// sphere flake bvh raytracer (c) 2005, thierry berger-perrin <tbptbp@gmail.com>
// this code is released under the GNU Public License.
#include <cmath>       // see http://ompf.org/ray/sphereflake/
#include <iostream>    // compile with ie g++ -O2 -ffast-math sphereflake.cc
#define GIMME_SHADOWS  // usage: ./sphereflake [lvl=6] >pix.ppm
enum { childs = 9, ss= 2, ss_sqr = ss*ss }; /* not really tweakable anymore */
static const double infinity = 1./0, epsilon = 1e-12;
struct v_t{ double x,y,z;v_t(){}
 v_t(const double a,const double b,const double c):x(a),y(b),z(c){}
 v_t operator+(const v_t&v)const{return v_t(x+v.x,y+v.y,z+v.z);}
 v_t operator-(const v_t&v)const{return v_t(x-v.x,y-v.y,z-v.z);}
 v_t operator-()const{return v_t(-x,-y,-z);}
 v_t operator*(const double d)const{return v_t(x*d,y*d,z*d);}
 v_t cross(const v_t&v)const{return v_t(y*v.z-z*v.y,z*v.x-x*v.z,x*v.y-y*v.x);}
 v_t norm()const{return*this*(1./sqrt(magsqr()));}
 double dot(const v_t&v)const{return x*v.x+y*v.y+z*v.z;}
 double magsqr()const{return dot(*this);} };
//static const v_t light(v_t(0.5,-.95,1.775).norm()); /*pick one*/
static const v_t light(v_t(-0.5,-.65,.9).norm()); /*fiat lux*/
struct ray_t{ v_t o,d;ray_t(const v_t&v):o(v){}
 ray_t(const v_t&v,const v_t&w):o(v),d(w){} };
struct hit_t { v_t n;double t;hit_t():n(v_t(0,0,0)),t(infinity){} };
struct sphere_t{ v_t o;double r; sphere_t(){}
 sphere_t(const v_t&v,double d):o(v),r(d){}
 v_t get_normal(const v_t&v)const{return(v-o)*(1./r);}
 double intersect(const ray_t&ray)const{
  const v_t v(o-ray.o); const double b=ray.d.dot(v),disc=b*b-v.magsqr()+r*r;
  if(disc < 0.) return infinity; /*branch away from the square root*/
  const double d=sqrt(disc), t2=b+d, t1=b-d; /*cond. move*/
  if(t2 < 0.) return infinity; else return(t1 > 0.? t1 : t2); } };
struct node_t; static node_t *pool=0, *end=0;
struct node_t { /*a bvh in array form+skip for navigation.*/
 sphere_t bound,leaf;long diff;/*far from optimal*/
 node_t(){} node_t(const sphere_t&b,const sphere_t&l,const long jump)
  :bound(b),leaf(l),diff(jump){}
 template<bool shadow> static void intersect(const ray_t &ray,hit_t &hit){
  const node_t*p=pool;
  while(p < end) {
   if(p->bound.intersect(ray)>=hit.t) /*missed bound*/
    p+=p->diff; /*skip subtree*/
   else{ const double t=p->leaf.intersect(ray);
    if(t < hit.t) { /*if hit, update, then break for shadows*/
     hit.t=t; if(shadow) break; hit.n=p->leaf.get_normal(ray.o+ray.d*t);
    } ++p; /*next!*/ }}}};
static double ray_trace(const node_t*const scene,const ray_t&ray){
 hit_t hit; scene->intersect<false>(ray,hit);// trace primary
 const double diffuse = hit.t==infinity ? 0. : -hit.n.dot(light);
 #ifdef GIMME_SHADOWS
  if (diffuse <= 0.) return 0.;
  const ray_t sray(ray.o+(ray.d*hit.t)+(hit.n*epsilon),-light);
  hit_t shit; scene->intersect<true>(sray,shit);// trace shadow
  return shit.t==infinity ? diffuse : 0.;
 #else
  return diffuse > 0. ? diffuse : 0.;
 #endif
} static const double grid[ss_sqr][2]={ /*our rotated grid*/
 {-3/3.,-1/3.},{+1/3.,-3/3.}, {-1/3.,+3/3.},{+3/3.,+1/3.} };
static void trace_rgss(const int width,const int height){
 const double w=width,h=height,rcp=1/double(ss),scale=256./double(ss_sqr);
 ray_t ray(v_t(0,0,-4.5)); /* eye, looking into Z */ v_t rgss[ss_sqr];
 for(int i=0;i<ss_sqr;++i) /*precomp.*/
  rgss[i]=v_t(grid[i][0]*rcp-w/2.,grid[i][1]*rcp-h/2.,0);
 v_t scan(0,w-1,std::max(w,h)); /*scan line*/
 for(int i=height;i;--i){ for(int j=width;j;--j){ double g=0;
   for(int idx=0;idx < ss_sqr;++idx){ /*AA*/
    ray.d=(scan+rgss[idx]).norm(); g+=ray_trace(pool,ray); /*trace*/ }
   std::cout << int(scale*g)<< " ";
 scan.x+=1; /*next pixel*/ } scan.x=0;scan.y-=1; /*next line*/ }
 std::cout << std::endl; }
struct basis_t{ /* bogus and compact, exactly what we need */
 v_t up,b1,b2; basis_t(const v_t&v){ const v_t n(v.norm());
 if((n.x*n.x !=1.)&(n.y*n.y !=1.)&(n.z*n.z !=1.)){/*cough*/
 b1=n; if(n.y*n.y>n.x*n.x){ if(n.y*n.y>n.z*n.z)b1.y=-b1.y; else b1.z=-b1.z; }
 else if(n.z*n.z > n.x*n.x)b1.z=-b1.z; else b1.x=-b1.x; }
 else b1=v_t(n.z,n.x,n.y);/*leaves some cases out,dodge them*/
 up=n; b2=up.cross(b1); b1=up.cross(b2); } };
static node_t*create(node_t*n,const int lvl,int dist,v_t c,v_t d,double r){
 n = 1 + new (n) node_t(sphere_t(c,2.*r),sphere_t(c,r), lvl > 1 ? dist : 1);
 if (lvl <= 1) return n; /*if not at the bottom, recurse a bit more*/
 dist=std::max((dist-childs)/childs,1); const basis_t b(d); 
 const double nr=r*1/3.,daL=2.*M_PI/6.,daU=2.*M_PI/3.; double a=0;
 for(int i=0;i<6;++i){ /*lower ring*/
  const v_t ndir((d*-.2+b.b1*sin(a)+b.b2*cos(a)).norm()); /*transcendentals?!*/
  n=create(n,lvl-1,dist,c+ndir*(r+nr),ndir,nr); a+=daL; } a-=daL/3.;/*tweak*/
 for(int i=0;i<3;++i){ /*upper ring*/
  const v_t ndir((d*+.6+b.b1*sin(a)+b.b2*cos(a)).norm());
  n=create(n,lvl-1,dist,c+ndir*(r+nr),ndir,nr); a+=daU; }
 return n; }
int main(int argc,char*argv[]){
 enum{ w = 1024, h = w }; /* resolution */
 const int lvl=(argc==2?std::max(atoi(argv[1]),2):6);
 int count=childs,dec=lvl;while(--dec > 1) count=(count*childs)+childs;++count;
 std::cerr<<count<<" spheres,claiming "<<(count*sizeof(node_t))/(1024.*1024)
  <<" MB."<<std::endl;
 pool=new node_t[count];end=pool+count; /* raw */
 create(pool,lvl,count,v_t(0,0,0),v_t(+.25,+1,-.5).norm(),1.); /* cooked */
 std::cout << "P2\n" << w << " " << h << "\n256\n";
 trace_rgss(w,h);return 0; /* served */
}