Implicit and Parametric Surfaces for POV-Ray

This patch is an unofficial version of POV-Ray and it is not supported by POV-Ray Team. It enxtends POV-Ray 2.2 with implicit functions F(x,y,z)=0 and parametric surfaces x(u,v),y(u,v),z(u,v).

parimp-0.92.tar.gz includes modified POV-Ray files and Makefile for Linux/GCC.

For solving intersection between ray and surface we use interval arithmetic. It requires $C0$ continuity for find correct solution of equality and $C1$ continuity for correct shading. Normals (partial derivates) are computed by numeric methods.

What does work now?

• Parsing functions
• Implicit surfaces f(x,y,z)=0
• Parametric surfaces x(u,v), y(u,v), z(u,v)
• New map_type 8 for maping on parametric surfaces
• Functions (+,-,*,/, abs, sqr, sqrt, cub, x^y, exp, log, sin, cos, atan, sinh, cosh, tanh, asinh, min, max)
• New keyword precompute for speeding up computations of parametric surface/ray intersections

Future

• docs ...
• new functions (asin, acos, tan, acosh, atanh, noise)
• speed improvments (octree for implicit surfaces,...)
• POV-Ray 3.0 (after official release)

Examples - Implicit Surfaces

Sphere

implicit {
   function sqr(x) + sqr(y) + sqr(z) - 1 
   < -1.5, -1.5, -1.5>,   <1.5, 1.5, 1.5>
   accuracy 0.001
   .
   .
   .
   
}

Blob

Classical blob (Jim Blinn) - no polynomial aproximation!

#declare delta= 1.1
#declare BLOB= function exp(1-sqr(x)-sqr(y+delta)-sqr(z)) 
                       + exp(1-sqr(x)-sqr(y-delta)-sqr(z)) - 1

implicit {
  function BLOB
  < -2,-2,-2>, < 2,2,2>
  accuracy 0.01
   .
   .
   .

 }

Torus as blob component

#declare Ro=0.4
#declare Ri=1.8

#declare P=Ri*Ri+Ro*Ro
#declare M=Ri*Ri-Ro*Ro
#declare MM=M*M

/*
#declare TORUS=
  function x^4+2*sqr(x)*(sqr(y)+sqr(z)-P)+y^4+2*sqr(y)*(sqr(z)+M)+
               z^4-2*sqr(z)*P+MM
*/
implicit
 { 
  function exp(-(x^4+2*sqr(x)*(sqr(y)+sqr(z)-P)+y^4+2*sqr(y)*(sqr(z)+M)+
           z^4-2*sqr(z)*P+MM)) +
           exp(-(x^4+2*sqr(x)*(sqr(z)+sqr(y)-P)+z^4+2*sqr(z)*(sqr(y)+M)+
           y^4-2*sqr(y)*P+MM)) +
           exp(-(y^4+2*sqr(y)*(sqr(x)+sqr(z)-P)+x^4+2*sqr(x)*(sqr(z)+M)+
           z^4-2*sqr(z)*P+MM)) - .7


  <-Ro-2*Ri,-Ro-2*Ri,-Ro-2*Ri>, <Ro+2*Ri,Ro+2*Ri,Ro+2*Ri>
  accuracy .01

  pigment { color rgb <0,1,1> } 
 }

Heart

6th order polynomial

#declare HEART= function cub(2*sqr(x)+sqr(y)+sqr(z)-1) - 
                               (0.1*sqr(x)+sqr(y))*cub(z)
   .
   .
   .

Klein Botte

#declare KLEINE=function (sqr(x)+sqr(y)+sqr(z)+2*y-1)*(sqr(sqr(x)+sqr(y)+sqr(z)
                           -2*y-1)-8*sqr(z))+16*x*z*(sqr(x)+sqr(y)+sqr(z)-2*y-1)

Goniometric functions

function_xy {
 function cos(10*(sqrt(sqr(x)+sqr(y))))
 <-2,-2,-2>,<2,2,2>
 accuracy 0.01
   .
   .
   .

}

CSG - Difference

#declare SPHERE = implicit {
  function sqr(x)+sqr(y)+sqr(z)-1
  accuracy 0.01
  all_intersections
  <-1.5,-1.5,-1.5>, <1.5,1.5,1.5>
  pigment { color rgb <1,1,0> }
 }

#declare BOX = 
  box {
    <-0.75,-0.75, -0.75>, <0.75,0.75,0.75>
    pigemnt { color rgb <1,1,1> }
  }

difference {
  object {BOX}
  object {SPHERE}
  pigment { color rgb <1,1,1> }
  finish { ambient 0.7 }
}

Examples - Parametric Surfaces

Plane

Just another plane.

parametric {
  function u,0,v
  <-1,-1>, <1,1>                  /* range of u and v */         
  <-1.5,-1.5,-1.5>,<1.5,1.5,1.5>  
  accuracy 0.01
    .
    .
    .

Cylinder

There appears strange bug with this cone - can you notice it?

7/1/96 - this bug is fixed.

#declare PI=3.14159265358979323

parametric {
  function  sin(v), u, cos(v)
  <-1,-PI>, <1,PI>     
    .
    .
    .

map_type 8
This is another parametetric surface ...

#declare PI=3.14159265358979323

parametric {
  function  v*cos(4*u), u, v*sin(4*u)
  <-PI/2,-1>, <PI/2, 1>     
 
  pigment {
    image_map {
      tga "bv17.tga"
      map_type 8
    }
  }
  finsih { ambient 0.7 }
}

POV-Ray releated links

• POV-Ray homepage
• Mother of all Ray Tracing Pages
• POV-AXF homepage
• POV Man by R. Mercier - extension, which allows RenderMan like shaders
• Equipotential surfaces for POV-Ray by Ryoichi Suzuki
• Isosurface patch for POV-Ray 3.0 by Ryoichi Suzuki
• MPOV patch - POV-Ray 3.0 with Macros by 0rfelyus