void computeL(MatrixType const & A,
MatrixType & L,
MatrixType & L_trans,
std::vector<VectorType1> & Y,
std::vector<std::vector<vcl_size_t> > & J)
{
typedef typename VectorType1::value_type ScalarType;
typedef std::vector<std::map<unsigned int, ScalarType> > STLSparseMatrixType;
STLSparseMatrixType L_temp(A.size1());
for (vcl_size_t k=0; k<A.size1(); ++k)
{
std::vector<vcl_size_t> const & Jk = J[k];
VectorType1 const & yk = Y[k];
//compute L(k,k):
ScalarType Lkk = A(k,k);
for (vcl_size_t i=0; i<Jk.size(); ++i)
Lkk -= A(Jk[i],k) * yk[i];
Lkk = ScalarType(1) / std::sqrt(Lkk);
L_temp[k][static_cast<unsigned int>(k)] = Lkk;
L_trans(k,k) = Lkk;
//write lower diagonal entries:
for (vcl_size_t i=0; i<Jk.size(); ++i)
{
L_temp[Jk[i]][static_cast<unsigned int>(k)] = -Lkk * yk[i];
L_trans(k, Jk[i]) = -Lkk * yk[i];
}
} //for k
//build L from L_temp
for (vcl_size_t i=0; i<L_temp.size(); ++i)
for (typename std::map<unsigned int, ScalarType>::const_iterator it = L_temp[i].begin();
it != L_temp[i].end();
++it)
L(i, it->first) = it->second;
}
glm::vec3 AllLightingIntegrator::LightIndirectEnergy(const Intersection &isx, unsigned int n_split, const glm::vec3 &woW)
{
int depth = 0;
Intersection isx_temp = isx;//reflected intersection
Intersection isx_light; //sampled intersection with "light source"
glm::vec3 color_accum(0.0f, 0.0f, 0.0f); //accumulated color
glm::vec3 color_temp(0.0f, 0.0f, 0.0f);
glm::vec3 wi_temp(0.0f, 0.0f, 0.0f);
glm::vec3 wo_temp(woW);
glm::vec3 brdf_energy_accum(1.0f, 1.0f, 1.0f);
glm::vec3 brdf_energy_temp(0.0f, 0.0f, 0.0f);
glm::vec3 L_temp(0.0f, 0.0f, 0.0f);
Material* M_temp = isx.object_hit->material;
Geometry* obj_temp; //stores the temporary sampled object
Ray sampler;
float pdf_temp_brdf(0);
float pdf_light_temp(0);
float W(0); //for MIS
float rand1 = unif_distribution(mersenne_generator);
float rand2 = unif_distribution(mersenne_generator);
float epsilon = 0.0001f;
float throughput = 1.000001f;
float russian = unif_distribution(mersenne_generator);
//default samples for direct lighting when estimating the irradiance of some other point in the scene
unsigned int n_light = 10;
unsigned int n_brdf = 10;
int light_source_choice(0);
while(depth < max_depth && (russian < throughput || depth < 2))
{
//sample a random point on a random object in the scene
light_source_choice = rand()%scene->objects.count();
obj_temp = scene->objects[light_source_choice];
//if I hit a real light source, kill the ray
if (scene->objects[light_source_choice]->material->is_light_source) break;
isx_light = obj_temp->GetRandISX(rand1, rand2, isx_temp.normal);
//update random numbers
rand1 = unif_distribution(mersenne_generator);
rand2 = unif_distribution(mersenne_generator);
//make ray towards these points
wi_temp = glm::normalize(isx_light.point - isx_temp.point);
sampler = Ray(isx_temp.point, wi_temp);
//update my light intersection
isx_light = intersection_engine->GetIntersection(sampler);
//this ray dies if it hit nothing or is blocked, kill the ray as well
if(isx_light.object_hit == NULL) break;
if(isx_light.object_hit != obj_temp) break;
//to avoid shadow acne
isx_light.point = isx_light.point + epsilon*isx_light.normal;
//find out the pdf w/r/t light
pdf_light_temp = obj_temp->RayPDF(isx_light, sampler);
//if my pdf is negative, kill the ray as well
if(pdf_light_temp <= 0) break;
//update accumulated brdf energy
brdf_energy_temp = M_temp->EvaluateScatteredEnergy(isx_temp, wo_temp, wi_temp, pdf_temp_brdf);
brdf_energy_accum = ComponentMult(brdf_energy_accum, brdf_energy_temp);
//find the direct lighting irradiance of this point towards my original intersection
wo_temp = -wi_temp; //now the old incoming ray is the outgoing ray for the new intersection
L_temp = EstimateDirectLighting(isx_light, n_light, n_brdf, wo_temp);
W = MIS(pdf_light_temp, pdf_temp_brdf);
//this is light source sampling so use the illumination equation for BRDF sampling to accumulate color
color_temp = ComponentMult(brdf_energy_accum, L_temp);
color_temp = ComponentMult(ComponentMult(color_temp, M_temp->base_color), isx_temp.texture_color);
color_temp = color_temp*W/pdf_light_temp*glm::abs(glm::dot(isx_temp.normal, wi_temp));
color_accum = color_accum + color_temp/static_cast<float>(n_split);
throughput = throughput * glm::max(glm::max(color_accum.r, color_accum.g), color_accum.b);
//update the temporary material
M_temp = isx_light.object_hit->material;
isx_temp = isx_light;
//update random number
//update depth
depth++;
russian = unif_distribution(mersenne_generator);
}
return color_accum;
}
glm::vec3 AllLightingIntegrator::BxDFIndirectEnergy(const Intersection &isx, unsigned int n_split, const glm::vec3 &woW)
{
int depth = 0;
Intersection isx_temp = isx;//reflected intersection
Intersection isx_light; //sampled intersection with "light source"
glm::vec3 color_accum(0.0f, 0.0f, 0.0f); //accumulated color
glm::vec3 color_temp(0.0f, 0.0f, 0.0f);
glm::vec3 wi_temp(0.0f, 0.0f, 0.0f);
glm::vec3 wo_temp(woW);
glm::vec3 brdf_energy_accum(1.0f, 1.0f, 1.0f);
glm::vec3 brdf_energy_temp(0.0f, 0.0f, 0.0f);
glm::vec3 L_temp(0.0f, 0.0f, 0.0f);
Material* M_temp = isx.object_hit->material;
Ray sampler;
float pdf_temp_brdf(0);
float pdf_light_temp(0);
float W(0); //for MIS
float rand1 = unif_distribution(mersenne_generator);
float rand2 = unif_distribution(mersenne_generator);
float epsilon = 0.0001;
float throughput = 1.000001f;
float russian = unif_distribution(mersenne_generator);
//default samples for direct lighting when estimating the irradiance of some other point in the scene
unsigned int n_light = 10;
unsigned int n_brdf = 10;
while(depth < max_depth && (russian < throughput || depth < 2))
{
//sample random brdf starting at the input isx direction to get reflected ray to begin
brdf_energy_temp = M_temp->SampleAndEvaluateScatteredEnergy(isx_temp, wo_temp, wi_temp, pdf_temp_brdf, rand1, rand2);
//update accumulated brdf energy
brdf_energy_accum = ComponentMult(brdf_energy_accum, brdf_energy_temp);
//use the sampled incoming ray to find a reflected intersection
sampler = Ray(isx_temp.point, wi_temp);
isx_light = intersection_engine->GetIntersection(sampler);
//this ray dies if I hit a real light source or nothing
if(isx_light.object_hit == NULL) break;
else if(isx_light.object_hit->material->is_light_source) break;
//
//to avoid shadow acne
isx_light.point = isx_light.point + epsilon*isx_light.normal;
//find the direct lighting irradiance of this point towards my original intersection
wo_temp = -wi_temp; //now the old incoming ray is the outgoing ray for the new intersection
L_temp = EstimateDirectLighting(isx_light, n_light, n_brdf, wo_temp); //the direct lighting towards the isx
pdf_light_temp = isx_light.object_hit->RayPDF(isx_light, sampler);
W = MIS(pdf_temp_brdf, pdf_light_temp);
//this is BRDF sampling so use the illumination equation for BRDF sampling to accumulate color
color_temp = ComponentMult(brdf_energy_accum, L_temp);
color_temp = ComponentMult(ComponentMult(color_temp, M_temp->base_color), isx_temp.texture_color);
color_temp = color_temp*W/pdf_temp_brdf*glm::abs(glm::dot(isx_temp.normal, wi_temp));
color_accum = color_accum + color_temp/static_cast<float>(n_split);
throughput = throughput * glm::max(glm::max(color_accum.r, color_accum.g), color_accum.b);
//update the temporary material
M_temp = isx_light.object_hit->material;
isx_temp = isx_light;
//update random number
rand1 = unif_distribution(mersenne_generator);
rand2 = unif_distribution(mersenne_generator);
//update depth
depth++;
russian = unif_distribution(mersenne_generator);
}
return color_accum;
}
