September 20th, 2013

Decyphering the Business Card Raytracer

I love you Hoi-En.
I recently came across Paul Heckbert's business card raytracer. For those that have never heard of it: It is a very famous challenge in the Computer Graphics field that started on May 4th, 1984 via a post on comp.graphics by Paul Heckbert ( More about this in his article "A Minimal Ray Tracer" from the book Graphics Gems IV).

The goal was to produce the source code for a raytracer...that would fit on the back of a business card.

Andrew Kensler's version is mesmerizing and one of the greatest hack that I have seen. Since I am curious, I decided to deconstruct it: Here is what I understood.

Edit : Andrew Kensler himself commented on Hacker News and adressed/elaborated on my observations: Thanks you so much Andrew :) !


The Business Card Code


    #include <stdlib.h>   // card > aek.ppm
    #include <stdio.h>
    #include <math.h>
    typedef int i;typedef float f;struct v{
    f x,y,z;v operator+(v r){return v(x+r.x
    ,y+r.y,z+r.z);}v operator*(f r){return
    v(x*r,y*r,z*r);}f operator%(v r){return
    x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r
    ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.
    y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v
    operator!(){return*this*(1/sqrt(*this%*
    this));}};i G[]={247570,280596,280600,
    249748,18578,18577,231184,16,16};f R(){
    return(f)rand()/RAND_MAX;}i T(v o,v d,f
    &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01
    <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;)
    for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k
    ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0
    ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!(
    p+d*t),m=2;}}return m;}v S(v o,v d){f t
    ;v n;i m=T(o,d,t,n);if(!m)return v(.7,
    .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R(
    ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l%
    n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b
    >0),99);if(m&1){h=h*.2;return((i)(ceil(
    h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b
    *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i
    main(){printf("P6 512 512 255 ");v g=!v
    (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a
    )*.002,c=(a+b)*-256+g;for(i y=512;y--;)
    for(i x=512;x--;){v p(13,13,13);for(i r
    =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)*
    99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b
    *(y+R())+c)*16))*3.5+p;}printf("%c%c%c"
    ,(i)p.x,(i)p.y,(i)p.z);}}
 
  
The code looks confusing but it compiles and run flawlessly !! On my MacBook Air, I can save this file on my Desktop as card.cpp, open Terminal and type :


    c++ -O3 -o card card.cpp
    ./card > card.ppm
  


Within 27 seconds, the following image is generated:



Business Card Raycaster features

The list of features is impressive :

All that fitting on the back of a business card ! Let's see how it works !


Vector class

    
    #include <stdlib.h>   // card > aek.ppm
    #include <stdio.h>
    #include <math.h>
    typedef int i;typedef float f;struct v{
    f x,y,z;v operator+(v r){return v(x+r.x
    ,y+r.y,z+r.z);}v operator*(f r){return
    v(x*r,y*r,z*r);}f operator%(v r){return
    x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r
    ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.
    y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v
    operator!(){return*this*(1/sqrt(*this%*
    this));}};i G[]={247570,280596,280600,
    249748,18578,18577,231184,16,16};f R(){
    return(f)rand()/RAND_MAX;}i T(v o,v d,f
    &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01
    <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;)
    for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k
    ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0
    ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!(
    p+d*t),m=2;}}return m;}v S(v o,v d){f t
    ;v n;i m=T(o,d,t,n);if(!m)return v(.7,
    .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R(
    ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l%
    n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b
    >0),99);if(m&1){h=h*.2;return((i)(ceil(
    h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b
    *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i
    main(){printf("P6 512 512 255 ");v g=!v
    (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a
    )*.002,c=(a+b)*-256+g;for(i y=512;y--;)
    for(i x=512;x--;){v p(13,13,13);for(i r
    =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)*
    99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b
    *(y+R())+c)*16))*3.5+p;}printf("%c%c%c"
    ,(i)p.x,(i)p.y,(i)p.z);}}

  
The main trick that helps reducing the code size dramatically it to use two define :

The other big space saver is the 'v' C++ class which is used for vector but also pixel processing.

Here is the code formated, highlighted and commented:


   #include <stdlib.h>   // card > aek.ppm
   #include <stdio.h>
   #include <math.h>

   typedef int i;       //Save space by using 'i' instead of 'int'
   typedef float f;     //Save even more space by using 'f' instead of 'float'

   //Define a vector class with constructor and operator: 'v'
   struct v{
      f x,y,z;  // Vector has three float attributes.
      v operator+(v r){return v(x+r.x,y+r.y,z+r.z);} //Vector add
      v operator*(f r){return v(x*r,y*r,z*r);}       //Vector scaling
      f operator%(v r){return x*r.x+y*r.y+z*r.z;}    //Vector dot product
      v(){}                                  //Empty constructor
      v operator^(v r){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.y-y*r.x);} //Cross-product
      v(f a,f b,f c){x=a;y=b;z=c;}            //Constructor
      v operator!(){return *this*(1 /sqrt(*this%*this));} // Used later for normalizing the vector
   };

  


Random() and World database

    
    #include <stdlib.h>   // card > aek.ppm
    #include <stdio.h>
    #include <math.h>
    typedef int i;typedef float f;struct v{
    f x,y,z;v operator+(v r){return v(x+r.x
    ,y+r.y,z+r.z);}v operator*(f r){return
    v(x*r,y*r,z*r);}f operator%(v r){return
    x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r
    ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.
    y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v
    operator!(){return*this*(1/sqrt(*this%*
    this));}};i G[]={247570,280596,280600,
    249748,18578,18577,231184,16,16};f R(){
    return(f)rand()/RAND_MAX;}i T(v o,v d,f
    &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01
    <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;)
    for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k
    ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0
    ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!(
    p+d*t),m=2;}}return m;}v S(v o,v d){f t
    ;v n;i m=T(o,d,t,n);if(!m)return v(.7,
    .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R(
    ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l%
    n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b
    >0),99);if(m&1){h=h*.2;return((i)(ceil(
    h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b
    *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i
    main(){printf("P6 512 512 255 ");v g=!v
    (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a
    )*.002,c=(a+b)*-256+g;for(i y=512;y--;)
    for(i x=512;x--;){v p(13,13,13);for(i r
    =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)*
    99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b
    *(y+R())+c)*16))*3.5+p;}printf("%c%c%c"
    ,(i)p.x,(i)p.y,(i)p.z);}}

  
The next section also saves a lot of code by defining a R function that return a random value within [0.0f-1.0f]. It is very useful for the stochastic sampling resulting in blur and soft-shadows.

The G array encodes the location of the spheres. The integers are interpreted as 9 lines and 19 columns bit vector.

Here is the code formated, highlighted and commented :

  

    //The set of sphere positions describing the world.
    //Those integers are in fact bit vectors.
   i G[]={247570,280596,280600,249748,18578,18577,231184,16,16};
   
   /*
 
   16                    1    
   16                    1    
   231184   111    111   1    
   18577       1  1   1  1   1
   18578       1  1   1  1  1 
   249748   1111  11111  1 1  
   280600  1   1  1      11   
   280596  1   1  1      1 1  
   247570   1111   111   1  1 
 
   */
   
   // Random generator, return a float within range [0-1]
   f R(){return(f)rand()/RAND_MAX;}


Main method

    
    #include <stdlib.h>   // card > aek.ppm
    #include <stdio.h>
    #include <math.h>
    typedef int i;typedef float f;struct v{
    f x,y,z;v operator+(v r){return v(x+r.x
    ,y+r.y,z+r.z);}v operator*(f r){return
    v(x*r,y*r,z*r);}f operator%(v r){return
    x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r
    ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.
    y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v
    operator!(){return*this*(1/sqrt(*this%*
    this));}};i G[]={247570,280596,280600,
    249748,18578,18577,231184,16,16};f R(){
    return(f)rand()/RAND_MAX;}i T(v o,v d,f
    &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01
    <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;)
    for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k
    ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0
    ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!(
    p+d*t),m=2;}}return m;}v S(v o,v d){f t
    ;v n;i m=T(o,d,t,n);if(!m)return v(.7,
    .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R(
    ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l%
    n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b
    >0),99);if(m&1){h=h*.2;return((i)(ceil(
    h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b
    *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i
    main(){printf("P6 512 512 255 ");v g=!v
    (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a
    )*.002,c=(a+b)*-256+g;for(i y=512;y--;)
    for(i x=512;x--;){v p(13,13,13);for(i r
    =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)*
    99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b
    *(y+R())+c)*16))*3.5+p;}printf("%c%c%c"
    ,(i)p.x,(i)p.y,(i)p.z);}}

  
The main method uses a simple image file format known as PPM. It is text based with a ridiculously simple header: P6 [WIDTH] [HEIGHT] [MAX_VALUE] followed by the RGB values for each pixels.
For each 512x512 pixels in the image, the program samples (S) the color of 64 rays, accumulates the result and write it to the output (stdout).

It applies a bit of random delta on each ray origin and ray direction in order to produce a nice Depth of View effect.

Here is the code formated, highlighted and commented :


  // The main function. It generates a PPM image to stdout.
  // Usage of the program is hence: ./card > erk.ppm
  i main(){
    
     printf("P6 512 512 255 "); // The PPM Header is issued
    
     // The '!' are for normalizing each vectors with ! operator. 
     v g=!v(-6,-16,0),       // Camera direction
       a=!(v(0,0,1)^g)*.002, // Camera up vector...Seem Z is pointing up :/ WTF !
       b=!(g^a)*.002,        // The right vector, obtained via traditional cross-product
       c=(a+b)*-256+g;       // WTF ? See https://news.ycombinator.com/item?id=6425965 for more.

     for(i y=512;y--;)    //For each column
     for(i x=512;x--;){   //For each pixel in a line
       
        //Reuse the vector class to store not XYZ but a RGB pixel color
        v p(13,13,13);     // Default pixel color is almost pitch black
       
        //Cast 64 rays per pixel (For blur (stochastic sampling) and soft-shadows. 
        for(i r=64;r--;){ 
          
            // The delta to apply to the origin of the view (For Depth of View blur).
            v t=a*(R()-.5)*99+b*(R()-.5)*99; // A little bit of delta up/down and left/right 
                                           
            // Set the camera focal point v(17,16,8) and Cast the ray 
            // Accumulate the color returned in the p variable
            p=S(v(17,16,8)+t, //Ray Origin
                !(t*-1+(a*(R()+x)+b*(y+R())+c)*16) // Ray Direction with random deltas
                                                   // for stochastic sampling
                )*3.5+p; // +p for color accumulation
        }
       
        printf("%c%c%c",(i)p.x,(i)p.y,(i)p.z);
       
     }
  }

  


Sampler

    
    #include <stdlib.h>   // card > aek.ppm
    #include <stdio.h>
    #include <math.h>
    typedef int i;typedef float f;struct v{
    f x,y,z;v operator+(v r){return v(x+r.x
    ,y+r.y,z+r.z);}v operator*(f r){return
    v(x*r,y*r,z*r);}f operator%(v r){return
    x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r
    ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.
    y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v
    operator!(){return*this*(1/sqrt(*this%*
    this));}};i G[]={247570,280596,280600,
    249748,18578,18577,231184,16,16};f R(){
    return(f)rand()/RAND_MAX;}i T(v o,v d,f
    &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01
    <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;)
    for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k
    ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0
    ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!(
    p+d*t),m=2;}}return m;}v S(v o,v d){f t
    ;v n;i m=T(o,d,t,n);if(!m)return v(.7,
    .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R(
    ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l%
    n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b
    >0),99);if(m&1){h=h*.2;return((i)(ceil(
    h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b
    *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i
    main(){printf("P6 512 512 255 ");v g=!v
    (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a
    )*.002,c=(a+b)*-256+g;for(i y=512;y--;)
    for(i x=512;x--;){v p(13,13,13);for(i r
    =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)*
    99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b
    *(y+R())+c)*16))*3.5+p;}printf("%c%c%c"
    ,(i)p.x,(i)p.y,(i)p.z);}}

  
The Sampler (S) is a function that returns a pixel color for a given Point Origin (o) and Vector Direction (d). It is recursive if it hits a sphere. If no sphere is hit by the ray (and a ray always ends up missing) then the function either returns a sky color gradient or a floor color based on a checkerboard texture.

Remark the calls to R when computing the light direction: This is how the soft-shadows are generated.

Here is the code formated, highlighted and commented :


   // (S)ample the world and return the pixel color for
   // a ray passing by point o (Origin) and d (Direction)
   v S(v o,v d){
      f t;
      v n;
    
      //Search for an intersection ray Vs World.
      i m=T(o,d,t,n);

    
      if(!m) // m==0
      //No sphere found and the ray goes upward: Generate a sky color  
      return v(.7,.6,1)*pow(1-d.z,4);

      //A sphere was maybe hit.
    
      v h=o+d*t,                    // h = intersection coordinate
      l=!(v(9+R(),9+R(),16)+h*-1),  // 'l' = direction to light (with random delta for soft-shadows).
      r=d+n*(n%d*-2);               // r = The half-vector
 
      //Calculated the lambertian factor
      f b=l%n;
    
      //Calculate illumination factor (lambertian coefficient > 0 or in shadow)?
      if(b<0||T(h,l,t,n))
         b=0;
   
      // Calculate the color 'p' with diffuse and specular component 
      f p=pow(l%r*(b>0),99);
    
      if(m&1){   //m == 1
         h=h*.2; //No sphere was hit and the ray was going downward: Generate a floor color
         return((i)(ceil(h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b*.2+.1);
      }
   
      //m == 2 A sphere was hit. Cast an ray bouncing from the sphere surface.
      return v(p,p,p)+S(h,r)*.5; //Attenuate color by 50% since it is bouncing (* .5)
  }


  


Tracer

    
    #include <stdlib.h>   // card > aek.ppm
    #include <stdio.h>
    #include <math.h>
    typedef int i;typedef float f;struct v{
    f x,y,z;v operator+(v r){return v(x+r.x
    ,y+r.y,z+r.z);}v operator*(f r){return
    v(x*r,y*r,z*r);}f operator%(v r){return
    x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r
    ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.
    y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v
    operator!(){return*this*(1/sqrt(*this%*
    this));}};i G[]={247570,280596,280600,
    249748,18578,18577,231184,16,16};f R(){
    return(f)rand()/RAND_MAX;}i T(v o,v d,f
    &t,v&n){t=1e9;i m=0;f p=-o.z/d.z;if(.01
    <p)t=p,n=v(0,0,1),m=1;for(i k=19;k--;)
    for(i j=9;j--;)if(G[j]&1<<k){v p=o+v(-k
    ,0,-j-4);f b=p%d,c=p%p-1,q=b*b-c;if(q>0
    ){f s=-b-sqrt(q);if(s<t&&s>.01)t=s,n=!(
    p+d*t),m=2;}}return m;}v S(v o,v d){f t
    ;v n;i m=T(o,d,t,n);if(!m)return v(.7,
    .6,1)*pow(1-d.z,4);v h=o+d*t,l=!(v(9+R(
    ),9+R(),16)+h*-1),r=d+n*(n%d*-2);f b=l%
    n;if(b<0||T(h,l,t,n))b=0;f p=pow(l%r*(b
    >0),99);if(m&1){h=h*.2;return((i)(ceil(
    h.x)+ceil(h.y))&1?v(3,1,1):v(3,3,3))*(b
    *.2+.1);}return v(p,p,p)+S(h,r)*.5;}i
    main(){printf("P6 512 512 255 ");v g=!v
    (-6,-16,0),a=!(v(0,0,1)^g)*.002,b=!(g^a
    )*.002,c=(a+b)*-256+g;for(i y=512;y--;)
    for(i x=512;x--;){v p(13,13,13);for(i r
    =64;r--;){v t=a*(R()-.5)*99+b*(R()-.5)*
    99;p=S(v(17,16,8)+t,!(t*-1+(a*(R()+x)+b
    *(y+R())+c)*16))*3.5+p;}printf("%c%c%c"
    ,(i)p.x,(i)p.y,(i)p.z);}}

  
The Tracer is in charge of casting a Ray (Origin o ,Direction d). It return an integer that is a code for the intersection test with the spheres in the world (0=miss toward sky,1=miss toward floor, 2=sphere hit). If a sphere is hit, it updates the references t (the parametric value to compute the distance of intersection) and n (the half-vector where the ray bounce).

Here is the code formated, highlighted and commented :


  
   //The intersection test for line [o,v].
   // Return 2 if a hit was found (and also return distance t and bouncing ray n).
   // Return 0 if no hit was found but ray goes upward
   // Return 1 if no hit was found but ray goes downward
   i T(v o,v d,f& t,v& n){ 
     t=1e9;
     i m=0;
     f p=-o.z/d.z;
      if(.01<p)›
       t=p,n=v(0,0,1),m=1;

     //The world is encoded in G, with 9 lines and 19 columns
     for(i k=19;k--;)  //For each columns of objects
     for(i j=9;j--;)   //For each line on that columns
      
     if(G[j]&1<<k){ //For this line j, is there a sphere at column i ?
        
        // There is a sphere but does the ray hits it ?
         
        v p=o+v(-k,0,-j-4);
        f b=p%d,c=p%p-1,q=b*b-c;
     
        //Does the ray hit the sphere ?
        if(q>0){
           //It does, compute the distance camera-sphere
           f s=-b-sqrt(q);
             
           if(s<t && s>.01)
             // So far this is the minimum distance, save it. And also
             // compute the bouncing ray vector into 'n'  
             t=s,
             n=!(p+d*t),
             m=2;
         }
     }
    
     return m;
  }


  


The Leet Number

Many readers have tried to shorten the code further with more or less success. The original author stopped with the current version for a very interesting reason:

  

      fabien$ wc card.cpp

      35      95    1337 card.cpp

   


The total size of the code is 1337 bytes: The Leet number. Beat that !


Script kiddie

And now that the business card is fully understood, we can generate our own :

    
   #include <stdlib.h>   // card > aek.ppm
   #include <stdio.h>
   #include <math.h>
   typedef int i;typedef float f;struct v{
   f x,y,z;v operator+(v r){return v(x+r.x
   ,y+r.y,z+r.z);}v operator*(f r){ return
   v(x*r,y*r,z*r);}f operator%(v r){return
   x*r.x+y*r.y+z*r.z;}v(){}v operator^(v r
   ){return v(y*r.z-z*r.y,z*r.x-x*r.z,x*r.
   y-y*r.x);}v(f a,f b,f c){x=a;y=b;z=c;}v
   operator!(){return*this*(1/sqrt(*this%*
   this));}};i G[]={133022, 133266,133266,
   133022, 254096, 131216, 131984, 131072,
   258048,};f R(){return(f)rand()/RAND_MAX
   ;}i T(v o,v d,f&t,v&n){t=1e9;i m=0;f p=
   -o.z/d.z; if(.01<p)t=p, n=v(0,0,1),m=1;
   for(i k=19;k--;)for(i j=9;j--;)if(G[j]&
   1<<k){v p=o+v(-k,0,-j-4);f b=p%d,c=p%p-
   1,q=b*b-c;if(q>0){f s=-b-sqrt(q);if(s<t
   &&s>.01)t=s,n=!(p+d*t),m=2;}}return m;}
   v S(v o,v d){f t;v n;i m=T(o,d,t,n);if(
   !m)return v(.7,.6,1)*pow(1-d.z,4);v h=o
   +d*t,l=!(v(9+R(),9+R(),16)+h*-1),r=d+n*
   (n%d*-2);f b=l%n;if(b<0||T(h,l,t,n))b=0
   ;f p=pow(l%r*(b>0),99);if(m&1){h=h*.2;
   return((i)(ceil(h.x)+ceil(h.y))&1?v(3,1
   ,1):v(3,3,3))*(b*.2+.1);}return v(p,p,p
   )+S(h,r)*.5;}i main(){printf("P6 512  "
   "512 255 ");v g=!v(-6,-16,0),a=!(v(0,0,
   1)^g)*.002,b=!(g^a)*.002,c=(a+b)*-256+g
   ;for(i y=512;y--;)for(i x=512;x--;){v p
   (9,9,9);for(i r=64;r--;){v t=a*(R()-.5)
   *99+b*(R()-.5)*99;p=S(v(17,16,8)+t,!(t*
   -1+(a*(R()+x)+b*(y+R())+c)*16))*3.5+p;}
   printf("%c%c%c",(i)p.x,(i)p.y,(i)p.z);}}
  


Recommended readings

Since I have spent as lot of time reading about raytracing, here are a few really good resources:

Comments

 

Fabien Sanglard @2013