Vec radiance(const Ray &r, int depth, unsigned short *Xi) {
double t; // distance to intersection
int id = 0; // id of intersected object
if(!intersect(r, t, id)) return Vec(); // if miss, return black
const Sphere &obj = spheres[id]; // the hit object
Vec x = r.o + r.d*t, n = (x - obj.p).norm(), nl = n.dot(r.d) < 0 ? n : n*-1, f = obj.c;
double p = f.x > f.y && f.x>f.z ? f.x : f.y > f.z ? f.y : f.z; // max refl
if(depth > 255) return obj.e;
if(++depth > 5) if(erand48(Xi) < p) f = f*(1 / p); else return obj.e; //R.R.
if(obj.refl == DIFF) { // Ideal DIFFUSE reflection
double r1 = 2 * M_PI*erand48(Xi), r2 = erand48(Xi), r2s = sqrt(r2);
Vec w = nl, u = ((fabs(w.x) > .1 ? Vec(0, 1) : Vec(1)) % w).norm(), v = w%u;
Vec d = (u*cos(r1)*r2s + v*sin(r1)*r2s + w*sqrt(1 - r2)).norm();
return obj.e + f.mult(radiance(Ray(x, d), depth, Xi));
}
else if(obj.refl == SPEC) // Ideal SPECULAR reflection
return obj.e + f.mult(radiance(Ray(x, r.d - n * 2 * n.dot(r.d)), depth, Xi));
Ray reflRay(x, r.d - n * 2 * n.dot(r.d)); // Ideal dielectric REFRACTION
bool into = n.dot(nl) > 0; // Ray from outside going in?
double nc = 1, nt = 1.5, nnt = into ? nc / nt : nt / nc, ddn = r.d.dot(nl), cos2t;
if((cos2t = 1 - nnt*nnt*(1 - ddn*ddn)) < 0) // Total internal reflection
return obj.e + f.mult(radiance(reflRay, depth, Xi));
Vec tdir = (r.d*nnt - n*((into ? 1 : -1)*(ddn*nnt + sqrt(cos2t)))).norm();
double a = nt - nc, b = nt + nc, R0 = a*a / (b*b), c = 1 - (into ? -ddn : tdir.dot(n));
double Re = R0 + (1 - R0)*c*c*c*c*c, Tr = 1 - Re, P = .25 + .5*Re, RP = Re / P, TP = Tr / (1 - P);
return obj.e + f.mult(depth > 2 ? (erand48(Xi) < P ? // Russian roulette
radiance(reflRay, depth, Xi)*RP : radiance(Ray(x, tdir), depth, Xi)*TP) :
radiance(reflRay, depth, Xi)*Re + radiance(Ray(x, tdir), depth, Xi)*Tr);
}
Vec radiance(const Ray &r, int depth, unsigned short *Xi,int E=1){
double t; // distance to intersection
int id=0; // id of intersected object
if (!intersect(r, t, id)) return Vec(); // if miss, return black
const Sphere &obj = spheres[id]; // the hit object
Vec x=r.o+r.d*t, n=(x-obj.p).norm(), nl=n.dot(r.d)<0?n:n*-1, f=obj.c;
double p = f.x>f.y && f.x>f.z ? f.x : f.y>f.z ? f.y : f.z; // max refl
if (++depth>5||!p) if (erand48(Xi)<p) f=f*(1/p); else return obj.e*E;
if (obj.refl == DIFF){ // Ideal DIFFUSE reflection
double r1=2*M_PI*erand48(Xi), r2=erand48(Xi), r2s=sqrt(r2);
Vec w=nl, u=((fabs(w.x)>.1?Vec(0,1):Vec(1))%w).norm(), v=w%u;
Vec d = (u*cos(r1)*r2s + v*sin(r1)*r2s + w*sqrt(1-r2)).norm();
// Loop over any lights
Vec e;
for (int i=0; i<numSpheres; i++){
const Sphere &s = spheres[i];
if (s.e.x<=0 && s.e.y<=0 && s.e.z<=0) continue; // skip non-lights
Vec sw=s.p-x, su=((fabs(sw.x)>.1?Vec(0,1):Vec(1))%sw).norm(), sv=sw%su;
double cos_a_max = sqrt(1-s.rad*s.rad/(x-s.p).dot(x-s.p));
double eps1 = erand48(Xi), eps2 = erand48(Xi);
double cos_a = 1-eps1+eps1*cos_a_max;
double sin_a = sqrt(1-cos_a*cos_a);
double phi = 2*M_PI*eps2;
Vec l = su*cos(phi)*sin_a + sv*sin(phi)*sin_a + sw*cos_a;
l.norm();
if (intersect(Ray(x,l), t, id) && id==i){ // shadow ray
double omega = 2*M_PI*(1-cos_a_max);
e = e + f.mult(s.e*l.dot(nl)*omega)*M_1_PI; // 1/pi for brdf
}
}
return obj.e*E+e+f.mult(radiance(Ray(x,d),depth,Xi,0));
} else if (obj.refl == SPEC) // Ideal SPECULAR reflection
return obj.e + f.mult(radiance(Ray(x,r.d-n*2*n.dot(r.d)),depth,Xi));
Ray reflRay(x, r.d-n*2*n.dot(r.d)); // Ideal dielectric REFRACTION
bool into = n.dot(nl)>0; // Ray from outside going in?
double nc=1, nt=1.5, nnt=into?nc/nt:nt/nc, ddn=r.d.dot(nl), cos2t;
if ((cos2t=1-nnt*nnt*(1-ddn*ddn))<0) // Total internal reflection
return obj.e + f.mult(radiance(reflRay,depth,Xi));
Vec tdir = (r.d*nnt - n*((into?1:-1)*(ddn*nnt+sqrt(cos2t)))).norm();
double a=nt-nc, b=nt+nc, R0=a*a/(b*b), c = 1-(into?-ddn:tdir.dot(n));
double Re=R0+(1-R0)*c*c*c*c*c,Tr=1-Re,P=.25+.5*Re,RP=Re/P,TP=Tr/(1-P);
return obj.e + f.mult(depth>2 ? (erand48(Xi)<P ? // Russian roulette
radiance(reflRay,depth,Xi)*RP:radiance(Ray(x,tdir),depth,Xi)*TP) :
radiance(reflRay,depth,Xi)*Re+radiance(Ray(x,tdir),depth,Xi)*Tr);
}
Vec radiance(const Ray &ray, int depth, unsigned short *Xi) {
float t; // distance to intersection
int id; // id of intersected object
Ray r=ray;
// L0 = Le0 + f0*(L1)
// = Le0 + f0*(Le1 + f1*L2)
// = Le0 + f0*(Le1 + f1*(Le2 + f2*(L3))
// = Le0 + f0*(Le1 + f1*(Le2 + f2*(Le3 + f3*(L4)))
// = ...
// = Le0 + f0*Le1 + f0*f1*Le2 + f0*f1*f2*Le3 + f0*f1*f2*f3*Le4 + ...
//
// So:
// F = 1
// while (1) {
// L += F*Lei
// F *= fi
// }
// accumulated color
Vec cl(0,0,0);
// accumulated reflectance
Vec cf(1,1,1);
while (1) {
// if miss, return accumulated color (black)
if (!intersect(r, t, id)) return cl;
// the hit object
const Solid &obj = *scene[id];
// calculate intersection point
Vec x=r.o+r.d*t;
// calculate surface normal vector in point x
Vec n=obj.normal(x);
Vec nl=n*r.d<0 ? n : n*-1;
// object base color
Vec f=obj.c;
float p = f.x>f.y && f.x>f.z ? f.x : f.y>f.z ? f.y : f.z; // max refl
cl = cl + cf.mult(obj.e);
if (++depth>5) {
if (erand48(Xi)<p) f=f*(1/p); else return cl;
} // R.R.
cf = cf.mult(f);
if (obj.refl == DIFF) { // Ideal DIFFUSE reflection
float r1=2*M_PI*erand48(Xi), r2=erand48(Xi), r2s=sqrt(r2);
Vec w=nl, u=((fabs(w.x)>.1 ? Vec(0,1) : Vec(1))%w).norm(), v=w%u;
Vec d = (u*cos(r1)*r2s+v*sin(r1)*r2s+w*sqrt(1-r2)).norm();
//return obj.e + f.mult(radiance(Ray(x,d), depth, Xi));
r = Ray(x, d);
continue;
} else if (obj.refl == SPEC) { // Ideal SPECULAR reflection
//return obj.e + f.mult(radiance(Ray(x,r.d-n*2*(n*r.d)), depth, Xi));
r = Ray(x, r.d-n*2*(n*r.d));
continue;
}
// Ideal dielectric REFRACTION
Ray reflRay(x, r.d-n*2*(n*r.d));
bool into = n*nl>0; // Ray from outside going in?
float nc=1, nt=1.5, nnt=into ? nc/nt : nt/nc, ddn=r.d*nl, cos2t;
if ((cos2t=1-nnt*nnt*(1-ddn*ddn))<0) { // Total internal reflection
//return obj.e + f.mult(radiance(reflRay, depth, Xi));
r = reflRay;
continue;
}
Vec tdir = (r.d*nnt-n*((into?1:-1)*(ddn*nnt+sqrt(cos2t)))).norm();
float a=nt-nc, b=nt+nc, R0=a*a/(b*b), c=1-(into?-ddn:tdir*n);
float Re=R0+(1-R0)*c*c*c*c*c, Tr=1-Re, P=.25+.5*Re, RP=Re/P, TP=Tr/(1-P);
//return obj.e + f.mult(depth>2 ? // Russian roulette
// (erand48(Xi)<P ? radiance(reflRay, depth, Xi)*RP : radiance(Ray(x,tdir), depth, Xi)*TP) :
// (radiance(reflRay, depth, Xi)*Re + radiance(Ray(x,tdir), depth, Xi)*Tr) );
if (erand48(Xi)<P) {
cf = cf*RP;
r = reflRay;
} else {
cf = cf*TP;
r = Ray(x,tdir);
}
continue;
}
/*
float t; // distance to intersection
int id; // id of intersected object
//fprintf(stderr, "r=(%f,%f,%f):(%f,%f,%f)\n", r.o.x, r.o.y, r.o.z, r.d.x, r.d.y, r.d.z);
// if miss, return black
if (!intersect(r, t, id)) return Vec();
// fprintf(stderr, "id=%d, t=%25.25f\n", id, t);
// the hit object
Solid& obj = *scene[id];
// calculate intersection point
Vec x=r.o+r.d*t;
// calculate surface normal vector in point x
Vec n=obj.normal(x);
Vec nl=n*r.d<0 ? n : n*-1;
// object base color
Vec f=obj.c;
float p = f.x>f.y && f.x>f.z ? f.x : f.y>f.z ? f.y : f.z; // max refl
if (++depth>5) {
if (erand48(Xi)<p) f=f*(1/p); else return obj.e;
} // R.R.
if (obj.refl == DIFF) { // Ideal DIFFUSE reflection
float r1=2*M_PI*erand48(Xi), r2=erand48(Xi), r2s=sqrt(r2);
Vec w=nl, u=((fabs(w.x)>.1 ? Vec(0,1) : Vec(1))%w).norm(), v=w%u;
Vec d = (u*cos(r1)*r2s+v*sin(r1)*r2s+w*sqrt(1-r2)).norm();
return obj.e + f.mult(radiance(Ray(x,d), depth, Xi));
} else if (obj.refl == SPEC) { // Ideal SPECULAR reflection
return obj.e + f.mult(radiance(Ray(x,r.d-n*2*(n*r.d)), depth, Xi));
}
// Ideal dielectric REFRACTION
Ray reflRay(x, r.d-n*2*(n*r.d));
bool into = n*nl>0; // Ray from outside going in?
float nc=1, nt=1.5, nnt=into ? nc/nt : nt/nc, ddn=r.d*nl, cos2t;
if ((cos2t=1-nnt*nnt*(1-ddn*ddn))<0) // Total internal reflection
return obj.e + f.mult(radiance(reflRay, depth, Xi));
Vec tdir = (r.d*nnt-n*((into?1:-1)*(ddn*nnt+sqrt(cos2t)))).norm();
float a=nt-nc, b=nt+nc, R0=a*a/(b*b), c=1-(into?-ddn:tdir*n);
float Re=R0+(1-R0)*c*c*c*c*c, Tr=1-Re, P=.25+.5*Re, RP=Re/P, TP=Tr/(1-P);
return obj.e + f.mult(depth>2 ? // Russian roulette
(erand48(Xi)<P ? radiance(reflRay, depth, Xi)*RP : radiance(Ray(x,tdir), depth, Xi)*TP) :
(radiance(reflRay, depth, Xi)*Re + radiance(Ray(x,tdir), depth, Xi)*Tr) );
*/
}
