minray.post

[Game.Programming].Academic - Graphics Gems (6 books source code)

 * of C tokens after processing by cpp.  For Paul Heckbert's contest,
 * May/June 1987.  WARNING: this style of coding results in increasing
 * execution time because the simplest brute force algorithms are used.
 * Maintenance of the code is harder than it should be for a program
 * of this size, because of the nasty coding style.
 *
 * I have 16 years of programming experience, including
 * 12 years in C, but I'm afraid it doesn't show in this program.
 *
 * Darwyn Peachey, University of Saskatchewan, Dept. of Computational Science.
 * [phone]  [e-mail]  [e-mail]
 *
 * This is the 956 token version of 13-Jun-87.
 */

#define PI360          8.7266462599716e-3      /* PI/360 */
#define INFINITY       1e30
#define EPSILON                1e-6

typedef struct { double x, y, z } triple;
typedef struct {
       triple ctr, color;      /* center and RGB coeffs of sphere */
       double radius, kd, ks, kt, kl, ir
} sphere;
#define SPHERE sphere sph[]
#define AMBIENT        triple v, zero, ambient

#include "ray.h"

double tan(), sqrt(), tmin, a, b, t;
/* int */ row, col, half = SIZE/2;     /* row initialized to 0 */

triple
combine(v1, a, v2)
       triple v1, v2;
       double a;
{
       v2.x += a * v1.x;
       v2.y += a * v1.y;
       v2.z += a * v1.z;
       return v2;
}
double
dot(v1, v2)
       triple v1, v2;
{
       return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;
}

triple
norm(vec)
       triple vec;
{
       return combine(vec, 1/sqrt(dot(vec,vec)), zero);
}

/*
 * Intersect and trace use the same global variable, tmin.
 */
sphere *
intersect(rayorg, rayvec)
       triple rayorg, rayvec;
{
       sphere *sp, *which = 0;


       tmin = INFINITY;
       for (sp = sph; sp < sph+NSPHERE; sp++) {
               /* determine coefficients of quadratic equation */
               /* at^2 + bt + c = 0 */
               a = dot(rayvec, rayvec);
               v = combine(sp->ctr, -1.0, rayorg);
               b = 2 * dot(rayvec, v);

               /* discriminant: b*b - 4*a*c */
               t = b*b - 4*a*(dot(v,v) - sp->radius*sp->radius);
               /* find (closest) root if any */
               if (t > EPSILON) {      /* there are two real roots */
                       t = sqrt(t);
                       t = 0.5 * ((-b > t + EPSILON ? -t : t) - b)/a;
                       if (t > EPSILON && t < tmin)
                               which = sp, tmin = t;
               }
       }
       return which;
}

triple
trace(N, rayvec, depth, inside)
       triple N, rayvec;       /* N used for ray origin & normal vec */
{
       triple loc, dir, color;
       sphere *which, *sp;
       double rcos1, rcos2, n;

       if (depth > DEPTH)
               return zero;

       if (which = intersect(N, rayvec)) {
               /* having found best "t" value, compute location and normal */
               N = combine(norm(combine(which->ctr, -1.0,
                       loc = combine(rayvec, tmin, N))),
                       inside ? -1.0 : 1.0, zero);

               /* do shading calculations, and fire subrays as necessary */
               color = ambient;        /* accumulate illumination in color */
               for (sp = sph; sp < sph+NSPHERE; sp++)
                       if ((n = dot(N,
                               dir = norm(combine(loc, -1.0, sp->ctr)))) > 0.0
                         && intersect(loc, dir) == sp)
                               color = combine(sp->color, n*sp->kl, color);
               /* color is now the total ambient + direct lighting */
               color.x *= which->color.x * which->kd;
               color.y *= which->color.y * which->kd;
               color.z *= which->color.z * which->kd;
               rcos1 = -dot(N, rayvec);
               n = inside ? which->ir : 1/which->ir;
               rcos2 = 1 - n*n * (1 - rcos1*rcos1);
               return combine( /* refracted color */
                               rcos2 > EPSILON ?
                               trace(loc, combine(rayvec, n,
                                       combine(N, n * rcos1 - sqrt(rcos2),
                                               zero)),
                                       depth+1, !inside) : zero, which->kt,
                               /* reflected color */
                               combine(trace(loc,combine(N,2 * rcos1,rayvec),
                                       depth+1, inside), which->ks,
                                       /* luminance + diffuse color */
                                       combine(which->color, which->kl,
                                               color)));
       }
       return ambient;
}

main()
{
       printf("%d %d\n", SIZE, SIZE);

       while (col = 0,row++ < SIZE)
               while (col < SIZE)
                       v.x = col++ - half,
                       v.y = half / tan(AOV * PI360),
                       v.z = half - row + 1,
                       v = trace(zero, norm(v), 1, 0),
                       printf("%.0f %.0f %.0f\n",
                               v.x*255, v.y*255, v.z*255);
}
EOF27904
cat <<'EOF27905' >michel.c
/*
 = MINIMAL RAY TRACER PROGRAMMING CONTEST ENTRY
 = 
 = By : Michel Burgess                   
 =      6750, rue St-Denis
 =      Montreal(Quebec)
 =      Canada  H2S 2S2
 =
 = Email:  CDNnet : [e-mail]
 =         CSNET  : [e-mail]
 =         UUCP   : ...!seismo!utgpu!utai!musocs!mcgill-vision!iros1!burgess
 =                                                         ...!iros1!babin
 =
 = Years programming : 9 (recently finished a M.Sc. C.S. Universite de Montreal)
 = 
 = Notes : This program is barely readable due to compacting.
 =         Reduced to fit in 80 columns.
 =         It is based on a program written by Turner Whitted, that raytraces
 =         quadric surfaces. ( picked it up at siggraph ).
 =         It uses a few defines for lisibility ( some variables are reused to
 =         save tokens).
 =         everything declared as double (floats,ints,shorts).
 =         Extensive use of affectations within if()s.
 =         AddMul(v1,r,V2) = V1 + r*V2 , cuts on declaring Add Sub and Mul
 =         for Vector Arithmethics.
 =         Vectors and Colors are declared the same e.g. Vector.
 =          -this causes problems on my SUN 3/50
 =         This program compiles and links with no problems on my VAX 780 VMS.
 =         I Can't find a Vax with 4.3 bsd on my network.
 =
 */
 
#define NULL 0
#define HUGEREAL 1e10  /* why not */
#define cmino vPrime   /* center of sphere minus origin of ray */
#define dist coeff     /* distance from origin to sphere */
#define Kf coeff       /* refraction coefficient */
#define Dot t          /* Dot product of incident ray and surface normal */
#define VplusN direction /* Vprime pls normal cf Whitted's article */
#define neworigin origin /* origin of reflected and refracted ray */
 
#define AMBIENT   Vector Ambient
#define SPHERE    Spheres sph[NSPHERE] 
 
typedef struct  { double x,y,z ; } Vector;  
 
typedef struct  {
        Vector  center,
  color;    
 double radius,
            kd,
            ks,
            kt,
            kL,
            ir; 
} Spheres;
 
#include "ray.h"
 
Spheres *spo = sph+NSPHERE ;
 
double  halfSIZE = SIZE/2.,
        level,
        lecos,
        sqrt(),
        tan();
Vector  zeros, 
        root,
        eyedir;
 
/* addmul compacts add mul sub div within one function */
 
Vector addmul(v1,r,v2)
Vector v1,v2;
double r;
{
 v1.x += r * v2.x;
 v1.y += r * v2.y;
 v1.z += r * v2.z;
 return v1;
}
 
/* scalar or dot product of 2 vectors */
 
double sc(v1,v2)
Vector v1,v2;
{
 return v1.x*v2.x+v1.y*v2.y+v1.z*v2.z;
}
 
/* rayHit : main recursive routine,
            does the hitting and shading of rays.
*/
 
Vector  rayHit(pSph,origin,direction,normal)
Spheres *pSph;
Vector  origin,direction,normal;
{
 Spheres *current,*spn;
 Vector  vPrime,Couleur;
 double  t = HUGEREAL,
 coeff;
 
  direction=addmul(zeros, 1.0/sqrt(sc( direction ,direction)),direction);
  for ( current=sph ; current < sph+NSPHERE ; current++)
    if(( lecos=sc((cmino=addmul(current->center,-1.,origin)), direction)) >0.0 
      &&
      ( coeff= lecos*lecos + current->radius*current->radius - sc(cmino,cmino))
       > 0.0 )
           if((dist = pSph==current ? lecos+sqrt(coeff):lecos-sqrt(coeff))< t)
           { t = dist;
             spn = current;
           }
  Couleur=Ambient;
  if ( spo != sph+NSPHERE ) 
     return addmul(zeros,((t = spn->kL*sc(direction,normal))>=0. 
                              && spn==spo ?t:0.),spn->color);
  if ( t < HUGEREAL )
  {
    neworigin = addmul( origin , t,direction);
    normal= addmul(zeros,1./spn->radius,addmul(neworigin ,-1., spn->center));
    Dot = sc( normal, direction);
    if ( Dot < 0.0 ) Dot = -Dot;
     else normal= addmul(zeros,-1.,normal);
 
    for (spo=sph ; spo < sph+NSPHERE ; spo++)
        Couleur = addmul(Couleur,1.,rayHit( spn,neworigin, 
                                    addmul(spo->center,-1.,neworigin),normal));
    vPrime = addmul(zeros,spn->kd,spn->color);
    Couleur.x *=  vPrime.x;
    Couleur.y *=  vPrime.y;
    Couleur.z *=  vPrime.z;
    if ( ++level < DEPTH  && Dot > 0.001) 
    {
       vPrime = addmul(zeros,1./Dot, direction );
       Couleur=addmul(Couleur,spn->ks,rayHit(spn,neworigin,
                                             addmul(vPrime, 2.0 ,normal),zeros));
       VplusN = addmul( vPrime , 1.,normal);
       coeff = pSph == spn ? 1.0/spn->ir : spn->ir;
       if((coeff = coeff*coeff*sc(vPrime,vPrime)-sc(VplusN,VplusN)) > 0.0 )
          Couleur = addmul( Couleur, spn->kt, rayHit(spn,neworigin,
                             addmul(addmul(zeros, 1.0/sqrt(coeff), VplusN),-1.
                                                    ,normal),normal));
    }
    level--;
    Couleur=addmul(Couleur , spn->kL , spn->color);
  }
  return Couleur;
}
 
main()
{
  printf("%d %d\n",SIZE,SIZE);
  eyedir.y =  halfSIZE / tan( AOV*0.008726646 );
  for ( eyedir.z = halfSIZE; eyedir.z > -halfSIZE ; eyedir.z-- )
    for (eyedir.x = -halfSIZE ;  eyedir.x < halfSIZE  ; 
        printf("%d %d %d\n",(int)root.x,(int)root.y,(int)root.z),eyedir.x++) 
     if ( DEPTH ) root = addmul(zeros,255.,rayHit(NULL,zeros,eyedir,zeros));
}
EOF27905
cat <<'EOF27906' >tony.c
/*
 * THE minimal ray tracer (or any other program): 10 tokens.
 * Tony Apodaca, Pixar
 */

#ifdef TRACER
main()
{
    printf("trace them rays!\n");
    /* insert your favorite ray tracer here */
}
#else
main()
{
    system("cc -DTRACER -o tmp tony.c -lm; tmp; rm tmp");
}
#endif
EOF27906
cat <<'EOF27907' >greg.c
/*
 *  ray.c - cheater's entry to minimal ray-tracing contest.
 *
 *	6/10/87
 *	Gregory J. Ward
 *	[e-mail]
 *	Lawrence Berkeley Lab
 *	1 Cyclotron Rd. 90-3111
 *	Berkeley, CA  94720
 *	[phone]
 *	3 years programming in C, a lifetime of cheating...
 */
main()
{
char *fopen(), *fp = fopen("/tmp/temp.c", "w");
fputs("typedef double VECT[3];\n#define AMBIENT VECT ambient\n#define SPHERE struct sphere {VECT  cent, col; double  rad, kd, ks, kt, kl, ir;} sph[NSPHERE]\n#include \"ray.h\"\n", fp);
fputs("struct ray{VECT org,dir,col;struct sphere*target;}pri;double tan(),sqrt();double dot(v1,v2)VECT v1,v2;{return*v1**v2+v1[1]*v2[1]+v1[2]*v2[2];}main(){int x,y= -1;printf(\"%d %d\\n\",SIZE,SIZE);while(x= -1,++y<SIZE)while(++x<SIZE)pri.dir[0]=x-SIZE/2,pri.dir[1]=SIZE/2/tan(AOV/114.591559),pri.dir[2]=SIZE/2-y,rayval(&pri,DEPTH),printf(\"%.0f %.0f %.0f\\n\",255*pri.col[0],255*pri.col[1],255*pri.col[2]);}rayval(r,depth)struct ray*r;{int i;struct sphere*s,*rs=0;VECT norm;double d1,d2,d3", fp);
fputs(",rt=1e20;struct ray dau;bzero(r->col,24);if(!depth--)return;d3=sqrt(dot(r->dir,r->dir));i=3;while(i--)r->dir[i]/=d3;s=sph+NSPHERE;while(s-->sph){bcopy(s->cent,norm,24);vsum(norm,r->org,-1.0);d1=dot(norm,r->dir);d3=s->rad*s->rad+d1*d1-dot(norm,norm);if(d3<0.0)continue;d3=sqrt(d3);d3=d1-d3>1e-7?d1-d3:d1+d3;if(d3>1e-7&&d3<rt)rt=d3,rs=s;}if(r->target){if(rs!=r->target)return;}else{vsum(r->col,ambient,1.0);if(!rs)return;i=3;while(i--)norm[i]=((dau.org[i]=r->org[i]+r->dir[i]*rt)-rs->cent[i])/rs->rad;", fp);
fputs("if(rs->kd!=0.0){s=sph+NSPHERE;while(s-->sph){if(s->kl==0.0)continue;dau.target=s;bcopy(s->cent,dau.dir,24);vsum(dau.dir,dau.org,-1.0);rayval(&dau,1);d1=dot(dau.dir,norm);if(d1>0.0)vsum(r->col,dau.col,d1);}}i=3;while(i--)r->col[i]*=rs->kd*rs->col[i];dau.target=0;d1= -dot(r->dir,norm);if(rs->ks!=0.0){bcopy(r->dir,dau.dir,24);vsum(dau.dir,norm,2.0*d1);rayval(&dau,depth);vsum(r->col,dau.col,rs->ks);}if(rs->kt!=0.0){d3=d1>0.0?1.0/rs->ir:rs->ir;d2=1.0-d3*d3*(1.0-d1*d1);if(d2>0.0){d2=sqrt(d2);if(d1>0.0", fp);
fputs(")d2= -d2;bzero(dau.dir,24);vsum(dau.dir,r->dir,d3);vsum(dau.dir,norm,d3*d1+d2);rayval(&dau,depth);vsum(r->col,dau.col,rs->kt);}}}vsum(r->col,rs->col,rs->kl);}vsum(v1,v2,s)VECT v1,v2;double s;{int i=3;while(i--)*v1+++= *v2++*s;}", fp);
fclose(fp);
system("cc -o /tmp/temp -I. /tmp/temp.c -lm;/tmp/temp");
}
EOF27907
cat <<'EOF27908' >test1.h
/* ray.h for test1, first test scene */
#define DEPTH 3		/* max ray tree depth */
#define SIZE 32		/* resolution of picture in x and y */
#define AOV 25		/* total angle of view in degrees */
#define NSPHERE 5	/* number of spheres */

AMBIENT = {.02, .02, .02};	/* ambient light color */

/* sphere: x y z  r g b  rad  kd ks kt kl  ir */
SPHERE = {
     0., 6., .5,    1., 1., 1.,   .9,   .05, .2, .85, 0.,  1.7,
    -1., 8., -.5,   1., .5, .2,   1.,   .7, .3, 0., .05,   1.2,
     1., 8., -.5,   .1, .8, .8,   1.,   .3, .7, 0., 0.,    1.2,
     3., -6., 15.,  1., .8, 1.,   7.,   0., 0., 0., .6,    1.5,
    -3., -3., 12.,  .8, 1., 1.,   5.,   0., 0., 0., .5,    1.5,
};
EOF27908
cat <<'EOF27909' >test2.h
/* ray.h for test2, second test scene */
#define DEPTH 4		/* max ray tree depth */
#define SIZE 32		/* resolution of picture in x and y */
#define AOV 30		/* total angle of view in degrees */
#define NSPHERE 3	/* number of spheres */

AMBIENT = {.04, .02, .02};	/* ambient light color */

/* sphere: x y z  r g b  rad  kd ks kt kl  ir */
SPHERE = {
     -.15, 5., 0.,  1., 1., 1.,   1.,   0., .2, .9, .02,    1.1,
     1., 8., .3,    .7, 1., .2,   1.,   .8, .2, 0., 0.,    1.5,
     -3., -3., 4.,  1., 1., 1.,   4.,   0., 0., 0., 1.,    1.1,
};
EOF27909
cat <<'EOF27910' >test3.h
/* ray.h for test3, third test scene */
#define DEPTH 3		/* max ray tree depth */
#define SIZE 31		/* resolution of picture in x and y */
#define AOV 15		/* total angle of view in degrees */
#define NSPHERE 7	/* number of spheres */

AMBIENT = {.05, .05, .05};	/* ambient light color */

/* sphere: x y z  r g b  rad  kd ks kt kl  ir */
SPHERE = {
     .75, 4., 0.,    1., 1., 1.,   .5,   .2, .8, 0., 0.,    1.2,
     .65, 6., 0.,    .9, .2, .9,   .5,   0., .2, .9, .05,   1.2,
     .55, 8., 0.,    .2, .7, .6,   .5,   .6, .4, 0., 0.,    1.2,
     -.75, 4., 0.,   .7, .3, .3,   .5,   .1, .3, .7, 0.,    1.4,
     -.65, 6., 0.,   1., .8, .1,   .5,   .2, .8, 0., 0.,    1.2,
     -.55, 8., 0.,   0., 0., 1.,   .5,   .5, .5, 0., 0.,    1.2,
     0., 0., 3.,    1., 1., 1.,   2.,   0., 0., 0., 1.,    1.1,
};
EOF27910
exit

Path: pixar!ph
From: [e-mail] (Paul Heckbert)
Newsgroups: comp.graphics
Subject: Re: Winners of Minimal Ray Tracer Contest
Summary: minimal ray tracing reaches new lows
Date: 25 Jun 87 07:29:42 GMT
Organization: Pixar -- Marin County, California

Minimal ray tracing reaches new lows!

I've taken some of the tricks from Darwyn Peachey's and Joe Cychosz's minimal
ray tracers (posted previously) and combined them with some of my own to
create a hybrid program that's the shortest of all: 888 tokens.
Recall that Joe Cychosz's winning entry had 916 tokens.
To compile the enclosed "paul.c", run "cc -o paul paul.c -lm".
If you're able to shorten the enclosed program further, please send me mail.

When my C code compacter program "squeeze.c" (also posted previously)
is run on paul.c,

    /lib/cpp paul.c | sed '/^#/d' | squeeze -77 > paul.squeeze.c

we get a rectangular block of C code that fits nicely on a standard 24x80
terminal screen.  See the enclosed file paul.squeeze.c.

An even more impressive thing to do with this file is reduce it to fit on
a small card.  If you've got the Adobe Transcript laser printer software, run:

    enscript -B -fCourier5 paul.squeeze.c

and you've got a ray-tracer-on-a-business-card!


Paul Heckbert
Pixar				415-499-3600
P.O. Box 13719			UUCP: {sun,ucbvax}!pixar!ph
San Rafael, CA 94913		ARPA: [e-mail]

------------------------------

# to unpack, cut here and run the following shell archive through sh
# contents: paul.c ray.h paul.squeeze.c
#
sed 's/^X//' <<'EOF14163' >paul.c
X/* minimal ray tracer, hybrid version - 888 tokens
X * Paul Heckbert, ucbvax!pixar!ph, 13 Jun 87
X * Using tricks from Darwyn Peachey and Joe Cychosz.
X
X#define TOL 1e-7
X#define AMBIENT vec U, black, amb
X#define SPHERE struct sphere {vec cen, color; double rad, kd, ks, kt, kl, ir} \
X    *s, *best, sph[]
Xtypedef struct {double x, y, z} vec;
X#include "ray.h"
Xyx;
Xdouble u, b, tmin, sqrt(), tan();
X
Xdouble vdot(A, B)
Xvec A, B;
X{
X    return A.x*B.x + A.y*B.y + A.z*B.z;
X}
X
Xvec vcomb(a, A, B)	/* aA+B */
Xdouble a;
Xvec A, B;
X{
X    B.x += a*A.x;
X    B.y += a*A.y;
X    B.z += a*A.z;
X    return B;
X}
X
Xvec vunit(A)
Xvec A;
X{
X    return vcomb(1./sqrt(vdot(A, A)), A, black);
X}
X
Xstruct sphere *intersect(P, D)
Xvec P, D;
X{
X    best = 0;
X    tmin = 1e30;
X    s = sph+NSPHERE;
X    while (s-->sph)
X	b = vdot(D, U = vcomb(-1., P, s->cen)),
X	u = b*b-vdot(U, U)+s->rad*s->rad,
X	u = u>0 ? sqrt(u) : 1e31,
X	u = b-u>TOL ? b-u : b+u,
X	tmin = u>=TOL && u<tmin ?
X	    best = s, u : tmin;
X    return best;
X}
X
Xvec trace(level, P, D)
Xvec P, D;
X{
X    double d, eta, e;
X    vec N, color;
X    struct sphere *s, *l;
X
X    if (!level--) return black;
X    if (s = intersect(P, D));
X    else return amb;
X
X    color = amb;
X    eta = s->ir;
X    d = -vdot(D, N = vunit(vcomb(-1., P = vcomb(tmin, D, P), s->cen)));
X    if (d<0)
X	N = vcomb(-1., N, black),
X	eta = 1/eta,
X	d = -d;
X    l = sph+NSPHERE;
X    while (l-->sph)
X	if ((e = l->kl*vdot(N, U = vunit(vcomb(-1., P, l->cen)))) > 0 &&
X	    intersect(P, U)==l)
X		color = vcomb(e, l->color, color);
X    U = s->color;
X    color.x *= U.x;
X    color.y *= U.y;
X    color.z *= U.z;
X    e = 1-eta*eta*(1-d*d);
X    /* the following is non-portable: we assume right to left arg evaluation.
X     * (use U before call to trace, which modifies U) */
X    return vcomb(s->kt,
X	e>0 ? trace(level, P, vcomb(eta, D, vcomb(eta*d-sqrt(e), N, black)))
X	    : black,
X	vcomb(s->ks, trace(level, P, vcomb(2*d, N, D)),
X	    vcomb(s->kd, color, vcomb(s->kl, U, black))));
X}
X
Xmain()
X{
X    printf("%d %d\n", SIZE, SIZE);
X    while (yx<SIZE*SIZE)
X	U.x = yx%SIZE-SIZE/2,
X	U.z = SIZE/2-yx++/SIZE,
X	U.y = SIZE/2/tan(AOV/114.5915590261),	/* 360/PI~=114 */
X	U = vcomb(255., trace(DEPTH, black, vunit(U)), black),
X	printf("%.0f %.0f %.0f\n", U);		/* yowsa! non-portable! */
X}
EOF14163
sed 's/^X//' <<'EOF14164' >ray.h
X/* ray.h for test1, first test scene */
X#define DEPTH 3		/* max ray tree depth */
X#define SIZE 32		/* resolution of picture in x and y */
X#define AOV 25		/* total angle of view in degrees */
X#define NSPHERE 5	/* number of spheres */
X
XAMBIENT = {.02, .02, .02};	/* ambient light color */
X
X/* sphere: x y z  r g b  rad  kd ks kt kl  ir */
XSPHERE = {
X     0., 6., .5,    1., 1., 1.,   .9,   .05, .2, .85, 0.,  1.7,
X    -1., 8., -.5,   1., .5, .2,   1.,   .7, .3, 0., .05,   1.2,
X     1., 8., -.5,   .1, .8, .8,   1.,   .3, .7, 0., 0.,    1.2,
X     3., -6., 15.,  1., .8, 1.,   7.,   0., 0., 0., .6,    1.5,
X    -3., -3., 12.,  .8, 1., 1.,   5.,   0., 0., 0., .5,    1.5,
X};
EOF14164
sed 's/^X//' <<'EOF14165' >paul.squeeze.c
Xtypedef struct{double x,y,z}vec;vec U,black,amb={.02,.02,.02};struct sphere{
Xvec cen,color;double rad,kd,ks,kt,kl,ir}*s,*best,sph[]={0.,6.,.5,1.,1.,1.,.9,
X.05,.2,.85,0.,1.7,-1.,8.,-.5,1.,.5,.2,1.,.7,.3,0.,.05,1.2,1.,8.,-.5,.1,.8,.8,
X1.,.3,.7,0.,0.,1.2,3.,-6.,15.,1.,.8,1.,7.,0.,0.,0.,.6,1.5,-3.,-3.,12.,.8,1.,
X1.,5.,0.,0.,0.,.5,1.5,};yx;double u,b,tmin,sqrt(),tan();double vdot(A,B)vec A
X,B;{return A.x*B.x+A.y*B.y+A.z*B.z;}vec vcomb(a,A,B)double a;vec A,B;{B.x+=a*
XA.x;B.y+=a*A.y;B.z+=a*A.z;return B;}vec vunit(A)vec A;{return vcomb(1./sqrt(
Xvdot(A,A)),A,black);}struct sphere*intersect(P,D)vec P,D;{best=0;tmin=1e30;s=
Xsph+5;while(s-->sph)b=vdot(D,U=vcomb(-1.,P,s->cen)),u=b*b-vdot(U,U)+s->rad*s
X->rad,u=u>0?sqrt(u):1e31,u=b-u>1e-7?b-u:b+u,tmin=u>=1e-7&&u<tmin?best=s,u:
Xtmin;return best;}vec trace(level,P,D)vec P,D;{double d,eta,e;vec N,color;
Xstruct sphere*s,*l;if(!level--)return black;if(s=intersect(P,D));else return
Xamb;color=amb;eta=s->ir;d= -vdot(D,N=vunit(vcomb(-1.,P=vcomb(tmin,D,P),s->cen
X)));if(d<0)N=vcomb(-1.,N,black),eta=1/eta,d= -d;l=sph+5;while(l-->sph)if((e=l
X->kl*vdot(N,U=vunit(vcomb(-1.,P,l->cen))))>0&&intersect(P,U)==l)color=vcomb(e
X,l->color,color);U=s->color;color.x*=U.x;color.y*=U.y;color.z*=U.z;e=1-eta*
Xeta*(1-d*d);return vcomb(s->kt,e>0?trace(level,P,vcomb(eta,D,vcomb(eta*d-sqrt
X(e),N,black))):black,vcomb(s->ks,trace(level,P,vcomb(2*d,N,D)),vcomb(s->kd,
Xcolor,vcomb(s->kl,U,black))));}main(){printf("%d %d\n",32,32);while(yx<32*32)
XU.x=yx%32-32/2,U.z=32/2-yx++/32,U.y=32/2/tan(25/114.5915590261),U=vcomb(255.,
Xtrace(3,black,vunit(U)),black),printf("%.0f %.0f %.0f\n",U);}/*pixar!ph*/
EOF14165
exit