// generate sample in two dimension void RegularSampler::Generate2D( float* sample , unsigned num , bool accept_uniform ) const { Sort_Assert( sample != 0 ); unsigned n = (unsigned)sqrt((float)num); Sort_Assert( n * n == num ); unsigned dn = 2 * n; for( unsigned i = 0 ; i < n ; ++i ) { unsigned offset = dn * i; for( unsigned j = 0 ; j < dn ; j+=2 ) { // fall back to random sampling if uniform sampling is not accepted. // For certain cases, like sampling brdf and light, uniform sampling is not acceptable if( !accept_uniform ) { sample[offset+j] = sort_canonical(); sample[offset+j+1] = sort_canonical(); continue; } sample[offset+j] = ( (float)j/2 + 0.5f ) / (float)n ; sample[offset+j+1] = ( (float)i + 0.5f ) / (float)n ; } } }
// Preprocess void InstantRadiosity::PreProcess() { m_pVirtualLightSources = new list<VirtualLightSource>[m_nLightPathSet]; for( int k = 0 ; k < m_nLightPathSet ; ++k ) { for( int i = 0 ; i < m_nLightPaths ; ++i ) { // pick a light first float light_pick_pdf; const Light* light = scene.SampleLight( sort_canonical() , &light_pick_pdf ); // sample a ray from the light source float light_emission_pdf = 0.0f; float light_pdfa = 0.0f; Ray ray; float cosAtLight = 1.0f; Spectrum le = light->sample_l( LightSample(true) , ray , &light_emission_pdf , &light_pdfa , &cosAtLight ); Spectrum throughput = le * cosAtLight / ( light_pick_pdf * light_emission_pdf ); int current_depth = 0; Intersection intersect; while( true ) { if (false == scene.GetIntersect(ray, &intersect)) break; VirtualLightSource ls; ls.power = throughput; ls.intersect = intersect; ls.wi = -ray.m_Dir; ls.depth = ++current_depth; m_pVirtualLightSources[k].push_back( ls ); float bsdf_pdf; Vector wo; Bsdf* bsdf = intersect.primitive->GetMaterial()->GetBsdf(&intersect); Spectrum bsdf_value = bsdf->sample_f(ls.wi, wo, BsdfSample(true), &bsdf_pdf, BXDF_ALL); if( bsdf_pdf == 0.0f ) break; // apply russian roulette float continueProperbility = min( 1.0f , throughput.GetIntensity() ); if( sort_canonical() > continueProperbility ) break; throughput /= continueProperbility; // update throughput throughput *= bsdf_value * ( AbsDot(wo, intersect.normal) / bsdf_pdf ); // update next ray ray = Ray(intersect.intersect, wo, 0, 0.001f); } } } }
// generate sample in two dimension void RandomSampler::Generate2D( float* sample , unsigned num , bool accept_uniform ) const { Sort_Assert( sample != 0 ); int count = 2 * num; for( int i = 0 ; i < count ; i += 2 ) { sample[i] = sort_canonical(); sample[i+1] = sort_canonical(); } }
// sample a ray from light void Square::sample_l( const LightSample& ls , Ray& r , Vector& n , float* pdf ) const { float u = 2 * ls.u - 1.0f; float v = 2 * ls.v - 1.0f; r.m_fMin = 0.0f; r.m_fMax = FLT_MAX; r.m_Ori = transform( Point( radius * u , 0.0f , radius * v ) ); r.m_Dir = transform( UniformSampleHemisphere( sort_canonical() , sort_canonical() ) ); n = transform.invMatrix.Transpose()( Vector( 0.0f , 1.0f , 0.0f ) ); if( pdf ) *pdf = 1.0f / ( SurfaceArea() * TWO_PI ); }
// generate sample in one dimension void RandomSampler::Generate1D( float* sample , unsigned num , bool accept_uniform ) const { Sort_Assert( sample != 0 ); for( unsigned i = 0 ; i < num ; ++i ) sample[i] = sort_canonical(); }
// generate sample in one dimension void StratifiedSampler::Generate1D( float* sample , unsigned num , bool accept_uniform ) const { Sort_Assert( sample != 0 ); for( unsigned i = 0 ; i < num ; ++i ) sample[i] = ( (float)i + sort_canonical() ) / (float)num ; }
// generate sample in two dimension void StratifiedSampler::Generate2D( float* sample , unsigned num , bool accept_uniform ) const { Sort_Assert( sample != 0 ); unsigned n = (unsigned)sqrt((float)num); Sort_Assert( n * n == num ); unsigned dn = 2 * n; for( unsigned i = 0 ; i < n ; ++i ) { unsigned offset = dn * i; for( unsigned j = 0 ; j < dn ; j+=2 ) { sample[offset+j] = ( (float)j/2 + sort_canonical() ) / (float)n ; sample[offset+j+1] = ( (float)i + sort_canonical() ) / (float)n ; } } }
// generate sample in one dimension void RegularSampler::Generate1D( float* sample , unsigned num , bool accept_uniform ) const { Sort_Assert( sample != 0 ); for( unsigned i = 0 ; i < num ; ++i ) { // fall back to random sampling if uniform sampling is not accepted. // For certain cases, like sampling brdf and light, uniform sampling is not acceptable if( !accept_uniform ) sample[i] = sort_canonical(); else sample[i] = ( (float)i + 0.5f ) / (float)num ; } }
// private method of li Spectrum InstantRadiosity::_li( const Ray& r , bool ignoreLe , float* first_intersect_dist ) const { // return if it is larger than the maximum depth if( r.m_Depth > max_recursive_depth ) return 0.0f; // get intersection from camera ray Intersection ip; if( false == scene.GetIntersect( r , &ip ) ) return ignoreLe?0.0f:scene.Le( r ); // eavluate light path less than two vertices Spectrum radiance = ignoreLe?0.0f:ip.Le( -r.m_Dir ); unsigned light_num = scene.LightNum(); for( unsigned i = 0 ; i < light_num ; ++i ) { const Light* light = scene.GetLight(i); radiance += EvaluateDirect( r , scene , light , ip , LightSample(true) , BsdfSample(true) , BXDF_TYPE( BXDF_ALL ) ); } if( first_intersect_dist ) *first_intersect_dist = ip.t; // pick a virtual light source randomly const unsigned lps_id = min( m_nLightPathSet - 1 , (int)(sort_canonical() * m_nLightPathSet) ); list<VirtualLightSource> vps = m_pVirtualLightSources[lps_id]; Bsdf* bsdf = ip.primitive->GetMaterial()->GetBsdf(&ip); // evaluate indirect illumination Spectrum indirectIllum; list<VirtualLightSource>::const_iterator it = vps.begin(); while( it != vps.end() ) { if( r.m_Depth + it->depth > max_recursive_depth ) { ++it; continue; } Vector delta = ip.intersect - it->intersect.intersect; float sqrLen = delta.SquaredLength(); float len = sqrt( sqrLen ); Vector n_delta = delta / len; Bsdf* bsdf1 = it->intersect.primitive->GetMaterial()->GetBsdf(&(it->intersect)); float gterm = AbsDot( n_delta , ip.normal ) * AbsDot( n_delta , it->intersect.normal ) / max( m_fMinSqrDist , sqrLen ); Spectrum f0 = bsdf->f( -r.m_Dir , -n_delta ); Spectrum f1 = bsdf1->f( n_delta , it->wi ); Spectrum contr = gterm * f0 * f1 * it->power; if( !contr.IsBlack() ) { Visibility vis(scene); vis.ray = Ray( it->intersect.intersect , n_delta , 0 , 0.001f , len - 0.001f ); if( vis.IsVisible() ) indirectIllum += contr; } ++it; } radiance += indirectIllum / (float)m_nLightPaths; if( m_fMinDist > 0.0f ) { Vector wi; float bsdf_pdf; Spectrum f = bsdf->sample_f( -r.m_Dir , wi , BsdfSample( true ) , &bsdf_pdf ); if( !f.IsBlack() && bsdf_pdf != 0.0f ) { PixelSample ps; float gather_dist; Ray gather_ray( ip.intersect , wi , r.m_Depth + 1 , 0.001f , m_fMinDist - 0.001f ); Spectrum li = _li( gather_ray , true , &gather_dist ); if( !li.IsBlack() ) { float dgterm = AbsDot( wi , ip.normal ) * max( 0.0f , 1.0f - gather_dist * gather_dist / m_fMinSqrDist ); radiance += f * li * dgterm / bsdf_pdf; } } } return radiance; }
// return the radiance of a specific direction // note : there are one factor makes the method biased. // there is a limitation on the number of vertexes in the path Spectrum PathTracing::Li( const Ray& ray , const PixelSample& ps ) const { Spectrum L = 0.0f; Spectrum throughput = 1.0f; int bounces = 0; Ray r = ray; while(true) { Intersection inter; // get the intersection between the ray and the scene // if it's a light , accumulate the radiance and break if( false == scene.GetIntersect( r , &inter ) ) { if( bounces == 0 ) return scene.Le( r ); break; } if( bounces == 0 ) L+=inter.Le(-r.m_Dir); // make sure there is intersected primitive Sort_Assert( inter.primitive != 0 ); // evaluate the light Bsdf* bsdf = inter.primitive->GetMaterial()->GetBsdf(&inter); float light_pdf = 0.0f; LightSample light_sample = (bounces==0)?ps.light_sample[0]:LightSample(true); BsdfSample bsdf_sample = (bounces==0)?ps.bsdf_sample[0]:BsdfSample(true); const Light* light = scene.SampleLight( light_sample.t , &light_pdf ); if( light_pdf > 0.0f ) L += throughput * EvaluateDirect( r , scene , light , inter , light_sample , bsdf_sample , BXDF_TYPE(BXDF_ALL) ) / light_pdf; // sample the next direction using bsdf float path_pdf; Vector wi; BXDF_TYPE bxdf_type; Spectrum f; BsdfSample _bsdf_sample = (bounces==0)?ps.bsdf_sample[1]:BsdfSample(true); f = bsdf->sample_f( -r.m_Dir , wi , _bsdf_sample , &path_pdf , BXDF_ALL , &bxdf_type ); if( f.IsBlack() || path_pdf == 0.0f ) break; // update path weight throughput *= f * AbsDot( wi , inter.normal ) / path_pdf; if( throughput.GetIntensity() == 0.0f ) break; if( bounces > 4 ) { float continueProperbility = min( 0.5f , throughput.GetIntensity() ); if( sort_canonical() > continueProperbility ) break; throughput /= continueProperbility; } r.m_Ori = inter.intersect; r.m_Dir = wi; r.m_fMin = 0.001f; ++bounces; // note : the following code makes the method biased // 'path_per_pixel' could be set very large to reduce the side-effect. if( bounces >= max_recursive_depth ) break; } return L; }