#include "colors.inc"
#include "include\stones.inc"
#include "textures.inc"

/*
Pov3 Parametric equation - Treefoil knot. 
With smooth triangles. 
*/
#version 3.0
global_settings { assumed_gamma 1.0  }
#declare counter = 1
#declare umin  = 0            //endpoints in the
#declare umax  = 4*pi            //parametric rectangle
#declare vmin  = 0  
#declare vmax  = 2*pi
#declare uiter = 80            //number of steps
#declare viter = 12             //this is max fot 4mb ram 
#declare iu    = (umax-umin)/uiter    //increment per step
#declare iv    = (vmax-vmin)/viter 
#declare a=1
#declare b=0.3
#declare c=0.5
#declare d=0.3
union{
  #declare uu = umin    
  #while (uu<=umax)                        //outer loop
    #declare vv = vmin
    #while (vv<=vmax)                      //inner loop
//POINTS      
    #declare r=a+b*cos(1.5*uu)
    #declare xx=r*cos(uu)
    #declare yy=r*sin(uu)
    #declare zz=c*sin(1.5*uu)
    #declare dx=-1.5*b*sin(1.5*uu)*cos(uu)-(a+b*cos(1.5*uu))*sin(uu)
    #declare dy=-1.5*b*sin(1.5*uu)*sin(uu)+(a+b*cos(1.5*uu))*cos(uu) 
    #declare dz=1.5*c*cos(1.5*uu)
    #declare qn=vnormalize(<dx,dy,dz>)
    #declare qvn=vnormalize(<qn.y,-qn.x,0>)
    #declare ww=vcross(qn,qvn)
    #declare x1=xx+d*(qvn.x*cos(vv)+ww.x*sin(vv)) //Calculate the
    #declare y1=yy+d*(qvn.y*cos(vv)+ww.y*sin(vv)) //four points in
    #declare z1=zz+d*ww.z*sin(vv)                 //the rectangle defined
    #declare nx1=qvn.x*cos(vv)+ww.x*sin(vv)
    #declare ny1=qvn.y*cos(vv)+ww.y*sin(vv)
    #declare nz1=ww.z*sin(vv)
      
      #declare vv=vv+iv                    //by uu,uu+iu,vv,vv+iv
    #declare r=a+b*cos(1.5*uu)
    #declare xx=r*cos(uu)
    #declare yy=r*sin(uu)
    #declare zz=c*sin(1.5*uu)
    #declare dx=-1.5*b*sin(1.5*uu)*cos(uu)-(a+b*cos(1.5*uu))*sin(uu)
    #declare dy=-1.5*b*sin(1.5*uu)*sin(uu)+(a+b*cos(1.5*uu))*cos(uu) 
    #declare dz=1.5*c*cos(1.5*uu)
    #declare qn=vnormalize(<dx,dy,dz>)
    #declare qvn=vnormalize(<qn.y,-qn.x,0>)
    #declare ww=vcross(qn,qvn)
    #declare x2=xx+d*(qvn.x*cos(vv)+ww.x*sin(vv)) //Calculate the
    #declare y2=yy+d*(qvn.y*cos(vv)+ww.y*sin(vv)) //four points in
    #declare z2=zz+d*ww.z*sin(vv)                 //the rectangle defined
    #declare nx2=qvn.x*cos(vv)+ww.x*sin(vv)
    #declare ny2=qvn.y*cos(vv)+ww.y*sin(vv)
    #declare nz2=ww.z*sin(vv)
      
      #declare uu=uu+iu  
      
    #declare r=a+b*cos(1.5*uu)
    #declare xx=r*cos(uu)
    #declare yy=r*sin(uu)
    #declare zz=c*sin(1.5*uu)
    #declare dx=-1.5*b*sin(1.5*uu)*cos(uu)-(a+b*cos(1.5*uu))*sin(uu)
    #declare dy=-1.5*b*sin(1.5*uu)*sin(uu)+(a+b*cos(1.5*uu))*cos(uu) 
    #declare dz=1.5*c*cos(1.5*uu)
    #declare qn=vnormalize(<dx,dy,dz>)
    #declare qvn=vnormalize(<qn.y,-qn.x,0>)
    #declare ww=vcross(qn,qvn)
    #declare x3=xx+d*(qvn.x*cos(vv)+ww.x*sin(vv)) //Calculate the
    #declare y3=yy+d*(qvn.y*cos(vv)+ww.y*sin(vv)) //four points in
    #declare z3=zz+d*ww.z*sin(vv)                 //the rectangle defined
    #declare nx3=qvn.x*cos(vv)+ww.x*sin(vv)
    #declare ny3=qvn.y*cos(vv)+ww.y*sin(vv)
    #declare nz3=ww.z*sin(vv)
      #declare vv=vv-iv
      
    #declare r=a+b*cos(1.5*uu)
    #declare xx=r*cos(uu)
    #declare yy=r*sin(uu)
    #declare zz=c*sin(1.5*uu)
    #declare dx=-1.5*b*sin(1.5*uu)*cos(uu)-(a+b*cos(1.5*uu))*sin(uu)
    #declare dy=-1.5*b*sin(1.5*uu)*sin(uu)+(a+b*cos(1.5*uu))*cos(uu) 
    #declare dz= 1.5*c*cos(1.5*uu)
    #declare qn=vnormalize(<dx,dy,dz>)
    #declare qvn=vnormalize(<qn.y,-qn.x,0>)
    #declare ww=vcross(qn,qvn)
    #declare x4=xx+d*(qvn.x*cos(vv)+ww.x*sin(vv)) //Calculate the
    #declare y4=yy+d*(qvn.y*cos(vv)+ww.y*sin(vv)) //four points in
    #declare z4=zz+d*ww.z*sin(vv)                 //the rectangle defined
    #declare nx4=qvn.x*cos(vv)+ww.x*sin(vv)
    #declare ny4=qvn.y*cos(vv)+ww.y*sin(vv)
    #declare nz4=ww.z*sin(vv)
      #declare uu=uu-iu
//CURVATURE  as difference between normals    
//      #declare ucur = vlength(vnormalize(n6)-vnormalize(n5))/2

//      #declare vcur = vlength(vnormalize(n2)-vnormalize(n5))/2 
//TRIANGLES      
      object{
        smooth_triangle{
          <x1,y1,z1>,<nx1,ny1,nz1>,
          <x2,y2,z2>,<nx2,ny2,nz2>,
          <x3,y3,z3>,<nx3,ny3,nz3>
         }
          texture{  T_Stone20   }
          
          }
      object{
        smooth_triangle{
          <x1,y1,z1>,<nx1,ny1,nz1>,  
          <x3,y3,z3>,<nx3,ny3,nz3>,   
          <x4,y4,z4>,<nx4,ny4,nz4> 
         }
        texture{  T_Stone20   }
        }

      #declare vv = vv+iv
   #end                 //inner loop
   #declare uu = uu+iu
      #debug concat("Looping on  ",str(counter,0,-1)," of ",str(uiter,0,-1),"\n")
   #declare counter = counter + 1

 #end                   //outer loop
//rotate <90,0,0>     //This is just changing the
//rotate <0,90,0>     //coordinate system.
}

//Lights, camera, action
camera
{ location  < 1.5, 2.25,-3.75>
  direction  1*z
  look_at   < 0, 0, 0>
} 

light_source { <0, 0,-5> color rgb 1 }
light_source { <5, 5, -4> color rgb 1 }
object {box{-6,6 inverse}pigment{color rgb 0.8}}