-twopi
              endwhile
              while hk<0
                 hk=hk+twopi
              endwhile
              if @functiontype==0 ; lemniscate
                 re=real(@p)*sqr(2*cos(2*hk))+imag(@p)*sqr(2*sin(2*hk))
              elseif @functiontype==1 ; rose
                 re=real(@p)*cos(real(@q)*hk)+imag(@p)*sin(imag(@q)*hk)
              elseif @functiontype==2 ; conchoid
                 re=real(@p)/cos((hk)+imag(@p))
              elseif @functiontype==3 ; limaçon
                 re=real(@p)*cos(hk)+imag(@p)
              elseif @functiontype==4 ; cissoid
                 re=@pp*cos(2*hk)/cos(hk)
              elseif @functiontype==5 ; trifolium
                 re=real(@p)*cos(hk)*cos(2*hk)+imag(@p) 
              elseif @functiontype==6 ; cassinoid 1
                 re=sqr(real(@p))*(cos(2*hk)+sqrt((imag(@p)/real(@p))^4-sqr(sin(2*hk))))
              elseif @functiontype==7 ; cassinoid 2
                 re=sqr(real(@p))*(cos(2*hk)-sqrt((imag(@p)/real(@p))^4-sqr(sin(2*hk))))
              elseif @functiontype==8 ; ellips
                 re=real(@p)+imag(@p)*cos(hk)
              elseif @functiontype==9 ; astroid generalized
                 re=sqrt(real(@p)*(cos(hk)^(real(@q)))+imag(@p)*(sin(hk)^(imag(@q))))
              elseif @functiontype==10 ; rectangle
                 if hk==halfpi || hk==3*halfpi
                    re=imag(@p) ; vertical
                 elseif hk==0 || hk==pi || hk==twopi
                    re=real(@p) ; horizontal
                 else
                    if hk>halfpi && hk<pi ; NW
                       temp=pi-hk
                    elseif hk>pi && hk<3*halfpi ; SW
                       temp=hk-pi
                    elseif hk>3*halfpi && hk<twopi ; SE
                       temp=twopi-hk
                    else ; NE
                       temp=hk
                    endif
                    if temp<=atan(imag(@p)/real(@p))
                       re=real(@p)/cos(temp)
                    else
                       re=imag(@p)/sin(temp)
                    endif
                 endif
              elseif @functiontype==11 ; flower
                 re=cos(@pp*hk)
              endif
              re=@re0+@es*real(@fe_sub(re))
           endif
;         
           if @gielis==true && @single==false && @extra==false
              r=rg
           elseif @gielis==false && @single==true && @extra==false
              r=rs
           elseif @gielis==false && @single==false && @extra==true
              r=re
           elseif @gielis==true && @single==true && @extra==false
              if @combi1=="g+s"
              r=rg+rs
              elseif @combi1=="g-s"
                 r=rg-rs
              elseif @combi1=="g*s"
                 r=rg*rs
              elseif @combi1=="g/s"
                 if rs==0
                    r=1e30
                 else
                    r=rg/rs
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi1=="s/g"
                  if rg==0
                    r=1e30
                 else
                    r=rs/rg
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi1=="harm.mean g,s"
                 r=2*(rg*rs)/(rg+rs)
              elseif @combi1=="contraharm.mean g,s"
                 r=(sqr(rg)+sqr(rs))/(rg+rs)
              elseif @combi1=="quadratic mean g,s"
                 r=sqrt(0.5*sqr(rg)+sqr(rs))
              elseif @combi1=="root mean g,s"
                 r=sqr(0.5*(sqrt(rg)+sqrt(rs)))
              elseif @combi1=="fantasy g,s"
                 r=(sqrt(rg)+sqrt(rs))/(rg+rs)
              elseif @combi1=="recipr.fantasy g,s"
                 r=(rg+rs)/(sqrt(rg)+sqrt(rs))
              endif    
           elseif @gielis==true && @single==false && @extra==true
              if @combi2=="g+e"
                 r=rg+re
              elseif @combi2=="g-e"
                 r=rg-re
              elseif @combi2=="g*e"
                 r=rg*re
              elseif @combi2=="g/e"
                 if re==0
                    r=1e30
                 else
                    r=rg/re
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi2=="e/g"
                 if rg==0
                    r=1e30
                 else
                    r=re/rg
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi2=="harm.mean g,e"
                 r=2*(rg*re)/(rg+re)
              elseif @combi2=="contraharm.mean g,e"
                 r=(sqr(rg)+sqr(re))/(rg+re)
              elseif @combi2=="quadratic mean g,e"
                 r=sqrt(0.5*sqr(rg)+sqr(re))
              elseif @combi2=="root mean g,e"
                 r=sqr(0.5*(sqrt(rg)+sqrt(re)))
              elseif @combi2=="fantasy g,e"
                 r=(sqrt(rg)+sqrt(re))/(rg+re)
              elseif @combi2=="recipr.fantasy g,e"
                 r=(rg+re)/(sqrt(rg)+sqrt(re))
              endif
           elseif @gielis==false && @single==true && @extra==true
              if @combi3=="s+e"
                 r=rs+re
              elseif @combi3=="s-e"
                 r=rs-re
              elseif @combi3=="s*e"
                 r=rs*re
              elseif @combi3=="s/e"
                 if re==0
                    r=1e30
                 else
                    r=rs/re
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi3=="e/s"
                  if rs==0
                    r=1e30
                 else
                    r=re/rs
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi3=="harm.mean s,e"
                 r=2*(rs*re)/(rs+re)
              elseif @combi3=="contraharm.mean s,e"
                 r=(sqr(rs)+sqr(re))/(rs+re)
              elseif @combi3=="quadratic mean s,e"
                 r=sqrt(0.5*sqr(rs)+sqr(re))
              elseif @combi3=="root mean s,e"
                 r=sqr(0.5*(sqrt(rs)+sqrt(re)))
              elseif @combi3=="fantasy s,e"
                 r=(sqrt(rs)+sqrt(re))/(rs+re)
              elseif @combi3=="recipr.fantasy s,e"
                 r=(rs+re)/(sqrt(rs)+sqrt(re))
              endif     
           elseif @gielis==true && @single==true && @extra==true
              if @combi4=="g+s+e" ; 0
                 r=rg+rs+re
              elseif @combi4=="g+s-e" ; 1
                 r=rg+rs-re
              elseif @combi4=="g-s+e" ; 2
                 r=rg-rs+re
              elseif @combi4=="g-s-e" ; 3
                 r=rg-rs-re
              elseif @combi4=="g*s+e" ; 4
                 r=rg*rs+re
              elseif @combi4=="g*e+s" ; 5
                 r=rg*re+rs
              elseif @combi4=="s*e+g" ; 6
                 r=rs*re+rg
              elseif @combi4=="g*s-e" ; 7
                 r=rg*rs-re
              elseif @combi4=="g*e-s" ; 8
                 r=rg*re-rs
              elseif @combi4=="s*e-g" ; 9
                 r=rs*re-rg
              elseif @combi4=="(g+s)e" ; 10
                 r=(rg+rs)*re
              elseif @combi4=="(g+e)s" ; 11
                 r=(rg+re)*rs
              elseif @combi4=="(s+e)g" ; 12
                 r=(rs+re)*rg
              elseif @combi4=="(g-s)e" ; 13
                 r=(rg-rs)*re
              elseif @combi4=="(g-e)s" ; 14
                 r=(rg-re)*rs
              elseif @combi4=="(s-e)g" ; 15
                 r=(rs-re)*rg
              elseif @combi4=="g*s*e"  ; 16
                 r=rg*rs*re
              elseif @combi4=="g*s/e"  ; 17
                 if re==0
                    r=1e30
                 else
                    r=rg*rs/re
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="g*e/s" ; 18
                 if rs==0
                    r=1e30
                 else
                    r=rg*re/rs
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="s*e/g" ; 19
                 if rg==0
                    r=1e30
                 else
                    r=rs*re/rg
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="e/(g*s)" ; 20
                 if rg+rs==0
                    r=1e30
                 else
                    r=re/(rg*rs)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="s/(g*e)" ; 21
                 if rg+re==0
                    r=1e30
                 else
                    r=rs/(rg*re)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="g/(s*e)" ; 22 
                 if rs*re==0
                    r=1e30
                 else
                    r=rg/(rs*re)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="(g+s)/e" ; 23
                 if re==0
                    r=1e30
                 else
                    r=(rg+rs)/re
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="(g+e)/s" ; 24
                 if rs==0
                    r=1e30
                 else
                    r=(rg+re)/rs
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="(s+e)/g" ; 25
                 if rg==0
                    r=1e30
                 else
                    r=(rs+re)/rg
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="e/(g+s)" ; 26
                 if rg+rs==0
                    r=1e30
                 else
                    r=re/(rg+rs)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                      r=@rc/r
                    endif
                 endif
              elseif @combi4=="s/(g+e)" ; 27
                 if rg+re==0
                    r=1e30
                 else
                    r=rs/(rg+re)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="g/(s+e)" ; 28
                 if rs+re==0
                    r=1e30
                 else
                    r=rg/(rs+re)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="(g-s)/e" ; 29
                 if re==0
                    r=1e30
                 else
                    r=(rg-rs)/re
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="(g-e)/s" ; 30
                 if rs==0
                    r=1e30
                 else
                    r=(rg-re)/rs
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="(s-e)/g" ; 31
                 if rg==0
                    r=1e30
                 else
                    r=(rs-re)/rg
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="e/(g-s)" ; 32
                 if rg-rs==0
                    r=1e30
                 else
                    r=re/(rg-rs)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="s/(g-e)" ; 33
                 if rg-re==0
                    r=1e30
                 else
                    r=rs/(rg-re)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="g/(s-e)" ; 34
                 if rs-re==0
                    r=1e30
                 else
                    r=rg/(rs-re)
                    if (@rf=="b" && r<@rc) || (@rf=="c" && r>@rc)
                       r=@rc/r
                    endif
                 endif
              elseif @combi4=="harm.mean g,s,e" ; 35
                 r=3*rg*rs*re/(rg*rs+rg*re+rs*re)
              elseif @combi4=="contraharm.mean g,s,e" ; 36
                 r=(sqr(rg)+sqr(rs)+sqr(re))/(rg+rs+re) 
              elseif @combi4=="quadratic mean g,s,e" ;37
                 r=sqrt(0.5*(sqr(rg)+sqr(rs)+sqr(re)))
              elseif @combi4=="root mean g,s,e" ;38
                 r=sqr(0.5*(sqrt(rg)+sqrt(rs)+sqrt(re)))
              elseif @combi4=="fantasy g,s,e" ; 39
                 r=(sqrt(rg)+sqrt(rs)+sqrt(re))/(rg+rs+re)
              elseif @combi4=="recipr.fantasy g,s,e" ;40
                 r=(rg+rs+re)/(sqrt(rg)+sqrt(rs)+sqrt(re))
              endif
           endif
        endif ; end err <>width  
;                        
        r=@scale*(@r0+r)
        if @rneg==true       
           err=r-cabs(z2) ; ignore r<0
        else                  ; @rneg=false, 
           err=|r|-|z2|   ; treat as positive
        endif
        #index=abs(log(abs(err)))
     endif 
; end colorby_1=4 (draw)
;                            
  else ; @coloring_mode!=0, no curve
     if incount==0
        #solid=true
     else
        if @coloring_mode==1                           ; first in
           tmp=first_in
        elseif @coloring_mode==2                       ; last in
           tmp=last_in
        elseif (@coloring_mode==3 || @coloring_mode>4) ; mean1, -3 en -4
           tmp=tmp/incount
        elseif @coloring_mode==4                       ; "mean2"
           tmp=0.5*tmp/incount
        endif
        if @colorby_2=="magnitude"
           #index = cabs(tmp)
        elseif @colorby_2=="angle"
           #index=(atan2(tmp)/#pi+1)/2 ; scale the angle
        elseif @colorby_2=="angle extra"
           #index=real(atan(tmp)) ; scale the angle
        elseif @colorby_2=="real"
           #index=real(tmp)
        elseif @colorby_2=="imag"
           #index=imag(tmp)
        endif
     endif
  endif
;              
default:                                                                                                                                                                                                                        
  title="Gielis plus 1.3."
  heading
    caption="general"
  endheading
  complex param r_center
    caption = "circle center"
    default = (0,0)
  endparam
  float param scale
    caption="overall scale"
    default=1.0
  endparam
  float param r0
    caption="overall baseline"
    default=0.0
  endparam 
  float param rot
    caption="overall rotation"
    default=0.0
  endparam
  int param skip
    caption="skip iterations"
    default=1
  endparam
  int param threshold
    caption="iter threshold"
    default=0
  endparam
  int param end
    caption="iter end"
    default=10000000
  endparam  
  float param width
    caption="width"
    default=150
    visible=@coloring_mode=="curve"
  endparam
  bool param rneg
    caption="ignore neg.r"
    default=false
    hint="disabled: ignore negative r values, enabled: treat as positive"
  endparam
  bool param gielis
    caption="gielis formula"
    default=false
  endparam
  bool param single
    caption="single formula"
    default=false
  endparam
  bool param extra
    caption="extra functions"
    default=false
  endparam
  param combi1
    caption="combinations"
    default=2 ; g*s
    enum="g+s" "g-s" "g*s" "g/s" "s/g" "harm.mean g,s" "contraharm.mean g,s" \
         "quadratic mean g,s" "root mean g,s" "fantasy g,s" "recipr.fantasy g,s"
    visible=(@gielis==true && @single==true && @extra==false)    
  endparam
  param combi2
    caption="combinations"
    default=2 ; g*e
    enum="g+e" "g-e" "g*e" "g/e" "e/g" "harm.mean g,e" "contraharm.mean g,e" \
         "quadratic mean g,e" "root mean g,e" "fantasy g,e" "recipr.fantasy g,e"
    visible=(@gielis==true && @single==false && @extra==true)    
  endparam
  param combi3
    caption="combinations"
    default=2 ; s*e
    enum="s+e" "s-e" "s*e" "s/e" "e/s" "harm.mean s,e" "contraharm.mean s,e" \
         "quadratic mean s,e" "root mean s,e" "fantasy s,e" "recipr.fantasy s,e"
    visible=(@gielis==false && @single==true && @extra==true)    
  endparam
  param combi4
    caption="combinations"
    default=16 ; g*s*e
    enum="g+s+e" "g+s-e" "g-s+e" "g-s-e" "g*s+e" "g*e+s" "s*e+g" "g*s-e" "g*e-s" "s*e-g" \
         "(g+s)e" "(g+e)s" "(s+e)g" "(g-s)e" "(g-e)s" "(s-e)g" "g*s*e" "g*s/e" \
         "g*e/s" "s*e/g" "e/(g*s)" "s/(g*e)" "g/(s*e)" "(g+s)/e" "(g+e)/s" "(s+e)/g" \
         "e/(g+s)" "s/(g+e)" "g/(s+e)" "(g-s)/e" "(g-e)/s" "(s-e)/g" "e/(g-s)" \
         "s/(g-e)" "g/(s-e)" "harm.mean g,s,e" "contraharm.mean g,s,e" \
         "quadratic mean g,s,e" "root mean g,s,e" "fantasy g,s,e" "recipr.fantasy g,s,e"     
    visible=(@gielis==true && @single==true && @extra==true)    
  endparam
  param rf
    caption="ratio option"
    default=0
    enum="a" "b" "c"
    visible=(@combi1=="g/s" || @combi1=="s/g" || \
     @combi2=="g/e" || @combi2=="e/g" || \
     @combi3=="s/e" || @combi3=="e/s" || \
     @combi4=="g*s/e" || @combi4=="g*e/s" || @combi4=="s*e/g" || \
     @combi4=="e/(g*s)" || @combi4=="s/(g*e)" || @combi4=="g/(s*e)" || \
     @combi4=="(g+s)/e" || @combi4=="(g+e)/s" || @combi4=="(s+e)/g" || \
     @combi4=="e/(g+s)" || @combi4=="s/(g+e)" || @combi4=="g/(s+e)" || \
     @combi4=="(g-s)/e" || @combi4=="(g-e)/s" || @combi4=="(s-e)/g" || \
     @combi4=="e/(g-s)" || @combi4=="s/(g-e)" || @combi4=="g/(s-e)")
    hint="inverting options, try both b and c"
  endparam    
  float param rc
    caption="ratio constant"
    default=1.0
    visible=(@combi1=="g/s" || @combi1=="s/g" || \
     @combi2=="g/e" || @combi2=="e/g" || \
     @combi3=="s/e" || @combi3=="e/s" || \
     @combi4=="g*s/e" || @combi4=="g*e/s" || @combi4=="s*e/g" || \
     @combi4=="e/(g*s)" || @combi4=="s/(g*e)" || @combi4=="g/(s*e)" || \
     @combi4=="(g+s)/e" || @combi4=="(g+e)/s" || @combi4=="(s+e)/g" || \
     @combi4=="e/(g+s)" || @combi4=="s/(g+e)" || @combi4=="g/(s+e)" || \
     @combi4=="(g-s)/e" || @combi4=="(g-e)/s" || @combi4=="(s-e)/g" || \
     @combi4=="e/(g-s)" || @combi4=="s/(g-e)" || @combi4=="g/(s-e)")
    hint="parameter to be use in connection with 'ratio option'"  
  endparam
  param coloring_mode
    caption="coloring mode"
    default=0
    enum="curve" "first_in" "last_in" "mean1" "mean2" "mean3" "mean4"
  endparam
  param colorby_1
    caption="color by"
    default=0
    enum="minimum distance" "iteration @ min" "angle @ min" \
      "in fraction" "draw curves"
    visible=@coloring_mode=="curve"
  endparam
  param colorby_2
    caption="color by"
    default=0
    enum="magnitude" "angle" "angle extra" "real" "imag"
    visible=@coloring_mode!="curve"
  endparam
;
  heading
    caption="gielis formla"
    visible=@gielis==true
  endheading
  bool param ge
    caption="gielis enhanced"
    default=false
    visible=@gielis==true
    hint="enabled = a variation on the original gielis formula"
  endparam
  bool param hyper
    caption="hyperbolic"
    default=false
    visible=@gielis==true
    hint="normal case = elliptic"
  endparam
  bool param hf
    caption="h function"
    default=false
    visible=@gielis==true
    hint="sinh and cosh in Gielis formula in stead of sin and cos"
  endparam
  float param gs
    caption="g-scale total"
    default=1.0
    visible=@gielis==true
  endparam
  complex param g
    caption="scale R=a I=b"
    default=(2,2)
    visible=@gielis==true
    hint="Gielis parameters a and b, combined into one complex number"
  endparam
  float param rg0
    caption="g-baseline"
    default=0.0
    visible=@gielis==true
  endparam
  float param rot_g
    caption="g-rotation"
    default=0.0
    visible=@gielis==true
  endparam
  float param m
    caption="G frequency (m)"
    default=3.0
    visible=@gielis==true
  endparam
  float param n1
    caption="g exponent n1"
    default=2.0
    visible=@gielis==true
    hint="n1, one of the Gielis parameters"
  endparam
  complex param ng
    caption="g exp. R=n2 I=n3"
    default=(2,2)
    visible=@gielis==true
    hint="Gielis parameters n1 and n2, combined into one complex number"
  endparam
  float param gc
    caption="wave"
    default=1.0
    visible=(@gielis==true && @ge==true)
    hint="variable to be used for the option enhanced "
  endparam
  func fg_main
    caption="gielis main function"
    default=ident()
    visible=(@gielis==true && @ge==true)
    hint="additional function to enhanced formula"
  endfunc
  func fg_sub
    caption="gielis sub function"
    default=ident()
    visible=@gielis==true
    hint="additional function"
  endfunc
;
  heading
    caption="single functions"
    visible=@single==true
  endheading
  float param a
    caption="amplitude (s-scale)"
    default=1.0
    visible=@single==true
  endparam
  float param rs0
    caption="s-baseline"
    default=0.0
    visible=@single==true
  endparam
  float param rot_s
    caption="s-rotation"
    default=0.0
    visible=@single==true
  endparam
  float param b
    caption="frequency"
    default=1.0
    visible=@single==true
  endparam
  float param n
    caption="exponent"
    default=1.0
    visible=@single==true
  endparam
  func fs_main
    caption="main function"
    default=sin()
    visible=@single==true
  endfunc
  func fs_sub
    caption="sub function"
    default=ident()
    visible=@single==true
  endfunc
;
  heading
    caption="extra functions"
    visible=@extra==true
  endheading
  float param es
    caption="e-scale"
    default=1.0
    visible=@extra==true
  endparam
  float param re0
    caption="e-baseline"
    default=0.0
    visible=@extra==true  
  endparam  
  float param rot_e
    caption="e-rotation"
    default=0.0
    visible=@extra==true 
  endparam
  float param be
    caption="frequency"
    default=1.0
    visible=@single==true
  endparam
  param functiontype
    caption="extra functie"
    default=0
    enum="lemniscate" "rose" "conchoid" "limaçon" "cissoid" "trifolium" \
         "cassinoid 1" "cassinoid 2" "ellips" "astroid" "rectangle" "flower"
    visible=@extra==true
  endparam
  float param pp
    caption="function parameter 1"
    default=1
    visible=@extra==true && (@functiontype=="cissoid" || @functiontype=="flower")
  endparam
  complex param p
    caption="function parameter 1"
    default=1
    visible=(@extra==true && @functiontype=="lemniscate") || (@extra==true && @functiontype=="rose") || \
            (@extra==true && @functiontype=="conchoid") || (@extra==true && @functiontype=="limaçon") || \
            (@extra==true && @functiontype=="trifolium") || (@extra==true && @functiontype=="cassinoid 1") || \
            (@extra==true && @functiontype=="cassinoid 2") || (@extra==true && @functiontype=="ellips") || \
            (@extra==true && @functiontype=="astroid") || (@extra==true && @functiontype=="rectangle")
  endparam
  complex param q
    caption="function parameter 2"
    default=(1,1)
    visible=(@extra==true && @functiontype=="rose") || (@extra==true && @functiontype=="astroid")
  endparam
  func fe_sub
    caption="sub function"
    default=ident()
    visible=@extra==true
  endfunc
}

Image {
;
; Image just displays an image from disk. It's best used on the Outside tab,
; together with the Pixel formula from Standard.ufm.
;
; The core of this coloring formula is the same as image.ucl in the Standard file.
; To use it in combination with some mapping formulas (e.g. foxtrot.uxf)
; there are in this version of image.ucl some new facilities.
; In particular when the images are abstracts, textures or fractal images 
; from UF or other sources, a lot of interesting 'horizontal kaleido' effects 
; are possible.

global:
  Image i = new @imageParam
  float pir=#pi/180
  float rota=@rot*pir
  float hshfa=@hshf
  float vshfa=@vshf
  float sca1=@sc1
  float sca2=@sc2
  float ccr=real(#center)
  float skangle=@skew
  float hsta=@hst
  float vsta=@vst

final:
  complex shfa = (0.0,0.0)
  complex c = 0.5 * #pixel
  float ratio
  if !i.getEmpty()
    ratio = i.getWidth() / i.getHeight()
  else
    ratio = 1
  endif

  c = sca1*c ; scaling before rotating

  if @mir1
    cr=real(c), ci=imag(c)
    cr = 2*ccr-cr
    c = cr + flip(ci)
  endif

  shfa = hshfa + flip(vshfa)
  ; with scaling after rotating
  c = sca2*exp(1i*rota)*(c+shfa)

  cr=real(c)/hsta
  ci=imag(c)/vsta
  cr=cr+ci*tan(skangle)

  if @mir2
    cr = 2*ccr-cr
  endif

  #color = i.getColor(cr + flip(ci) * ratio)

default:
  title = "Image"
  int param version, caption="version", default=100, visible=false, endparam
  heading
    text = "Tip: the Image coloring algorithm works best with the standard \
      Pixel fractal formula."
  endheading
  Image param imageParam
    caption = "Image"
    hint = "The image selected here will fill the entire layer, if combined \
      with the Pixel fractal formula and if the location is set to the \
      default. To do this, click the Reset button on the Location tab."
  endparam
  bool param mir1
    caption = "mirror of original image"
    default = false
  endparam
  float param sc1
    caption = "scaling original image"
    default = 1.0
  endparam
  float param hshf
    caption = "horizontal shift"
    default = 0.0
  endparam
  float param vshf
    caption = "vertical shift"
    default = 0.0
  endparam
  float param rot
    caption = "rotation (°)"
    default = 0.0
  endparam
  float param hst
    caption = "horizontal stretch"
    default = 1.0
  endparam
  float param vst
    caption = "vertical stretch"
    default = 1.0
  endparam
  float param skew
    caption = "skew angle"
    default = 0.0
  endparam
  float param sc2
    caption = "scaling processed image"
    default = 1.0
  endparam
  bool param mir2
    caption = "mirror of processed image"
    default = false
  endparam
}

Sphere Shadow {
; Sept.22, 2015
;
; Based on 'smooth' formula of D.M.Jones
; To be used as an outside coloring.
; When used as a "shadow layer: no mapping, formula = pixel
;
init:
  complex q = (0.0,0.0)
  float s = 0.0
  float noise = 0.0

final:
  #solid = false
  if cabs(#z) >= @rd
    #solid = true
  endif
  q = #z-@vct
  s = cabs(q)
  if (@userandom==true)
    noise = 0.01*@noiseamount*real(#random)
  endif
  #index = @p-0.1*log(log(s/@corr)) + noise

default:
  title = "Sphere Shadow"
  int param version
    caption = "version"
    default = 100
    visible = false
  endparam
  float param p
    caption = "general light tuning"
    default = 0.22
    hint = "Higher values: lamp closer to sphere"
  endparam
  complex param vct
    caption = "light center"
    default = (0.0,0.0)
    hint = "Position of point with highest light inensity, to be adjusted by manipulating \
            gradient points. Proposed gradient to start: 2 points: point 1: rot. = 0, \
            pos. = 31, HSL = 0/0/255; point 2: rot.=0, pos. = 236, HSL= 0/0/0."
  endparam
  float param rd
    caption = "radius sphere"
    default = 0.99
  endparam
  float param corr
    caption = "radius correction"
    default = 1.0
    min = 0.0001
    hint = "If light center differs from circle center the disturbing crescent \
            can be removed by using this correction to enhance the radius of the light circle."
  endparam
  bool param userandom
    caption = "add random noise"
    default = false
  endparam
  float param noiseamount
    caption = "noise amount"
    hint = "Best results between 1 and 6"
    default = 2
    visible = @userandom==true
   endparam
}