// Tétraèdre de Sierpinski

#include "colors.inc"
#include "sable.inc"

light_source { <6,10,-8> color rgb <0.95,0.95,1>*1.2 }
light_source { <-10,6,6> color rgb <1,0,1>*0.6 }
light_source { <-10,4,20> color rgb <1,0,1>*0.6 }
background { SkyBlue*1.2 }
 
camera { location <2,1.5,-7>
         look_at  <2.2,0.45,1>
}
 
#macro vmilieu(a,b)
     <(a.x+b.x)/2, (a.y+b.y)/2, (a.z+b.z)/2 >
#end

#macro tetraedre (a,b,c,d)
  union {
        triangle { a,b,c}
        triangle { a,b,d}
        triangle { d,b,c}
        triangle { a,d,c}
 }
#end 

 /* 
// variante de tétraedre (supprimer le pigment dans l'object final)
#macro tetraedre (a,b,c,d)
  union {
        triangle { a,b,c pigment {Red*1.7}}
        triangle { a,b,d pigment {Green}}
        triangle { d,b,c  texture {sable2 }}
        triangle { a,d,c pigment {White} }
 }
#end 
*/

#macro sierpinski(a,b,c,d,n)
  #if (n=0) tetraedre(a,b,c,d)
  #else
       sierpinski(a,vmilieu(a,b),vmilieu(a,c),vmilieu(a,d),n-1)
       sierpinski(vmilieu(a,b),b,vmilieu(b,c),vmilieu(b,d),n-1)
       sierpinski(vmilieu(a,c),c,vmilieu(c,b),vmilieu(c,d),n-1)
       sierpinski(vmilieu(a,d),vmilieu(d,b),vmilieu(d,c),d,n-1) 
  #end
#end

// n est le nombre d'itérations
#declare n=2; 

  
union{ sierpinski (<0,0,0>,<4,0,0>,<2,3.464,0>,<2,1.155,3>,n)
       pigment {
               gradient <0,1,-0.38>
               color_map {
                   [ 0.1  color red 1.0 green 1.0 blue 1]
                   [ 0.2  color red 1.0 green 1.0 blue 0]
                   [ 0.3  color red 1 green 0.8 blue 0.]
                   [ 0.5  color red 0.8 green 0.6 blue 0 filter 0.5] 
                    } // color_map
               scale 0.2/n}
      
        finish {ambient 0.55 diffuse 0.7 specular 0.6 reflection 0.1 roughness 0.01} 
        rotate <0,75,-20>
        scale <1.5,1,1>
          
     }