//alg for calculating shading. Calls diffuseShade and SpecularShade
Color RT_lights(Figure* obj, const Ray& ray, const Vec& thePoint, const Vec& normal)
{
Color c = Color();
for (list<Light*>::iterator iterator = lightList.begin(), end = lightList.end(); iterator != end; ++iterator) {
Light* theLight = *iterator;
pair<double, Figure*> inter = nearestIntersection(Ray(Vec(thePoint), theLight->getPos()), MIN_T / SHAD_RES, 1.0, EPSILON, false);
if (inter.first <= 0) {
Vec* toLight = thePoint.normalize(theLight->getPos());
double dotProduct = toLight->dot(normal);
Vec* subt = (thePoint.sub(theLight->getPos()));
double dist = abs(subt->getMag());
Color dif = diffuseShade(obj, theLight, max(dotProduct, 0.0), dist);
Vec* Q = normal.scale(normal.dot(*toLight));
Vec* S = Q->sub(*toLight);
Vec* S2 = S->scale(2.0);
Vec* R = toLight->add(*S2);
Vec* norm = ray.getNorm();
Vec* scaledNorm = norm->scale(-1.0);
dotProduct = max(0.0, R->dot(*scaledNorm));
Color spec = specularShade(obj, normal, theLight, *toLight, pow(dotProduct, obj->getShininess()), ray, dist);
c = c.add(dif.add(spec));
delete(toLight);
delete(Q);
delete(S);
delete(R);
delete(S2);
delete(subt);
delete(norm);
delete(scaledNorm);
}
}
return c;
}
inline double bssrdf(const Vec& xi, const Vec& ni, const Vec& wi, const Vec& xo, const Vec& no, const Vec& wo, const int j) {
// distance
const Vec xoxi = xo - xi;
const double r = xoxi.len();
// modified normal
const Vec ni_s = (xoxi.normalized()) % ((ni % xoxi).normalized());
// directions of ray sources
const double nnt = 1.0 / eta, ddn = -wi.dot(ni);
const Vec wr = (wi * -nnt - ni * (ddn * nnt + sqrt(1.0 - nnt * nnt * (1.0 - ddn * ddn)))).normalized();
const Vec wv = wr - ni_s * (2.0 * wr.dot(ni_s));
// distance to real sources
const double cos_beta = -sqrt((r * r - xoxi.dot(wr) * xoxi.dot(wr)) / (r * r + de[j] * de[j]));
double dr;
const double mu0 = -no.dot(wr);
if (mu0 > 0.0) {
dr = sqrt((D[j] * mu0) * ((D[j] * mu0) - de[j] * cos_beta * 2.0) + r * r);
} else {
dr = sqrt(1.0 / (3.0 * sigma_t[j] * 3.0 * sigma_t[j]) + r * r);
}
// distance to virtual source
const Vec xoxv = xo - (xi + ni_s * (2.0 * A * de[j]));
const double dv = xoxv.len();
// BSSRDF
const double result = Sp_d(xoxi, wr, dr, no, j) - Sp_d(xoxv, wv, dv, no, j);
// clamping to zero
return (result < 0.0) ? 0.0 : result;
}
double intersect(const Ray &r) const { // returns distance, 0 if nohit
Vec op = p - r.o; // Solve t^2*d.d + 2*t*(o-p).d + (o-p).(o-p)-R^2 = 0
double t, eps = 1e-4, b = op.dot(r.d),
det = b * b - op.dot(op) + rad * rad;
if (det < 0)
return 0;
else
det = sqrt(det);
return (t = b - det) > eps ? t : ((t = b + det) > eps ? t : 0);
}
inline double intersect(const Ray& r) const {
// ray-sphere intersection returns the distance
const Vec op = p - r.o;
double t, b = op.dot(r.d), det = b * b - op.dot(op) + rad * rad;
if (det < 0) {
return 1e20;
}
else {
det = sqrt(det);
}
return (t = b - det) > 1e-4 ? t : ((t = b + det) > 1e-4 ? t : 1e20);
}
// directional dipole
// --------------------------------
inline double Sp_d(const Vec& x, const Vec& w, const double& r, const Vec& n, const int j) {
// evaluate the profile
const double s_tr_r = sigma_tr[j] * r;
const double s_tr_r_one = 1.0 + s_tr_r;
const double x_dot_w = x.dot(w);
const double r_sqr = r * r;
const double t0 = Cp_norm * (1.0 / (4.0 * PI * PI)) * exp(-s_tr_r) / (r * r_sqr);
const double t1 = r_sqr / D[j] + 3.0 * s_tr_r_one * x_dot_w;
const double t2 = 3.0 * D[j] * s_tr_r_one * w.dot(n);
const double t3 = (s_tr_r_one + 3.0 * D[j] * (3.0 * s_tr_r_one + s_tr_r * s_tr_r) / r_sqr * x_dot_w) * x.dot(n);
return t0 * (Cp * t1 - Ce * (t2 - t3));
}
Number Sphere::do_intersect(const Vec & start_p, const Vec & dir) const {
Vec p = start_p - center;
Vec x = (-dir.dot(p)) * dir;
Vec y = p + x;
auto y_norm = y.norm();
if(y_norm > radius)
return -1;
auto x_dot = x.dot(dir);
auto s = std::sqrt(radius * radius - y_norm * y_norm);
auto t_norm = x_dot - s;
if(t_norm < 0)
t_norm += 2 * s;
return t_norm; // may < 0, which means no intersection
}
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 receivedRadiance(const Ray &r, int depth, bool flag) {
double t; // Distance to intersection
int id = 0; // id of intersected sphere
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; // The intersection point
Vec o = (Vec() - r.d).normalize(); // The outgoing direction (= -r.d)
Vec n = (x - obj.p).normalize(); // The normal direction
if ( n.dot(o) < 0 ) n = n*-1.0;
/*
Tips
1. Other useful quantities/variables:
Vec Le = obj.e; // Emitted radiance
const BRDF &brdf = obj.brdf; // Surface BRDF at x
2. Call brdf.sample() to sample an incoming direction and continue the recursion
*/
Vec Le = obj.e; // Emitted radiance
const BRDF &brdf = obj.brdf; // Surface BRDF at x
const int rrDepth = 5;
const double survivalProbability = 0.9;
double p = 1.0;
if (depth > rrDepth)
p = survivalProbability;
if (rng() < p)
{
Vec o_i;
double pdf;
brdf.sample(n, o, o_i, pdf);
Ray y(x, o_i.normalize());
Vec reflected = receivedRadiance(y, depth + 1, false)
.mult(brdf.eval(n, o, o_i))
* (n.dot(o_i)
/ (pdf*p));
return Le + reflected;
}
return Le;
}
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);
}
int main() {
double y_vals[] = {-1.5, 2, -2.5};
double z_vals[] = {3, -2, 1};
Vec<double> zeroes(3); // Vec size 3 (entries initialize to zero)
Vec<double> x = Vec<double>::constantVec(3, 2.5); // Vec size 3 with all entries set to 2.5
Vec<double> y = Vec<double>(y_vals, 3);
Vec<double> z(3);
z.setEntries(z_vals, 3);
Vec<int> ix(x);
cout << "zeroes = " << zeroes << endl;
cout << "x = " << x << endl;
cout << "y = " << y << endl;
cout << "z = " << z << endl;
cout << "ix = " << ix << endl;
cout << "z[0] = " << z[0] << ", z[1] = " << z[1] << ", z[2] = " << z[2] << endl;
cout << "3.5 * x = " << (3.5 * x) << endl;
cout << "x / 3.5 = " << (x / 3.5) << endl;
cout << "x + y = " << (x + y) << endl;
cout << "x - y = " << (x - y) << endl;
cout << "x.concatenate(y) = " << x.concatenate(y) << endl;
cout << "x.dot(y) = " << x.dot(y) << endl;
cout << "x.cross(y) = " << x.cross(y) << endl;
cout << "x.norm() = " << x.norm() << endl;
cout << "x.unit_vector() = " << x.unit_vector() << endl;
cout << "ix.norm() = " << ix.norm() << endl;
cout << "ix.norm<double>() = " << ix.norm<double>() << endl;
cout << "ix.unit_vector<double>() = " << ix.unit_vector<double>() << endl;
cout << "scalar_triple_product(x, y, z) = "
<< Vec<double>::scalar_triple_product(x, y, z) << endl;
cout << "vector_triple_product(x, y, z) = "
<< Vec<double>::vector_triple_product(x, y, z) << endl;
}
bool UVSphere::intersect(const Ray& r, float tmin, float tmax, float time, HitRecord& record)const{
Vec temp = r.origin() - center;
float a = r.direction().dot(r.direction());
float b = 2 * r.direction().dot(temp);
float c = temp.dot(temp) - radius * radius;
float discriminant = b*b - 4*a*c;
if(discriminant > 0){
discriminant = sqrt(discriminant);
float t = (-b -discriminant) /(2*a);
if(t < tmin) t = (-b + discriminant) / (2*a);
if(t < tmin || t > tmax) return false;
record.t = t;
record.hit_p = r.origin() + r.direction() * t;
record.reflect = reflectionCoef;
record.transparency = refractionCoef;
Vec n = record.normal = normalize(r.origin() + r.direction()*t - center);
//calculate UV coordinates
float theta = acos(n.y);
float phi = atan2(n.z, n.x);
if(phi < 0) phi += M_PI * 2;
record.uv = Vec(phi/(2* M_PI), (M_PI - theta)/M_PI, 0);
record.hit_tex = tex;
return true;
}
return false;
}
//----------------------------------------------------------------------
void BLCSSS::rwm_draw_chunk(int chunk){
clock_t start = clock();
const Selector &inc(m_->coef().inc());
int nvars = inc.nvars();
Vec full_nonzero_beta = m_->beta(); // only nonzero components
// Compute information matrix for proposal distribution. For
// efficiency, also compute the log-posterior of the current beta.
Vec mu(inc.select(pri_->mu()));
Spd siginv(inc.select(pri_->siginv()));
double original_logpost = dmvn(full_nonzero_beta, mu, siginv, 0, true);
const std::vector<Ptr<BinomialRegressionData> > &data(m_->dat());
int nobs = data.size();
int full_chunk_size = compute_chunk_size();
int chunk_start = chunk * full_chunk_size;
int elements_remaining = nvars - chunk_start;
int this_chunk_size = std::min(elements_remaining, full_chunk_size);
Selector chunk_selector(nvars, false);
for(int i = chunk_start; i< chunk_start + this_chunk_size; ++i) {
chunk_selector.add(i);
}
Spd proposal_ivar = chunk_selector.select(siginv);
for(int i = 0; i < nobs; ++i){
Vec x = inc.select(data[i]->x());
double eta = x.dot(full_nonzero_beta);
double prob = plogis(eta);
double weight = prob * (1-prob);
VectorView x_chunk(x, chunk_start, this_chunk_size);
// Only upper triangle is accessed. Need to reflect at end of loop.
proposal_ivar.add_outer(x_chunk, weight, false);
int yi = data[i]->y();
int ni = data[i]->n();
original_logpost += dbinom(yi, ni, prob, true);
}
proposal_ivar.reflect();
VectorView beta_chunk(full_nonzero_beta, chunk_start, this_chunk_size);
if(tdf_ > 0){
beta_chunk = rmvt_ivar_mt(
rng(), beta_chunk, proposal_ivar / rwm_variance_scale_factor_, tdf_);
}else{
beta_chunk = rmvn_ivar_mt(
rng(), beta_chunk, proposal_ivar / rwm_variance_scale_factor_);
}
double logpost = dmvn(full_nonzero_beta, mu, siginv, 0, true);
Vec full_beta(inc.expand(full_nonzero_beta));
logpost += m_->log_likelihood(full_beta, 0, 0, false);
double log_alpha = logpost - original_logpost;
double logu = log(runif_mt(rng()));
++rwm_chunk_attempts_;
if(logu < log_alpha){
m_->set_beta(full_nonzero_beta);
++rwm_chunk_successes_;
}
clock_t end = clock();
rwm_chunk_times_ += double(end - start) / CLOCKS_PER_SEC;
}
/** Cast reflected ray
** @param ray incoming ray
** @param pt intersection point
** @param normal normal of pt
** @return reflected ray
**/
Ray reflect(Ray ray, Vec pt, Vec normal){
Vec v = ray.getOrig() - pt; v = v.normalize();
Vec dir = normal * (2 * v.dot(normal)) - v; dir = dir.normalize(); // reflected direction
Ray t(pt, dir, 0, 9999, ReflectedRay);
if (debugMode) {
printf("reflected ray: origin = "); t.getOrig().print();
printf("reflected ray: direction = "); t.getDir().print();
}
return t;
}
void HardSpherePressureTracker::update_collision(Box &box, AtomID a1, AtomID a2,
flt time, Vec delta_p) {
if (isnan(t0)) {
t0 = time;
lastt = t0;
return;
}
Vec dr = box.diff(a1->x, a2->x);
collisionsum += dr.dot(delta_p);
Ksum += kinetic_energy_com(*atoms);
Ncollisions++;
lastt = time;
};
/// Kinetic energy relative to center of mass
// K = ½Σmᵢvᵢ² - ½(Σmᵢvᵢ)² / (Σmᵢ)
flt kinetic_energy_com(AtomGroup &atoms) {
flt Ksum = 0;
Vec mvsum = Vec::Zero();
flt msum = 0;
for (uint i = 0; i < atoms.size(); i++) {
Atom &a = atoms[i];
Vec mv = a.m * a.v;
Ksum += mv.dot(a.v);
mvsum += mv;
msum += a.m;
}
return (Ksum - mvsum.squaredNorm() / msum) / 2;
};
void uniformRandom(const Vec &normal, Vec &i, double &pdf) {
double z = std::sqrt(rng());
double r = std::sqrt(1.0 - z * z);
double phi = 2.0 * PI * rng();
double x = r * std::cos(phi);
double y = r * std::sin(phi);
Vec u, v, w;
createLocalCoord(normal, u, v, w);
i = (u * x) + (v *y) + (w*z);
pdf = normal.dot(i)/ PI;
}
/** Cast transmitted ray
** @param ray incoming ray
** @param pt intersection point
** @param normal normal of pt
** @param ior2 index of refraction of the object
** @return transmitted ray
**/
Ray transmit(Ray ray, Vec pt, Vec normal, float ior1, float ior2){
Vec r = ray.getDir();
float alpha = ior1 / ior2;
float c1 = normal.dot(r) * -1;
float c2 = sqrt(1 - pow(alpha,2) * (1 - pow(c1,2)));
Vec v = r * alpha + normal * (c1 * alpha - c2);
Ray t(pt, v, 0, 9999, TransmittedRay);
if (debugMode) {
printf("transmitted ray origin: "); t.getOrig().print();
printf("transmitted ray direction: "); t.getDir().print();
}
return t;
}
/** Texture mapping for spheres
** @param pt intersection point
** @param n normal at pt
** @param p pigment of the object
** @return the color of pt at texture coordinate
**/
Vec sphereMapping(Vec pt, Vec n, Pigment p){
Vec vn = scene.up; // unit-length vector from the center to the north pole
Vec tmp[3] = {Vec(1.0, 0.0, 0.0), Vec(0.0, 1.0, 0.0), Vec(0.0, 0.0, 1.0)};
Vec ve; // unit-length vector from the center to a point on the equator
for (int i = 0; i<3; i++) {
if (tmp[i].dot(vn) == 0) { ve = tmp[i]; break; }
}
Vec vp = n; // unit-length vector from the center to intersection point
int s, t;
float u, v, theta, phi;
phi = acos(vn.dot(vp) * -1);
v = phi / PI;
theta = (acos(vp.dot(ve) / sin(phi))) / (2*PI);
if ((vn.cross(ve)).dot(vp) > 0) u = theta;
else u = 1 - theta;
// find the color of pt at texture cooridnates
s = (int)p.image.width * u;
t = (int)p.image.height * v;
if ((s < p.image.width && s >= 0) && (t < p.image.height && t >= 0))
return p.image.textures[s][t];
else return background;
}
double VarRTM::PredictAUC(RTMC &m, Mat &z_bar) {
VReal real,pre;
for (int d = 0; d < held_out_net_.cols(); d++) {
for (SpMatInIt it(held_out_net_, d); it; ++it) {
double label = it.value();
Vec pi = z_bar.col(d).cwiseProduct(z_bar.col(it.index()));
double prob = Sigmoid(pi.dot(m.eta));
real.push_back(label);
pre.push_back(prob);
}
}
return AUC(real,pre);
}
double logit_loglike_1(const Vec & beta, bool y, const Vec &x,
Vec *g, Mat *h, double mix_wgt){
double eta = x.dot(beta);
double lognc = lse2(0, eta);
double ans = y? eta : 0;
ans -= lognc;
if(g){
double p = exp(eta-lognc);
g->axpy(x, mix_wgt* (y-p));
if(h){
double q = 1-p;
h->add_outer( x,x, -mix_wgt * p*q);}}
return mix_wgt * ans;
}
void dot()
{
const U size = Vec::SIZE;
using T = typename Vec::Scalar;
T res = 0;
Vec vec;
for(U i = 0; i < size; i++)
{
T x = i * 666 + 1;
vec[i] = x;
res += x * x;
}
ANKI_TEST_EXPECT_EQ(vec.dot(vec), res);
}
bool UVSphere::isIntersect(const Ray& r, float tmin, float tmax, float time)const{
Vec temp = r.origin() - center;
float a = r.direction().dot(r.direction());
float b = 2 * r.direction().dot(temp);
float c = temp.dot(temp) - radius * radius;
float discriminant = b*b - 4*a*c;
if(discriminant > 0){
discriminant = sqrt(discriminant);
float t = (-b -discriminant) /(2*a);
if(t < tmin) t = (-b + discriminant) / (2*a);
if(t < tmin || t > tmax) return false;
return true;
}
return false;
}
//calctulates refractions. Recursively calls RT_Trace
Color RT_transmit(Figure* obj, const Ray& ray, const Vec& i, const Vec& normal,
bool inside, double depth)
{
Color returnColor = Color(0, 0, 0);
if (obj->isT()) {
double ratio = 0;
Ray transmittedRay = Ray();
double dir = 1.0;
if (!inside) {
ratio = SPACE_INDEX / obj->getIOR();
}
else {
ratio = obj->getIOR() / SPACE_INDEX;
dir = -1.0;
}
Vec* norm = normal.scale(dir);
Vec* V = ray.getV2().normalize(ray.getV1());
double dp = norm->dot(*V);
double rsqrd = pow(ratio, 2.0);
double coeff = (ratio * dp) - pow(((1 - rsqrd) + (rsqrd * pow(dp, 2.0))), 0.5);
Vec* scaledN = norm->scale(coeff);
Vec* rV = V->scale(ratio);
Vec* T = scaledN->sub(*rV);
Vec* dest = i.add(*T);
Vec* iCopy = new Vec(i);
Ray* tranRay = new Ray(*iCopy, *dest);
if (inside) {
tranRay->setInside(nullptr);
}
else tranRay->setInside(obj);
returnColor = RT_Trace(*tranRay, depth + 1);
delete(scaledN);
delete(rV);
delete(V);
delete(T);
delete(dest);
delete(iCopy);
delete(tranRay);
delete(norm);
}
return returnColor;
}
Vec RQR_Multiply(const VECTOR &v,
const SparseKalmanMatrix &RQR,
const SparseVector &Z,
double H) {
int state_dim = Z.size();
if(v.size() != state_dim + 2) {
report_error("wrong sizes in RQR_Multiply");
}
// Partition v = [eta, epsilon, 0]
ConstVectorView eta(v, 0, state_dim);
double epsilon = v[state_dim];
// Partition this
Vec RQRZ = RQR * Z.dense();
double ZRQRZ_plus_H = Z.dot(RQRZ) + H;
Vec ans(v.size());
VectorView(ans, 0, state_dim) = (RQR * eta).axpy(RQRZ, epsilon);
ans[state_dim] = RQRZ.dot(eta) + ZRQRZ_plus_H * epsilon;
return ans;
}
void ArPosteriorSampler::draw_phi_univariate() {
int p = model_->phi().size();
Vec phi = model_->phi();
if (!model_->check_stationary(phi)) {
report_error("ArPosteriorSampler::draw_phi_univariate was called with an "
"illegal initial value of phi. That should never happen.");
}
const Spd &xtx(model_->suf()->xtx());
const Vec &xty(model_->suf()->xty());
for (int i = 0; i < p; ++i) {
double initial_phi = phi[i];
double lo = -1;
double hi = 1;
// y - xb y - xb
// bt xtx b - 2 bt xty + yty
// bt xtx b = sum_i sum_j beta[i] beta[j] xtx[i, j]
// = beta [i]^2 xtx[i,i] + 2 * sum_{j != i} beta[i] xtx[i, j] * beta[j]
// - 2 * beta[i] * xty[i];
// mean is (xty[i] - sum_{j != i} )
double ivar = xtx(i, i);
double mu = (xty[i] - (phi.dot(xtx.col(i)) - phi[i] * xtx(i, i))) / ivar;
bool ok = false;
while (!ok) {
double candidate = rtrun_norm_2_mt(rng(), mu, sqrt(1.0/ivar), lo, hi);
phi[i] = candidate;
if (ArModel::check_stationary(phi)) {
ok = true;
} else {
if (candidate > initial_phi) hi = candidate;
else lo = candidate;
}
}
}
model_->set_phi(phi);
}
Vec trace(const Ray& r, const int index, const int num_samps) {
// ray-sphere intersection
double t;
if (!intersect(r, t)) return Vec();
// compute the intersection data
const Vec x = r.o + r.d * t, n = (x - sph.p).normalized(), w = -r.d;
// compute Fresnel transmittance at point of emergence
const double T21 = 1.0 - fresnel(w.dot(n), eta);
// integration of the BSSRDF over the surface
unsigned int xi = next_rand(index);
Vec result;
for (int i = 0; i < num_samps; i++) {
// generate a sample
Vec sp, sn, sw;
sample(i, Vec(hal(2, index), hal(3, index), 0.0), sp, sn);
sw = Vec(1, 1, -0.5).normalized();
// directional light source
const double radiance = 8.0*PI;
const double cos_wi_n = sn.dot(sw);
if (cos_wi_n > 0.0) {
// Russian roulette (note that accept_prob can be any value in (0, 1))
const double accept_prob = exp(-(sp - x).len() * min_sigma_tr);
if ((xi / rand_range) < accept_prob) {
const double T12 = 1.0 - fresnel(cos_wi_n, eta);
const double Li_cos = T12 * radiance * cos_wi_n / (samplePDF * accept_prob);
for (int j = 0; j < 3; j++) result[j] += bssrdf(sp, sn, sw, x, n, w, j) * Li_cos;
// reciprocal evaulation with the reciprocity hack
//for (int j = 0; j < 3; j++) result[j] += 0.5 * (bssrdf(sp, sn, sw, x, n, w, j) + bssrdf(x, n, w, sp, sn, sw, j)) * Li_cos;
}
xi = next_rand(xi);
}
}
return T21 * result / (double)num_samps;
}
//calculates reflections. Recursively calls RT_Trace
Color RT_reflect(Figure* obj, const Ray& ray, const Vec& i, const Vec& normal, double depth)
{
if (obj->isR()) {
Vec* V = ray.getV2().normalize(ray.getV1());
Vec* Q = normal.scale(normal.dot(*V));
Vec* S = Q->sub(*V);
Vec* S2 = S->scale(2.0);
Vec* R = V->add(*S2);
Vec* inter = new Vec(i);
Vec* dest = R->add(*inter);
Ray* theRay = new Ray(*inter, *dest);
Color newColor = RT_Trace(*theRay, depth + 1).mult(obj->getRef());
delete(V);
delete(Q);
delete(S);
delete(S2);
delete(R);
delete(inter);
delete(dest);
delete(theRay);
return newColor;
}
else return Color(0, 0, 0);
}
//----------------------------------------------------------------------
double LSB::log_model_prob(const Selector &g)const{
double num = vs_->logp(g);
if(num==BOOM::negative_infinity()) return num;
Ominv = g.select(pri_->siginv());
num += .5*Ominv.logdet();
if(num == BOOM::negative_infinity()) return num;
Vec mu = g.select(pri_->mu());
Vec Ominv_mu = Ominv * mu;
num -= .5*mu.dot(Ominv_mu);
bool ok=true;
iV_tilde_ = Ominv + g.select(suf()->xtx());
Mat L = iV_tilde_.chol(ok);
if(!ok) return BOOM::negative_infinity();
double denom = sum(log(L.diag())); // = .5 log |Ominv|
Vec S = g.select(suf()->xty()) + Ominv_mu;
Lsolve_inplace(L,S);
denom-= .5*S.normsq(); // S.normsq = beta_tilde ^T V_tilde beta_tilde
return num-denom;
}
/** Phong lighting model
** @param pt intersection point
** @param n normal of pt
** @param light pointer to the light source
** @param obj pointer to the object
** @param ray ray
** @return color calculated from local shading using phong model
**/
Vec phongModel(Vec pt, Vec n, Light* light, Shape* obj, Ray ray) {
float t;
Vec v = ray.getOrig() - pt; v = v.normalize(); // vector to viewer
Vec l = light->pos - pt;
float dis = l.mag(); // distance to light source
l = l.normalize(); // vector to light source
Vec ir = n * (2 * n.dot(l)) - l; ir = ir.normalize(); // vector of ideal reflector
Vec intensity = light->intensity; // light intensity
Ray shadowRay(pt, l, 0, 9999, ShadowRay); // shadow ray to the light source
float f = light->attenFac(dis); // attentuation factor
Pigment p = obj->getPigment();
Vec obj_color; // object color
float scalar; int tmp;
if (p.type == SOLID) {
obj_color = p.c1;
} else if (p.type == CHECKER) {
scalar = p.width;
tmp = (int)(pt.x/scalar) + (int)(pt.y/scalar) + (int)(pt.z/scalar);
if (tmp % 2 == 0) obj_color = p.c1;
else obj_color = p.c2;
} else if (p.type == TEXTURE) {
if (obj->getType() == sphere)
obj_color = sphereMapping(pt, n, p);
}
// get the surface parameters
SurFinish appearance = obj->getSurFin();
float Ka = appearance.ambient; // ambient coefficient
float Kd = appearance.diffuse; // diffuse coefficient
float Ks = appearance.specular; // specular coefficient
float shininess = appearance.shininess;
// for each object in the scene, see if is blocks the light
if (light->type != ambient) {
for (ShapeIter its = scene.shapes.begin(); its != scene.shapes.end(); its++) {
if ((*its) == obj) continue;
if ((*its)->getType() == sphere) {
Sphere *shape = dynamic_cast<Sphere*>(*its);
if (shape->intersect(shadowRay, t) && t < dis)
return black;
} else if((*its)->getType() == polyhedron){
Polyhedron *shape = dynamic_cast<Polyhedron*>(*its);
if (shape->intersect(shadowRay, t) && t < dis) {
return black;
}
} else if((*its)->getType() == triangleMesh){
TriangleMesh *shape = dynamic_cast<TriangleMesh*>(*its);
if (shape->intersect(shadowRay, t) && shadowRay.calcDest(t).mag() < dis)
return black;
}
}
}
Vec diffuse(0.0, 0.0, 0.0);
Vec specular(0.0, 0.0, 0.0);
// if the light is casted from front
if (n.dot(l) > 0) {
diffuse = intensity * (Kd * n.dot(l) * f);
specular = white * (Ks * pow(v.dot(ir),shininess) * f);
// update light color
intensity.x = (light->type != ambient) ? diffuse.x * obj_color.x + specular.x : obj_color.x * Ka;
intensity.y = (light->type != ambient) ? diffuse.y * obj_color.y + specular.y : obj_color.y * Ka;
intensity.z = (light->type != ambient) ? diffuse.z * obj_color.z + specular.z : obj_color.z * Ka;
} // if the light is casted from behind
else {
intensity.x = (light->type != ambient) ? black.x : obj_color.x * Ka;
intensity.y = (light->type != ambient) ? black.y : obj_color.y * Ka;
intensity.z = (light->type != ambient) ? black.z : obj_color.z * Ka;
}
return intensity;
}
ftype angle(const Vec& a, const Vec& b) {
return acos(a.dot(b) / sqrt(a.norm_sq()*b.norm_sq()));
}