// Integrator Utility Functions Spectrum UniformSampleAllLights(const Interaction &it, const Scene &scene, MemoryArena &arena, Sampler &sampler, const std::vector<int> &nLightSamples, bool handleMedia) { ProfilePhase p(Prof::DirectLighting); Spectrum L(0.f); for (size_t j = 0; j < scene.lights.size(); ++j) { // Accumulate contribution of _j_th light to _L_ const std::shared_ptr<Light> &light = scene.lights[j]; int nSamples = nLightSamples[j]; const Point2f *uLightArray = sampler.Get2DArray(nSamples); const Point2f *uScatteringArray = sampler.Get2DArray(nSamples); if (!uLightArray || !uScatteringArray) { // Use a single sample for illumination from _light_ Point2f uLight = sampler.Get2D(); Point2f uScattering = sampler.Get2D(); L += EstimateDirect(it, uScattering, *light, uLight, scene, sampler, arena, handleMedia); } else { // Estimate direct lighting using sample arrays Spectrum Ld(0.f); for (int k = 0; k < nSamples; ++k) Ld += EstimateDirect(it, uScatteringArray[k], *light, uLightArray[k], scene, sampler, arena, handleMedia); L += Ld / nSamples; } } return L; }
Spectrum UniformSampleOneLight(const Interaction &it, const Scene &scene, MemoryArena &arena, Sampler &sampler, bool handleMedia) { ProfilePhase p(Prof::DirectLighting); // Randomly choose a single light to sample, _light_ int nLights = int(scene.lights.size()); if (nLights == 0) return Spectrum(0.f); int lightNum = std::min((int)(sampler.Get1D() * nLights), nLights - 1); const std::shared_ptr<Light> &light = scene.lights[lightNum]; Point2f uLight = sampler.Get2D(); Point2f uScattering = sampler.Get2D(); return (Float)nLights * EstimateDirect(it, uScattering, *light, uLight, scene, sampler, arena, handleMedia); }
int GenerateLightSubpath( const Scene &scene, Sampler &sampler, MemoryArena &arena, int maxDepth, Float time, const Distribution1D &lightDistr, const std::unordered_map<const Light *, size_t> &lightToIndex, Vertex *path) { if (maxDepth == 0) return 0; // Sample initial ray for light subpath Float lightPdf; int lightNum = lightDistr.SampleDiscrete(sampler.Get1D(), &lightPdf); const std::shared_ptr<Light> &light = scene.lights[lightNum]; RayDifferential ray; Normal3f nLight; Float pdfPos, pdfDir; Spectrum Le = light->Sample_Le(sampler.Get2D(), sampler.Get2D(), time, &ray, &nLight, &pdfPos, &pdfDir); if (pdfPos == 0 || pdfDir == 0 || Le.IsBlack()) return 0; // Generate first vertex on light subpath and start random walk path[0] = Vertex::CreateLight(light.get(), ray, nLight, Le, pdfPos * lightPdf); Spectrum beta = Le * AbsDot(nLight, ray.d) / (lightPdf * pdfPos * pdfDir); VLOG(2) << "Starting light subpath. Ray: " << ray << ", Le " << Le << ", beta " << beta << ", pdfPos " << pdfPos << ", pdfDir " << pdfDir; int nVertices = RandomWalk(scene, ray, sampler, arena, beta, pdfDir, maxDepth - 1, TransportMode::Importance, path + 1); // Correct subpath sampling densities for infinite area lights if (path[0].IsInfiniteLight()) { // Set spatial density of _path[1]_ for infinite area light if (nVertices > 0) { path[1].pdfFwd = pdfPos; if (path[1].IsOnSurface()) path[1].pdfFwd *= AbsDot(ray.d, path[1].ng()); } // Set spatial density of _path[0]_ for infinite area light path[0].pdfFwd = InfiniteLightDensity(scene, lightDistr, lightToIndex, ray.d); } return nVertices + 1; }
int GenerateLightSubpath(const Scene &scene, Sampler &sampler, MemoryArena &arena, int maxdepth, Float time, const Distribution1D &lightDistr, Vertex *path) { if (maxdepth == 0) return 0; // Sample initial ray for light subpath Float lightPdf; int lightNum = lightDistr.SampleDiscrete(sampler.Get1D(), &lightPdf); const std::shared_ptr<Light> &light = scene.lights[lightNum]; RayDifferential ray; Normal3f Nl; Float pdfPos, pdfDir; Spectrum Le = light->Sample_L(sampler.Get2D(), sampler.Get2D(), time, &ray, &Nl, &pdfPos, &pdfDir); if (pdfPos == 0.f || pdfDir == 0.f || Le.IsBlack()) return 0; // Generate first vertex on light subpath and start random walk Spectrum weight = Le * AbsDot(Nl, ray.d) / (lightPdf * pdfPos * pdfDir); path[0] = Vertex(VertexType::Light, EndpointInteraction(light.get(), ray, Nl), Le); path[0].pdfFwd = pdfPos * lightPdf; int nvertices = RandomWalk(scene, ray, sampler, arena, weight, pdfDir, maxdepth - 1, TransportMode::Importance, path + 1); // Correct sampling densities for infinite area lights if (path[0].IsInfiniteLight()) { // Set positional density of _path[1]_ if (nvertices > 0) { path[1].pdfFwd = pdfPos; if (path[1].IsOnSurface()) path[1].pdfFwd *= AbsDot(ray.d, path[1].GetGeoNormal()); } // Set positional density of _path[0]_ path[0].pdfFwd = InfiniteLightDensity(scene, lightDistr, ray.d); } return nvertices + 1; }
Spectrum SamplerIntegrator::SpecularTransmit( const RayDifferential &ray, const SurfaceInteraction &isect, const Scene &scene, Sampler &sampler, MemoryArena &arena, int depth) const { Vector3f wo = isect.wo, wi; Float pdf; const Point3f &p = isect.p; const Normal3f &ns = isect.shading.n; const BSDF &bsdf = *isect.bsdf; Spectrum f = bsdf.Sample_f(wo, &wi, sampler.Get2D(), &pdf, BxDFType(BSDF_TRANSMISSION | BSDF_SPECULAR)); Spectrum L = Spectrum(0.f); if (pdf > 0.f && !f.IsBlack() && AbsDot(wi, ns) != 0.f) { // Compute ray differential _rd_ for specular transmission RayDifferential rd = isect.SpawnRay(wi); if (ray.hasDifferentials) { rd.hasDifferentials = true; rd.rxOrigin = p + isect.dpdx; rd.ryOrigin = p + isect.dpdy; Float eta = bsdf.eta; Vector3f w = -wo; if (Dot(wo, ns) < 0) eta = 1.f / eta; Normal3f dndx = isect.shading.dndu * isect.dudx + isect.shading.dndv * isect.dvdx; Normal3f dndy = isect.shading.dndu * isect.dudy + isect.shading.dndv * isect.dvdy; Vector3f dwodx = -ray.rxDirection - wo, dwody = -ray.ryDirection - wo; Float dDNdx = Dot(dwodx, ns) + Dot(wo, dndx); Float dDNdy = Dot(dwody, ns) + Dot(wo, dndy); Float mu = eta * Dot(w, ns) - Dot(wi, ns); Float dmudx = (eta - (eta * eta * Dot(w, ns)) / Dot(wi, ns)) * dDNdx; Float dmudy = (eta - (eta * eta * Dot(w, ns)) / Dot(wi, ns)) * dDNdy; rd.rxDirection = wi + eta * dwodx - Vector3f(mu * dndx + dmudx * ns); rd.ryDirection = wi + eta * dwody - Vector3f(mu * dndy + dmudy * ns); } L = f * Li(rd, scene, sampler, arena, depth + 1) * AbsDot(wi, ns) / pdf; } return L; }
// WhittedIntegrator Method Definitions Spectrum WhittedIntegrator::Li(const RayDifferential &ray, const Scene &scene, Sampler &sampler, MemoryArena &arena, int depth) const { Spectrum L(0.); // Find closest ray intersection or return background radiance SurfaceInteraction isect; if (!scene.Intersect(ray, &isect)) { for (const auto &light : scene.lights) L += light->Le(ray); return L; } // Compute emitted and reflected light at ray intersection point // Initialize common variables for Whitted integrator const Normal3f &n = isect.shading.n; Vector3f wo = isect.wo; // Compute scattering functions for surface interaction isect.ComputeScatteringFunctions(ray, arena); if (!isect.bsdf) return Li(isect.SpawnRay(ray.d), scene, sampler, arena, depth); // Compute emitted light if ray hit an area light source L += isect.Le(wo); // Add contribution of each light source for (const auto &light : scene.lights) { Vector3f wi; Float pdf; VisibilityTester visibility; Spectrum Li = light->Sample_Li(isect, sampler.Get2D(), &wi, &pdf, &visibility); if (Li.IsBlack() || pdf == 0) continue; Spectrum f = isect.bsdf->f(wo, wi); if (!f.IsBlack() && visibility.Unoccluded(scene)) L += f * Li * AbsDot(wi, n) / pdf; } if (depth + 1 < maxDepth) { // Trace rays for specular reflection and refraction L += SpecularReflect(ray, isect, scene, sampler, arena, depth); L += SpecularTransmit(ray, isect, scene, sampler, arena, depth); } return L; }
int GenerateCameraSubpath(const Scene &scene, Sampler &sampler, MemoryArena &arena, int maxDepth, const Camera &camera, Point2f &pFilm, Vertex *path) { if (maxDepth == 0) return 0; // Sample initial ray for camera subpath CameraSample cameraSample; cameraSample.pFilm = pFilm; cameraSample.time = sampler.Get1D(); cameraSample.pLens = sampler.Get2D(); RayDifferential ray; Spectrum beta = camera.GenerateRayDifferential(cameraSample, &ray); ray.ScaleDifferentials(1 / std::sqrt(sampler.samplesPerPixel)); // Generate first vertex on camera subpath and start random walk Float pdfPos, pdfDir; path[0] = Vertex::CreateCamera(&camera, ray, beta); camera.Pdf_We(ray, &pdfPos, &pdfDir); return RandomWalk(scene, ray, sampler, arena, beta, pdfDir, maxDepth - 1, TransportMode::Radiance, path + 1) + 1; }
int GenerateCameraSubpath(const Scene &scene, Sampler &sampler, MemoryArena &arena, int maxdepth, const Camera &camera, Point2f &rasterPos, Vertex *path) { if (maxdepth == 0) return 0; // Sample initial ray for camera subpath CameraSample cameraSample; cameraSample.pFilm = rasterPos; cameraSample.time = sampler.Get1D(); cameraSample.pLens = sampler.Get2D(); RayDifferential ray; Spectrum rayWeight(camera.GenerateRayDifferential(cameraSample, &ray)); ray.ScaleDifferentials(1.f / std::sqrt(sampler.samplesPerPixel)); // Generate first vertex on camera subpath and start random walk path[0] = Vertex(VertexType::Camera, EndpointInteraction(&camera, ray), Spectrum(1.0f)); return RandomWalk(scene, ray, sampler, arena, rayWeight, camera.Pdf(path[0].ei, ray.d), maxdepth - 1, TransportMode::Radiance, path + 1) + 1; }
Spectrum SamplerIntegrator::SpecularReflect( const RayDifferential &ray, const SurfaceInteraction &isect, const Scene &scene, Sampler &sampler, MemoryArena &arena, int depth) const { // Compute specular reflection direction _wi_ and BSDF value Vector3f wo = isect.wo, wi; Float pdf; BxDFType type = BxDFType(BSDF_REFLECTION | BSDF_SPECULAR); Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdf, type); // Return contribution of specular reflection const Normal3f &ns = isect.shading.n; if (pdf > 0.f && !f.IsBlack() && AbsDot(wi, ns) != 0.f) { // Compute ray differential _rd_ for specular reflection RayDifferential rd = isect.SpawnRay(wi); if (ray.hasDifferentials) { rd.hasDifferentials = true; rd.rxOrigin = isect.p + isect.dpdx; rd.ryOrigin = isect.p + isect.dpdy; // Compute differential reflected directions Normal3f dndx = isect.shading.dndu * isect.dudx + isect.shading.dndv * isect.dvdx; Normal3f dndy = isect.shading.dndu * isect.dudy + isect.shading.dndv * isect.dvdy; Vector3f dwodx = -ray.rxDirection - wo, dwody = -ray.ryDirection - wo; Float dDNdx = Dot(dwodx, ns) + Dot(wo, dndx); Float dDNdy = Dot(dwody, ns) + Dot(wo, dndy); rd.rxDirection = wi - dwodx + 2.f * Vector3f(Dot(wo, ns) * dndx + dDNdx * ns); rd.ryDirection = wi - dwody + 2.f * Vector3f(Dot(wo, ns) * dndy + dDNdy * ns); } return f * Li(rd, scene, sampler, arena, depth + 1) * AbsDot(wi, ns) / pdf; } else return Spectrum(0.f); }
// VolPathIntegrator Method Definitions Spectrum VolPathIntegrator::Li(const RayDifferential &r, const Scene &scene, Sampler &sampler, MemoryArena &arena, int depth) const { ProfilePhase p(Prof::SamplerIntegratorLi); Spectrum L(0.f), alpha(1.f); RayDifferential ray(r); bool specularBounce = false; for (int bounces = 0;; ++bounces) { // Store intersection into _isect_ SurfaceInteraction isect; bool foundIntersection = scene.Intersect(ray, &isect); // Sample the participating medium, if present MediumInteraction mi; if (ray.medium) alpha *= ray.medium->Sample(ray, sampler, arena, &mi); if (alpha.IsBlack()) break; // Handle an interaction with a medium or a surface if (mi.IsValid()) { // Handle medium scattering case Vector3f wo = -ray.d, wi; L += alpha * UniformSampleOneLight(mi, scene, sampler, arena, true); Point2f phaseSample = sampler.Get2D(); mi.phase->Sample_p(wo, &wi, phaseSample); ray = mi.SpawnRay(wi); } else { // Handle surface scattering case // Possibly add emitted light and terminate if (bounces == 0 || specularBounce) { // Add emitted light at path vertex or from the environment if (foundIntersection) L += alpha * isect.Le(-ray.d); else for (const auto &light : scene.lights) L += alpha * light->Le(ray); } if (!foundIntersection || bounces >= maxDepth) break; // Compute scattering functions and skip over medium boundaries isect.ComputeScatteringFunctions(ray, arena, true); if (!isect.bsdf) { ray = isect.SpawnRay(ray.d); bounces--; continue; } // Sample illumination from lights to find attenuated path // contribution L += alpha * UniformSampleOneLight(isect, scene, sampler, arena, true); // Sample BSDF to get new path direction Vector3f wo = -ray.d, wi; Float pdf; BxDFType flags; Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0.f) break; alpha *= f * AbsDot(wi, isect.shading.n) / pdf; Assert(std::isinf(alpha.y()) == false); specularBounce = (flags & BSDF_SPECULAR) != 0; ray = isect.SpawnRay(wi); // Account for attenuated subsurface scattering, if applicable if (isect.bssrdf && (flags & BSDF_TRANSMISSION)) { // Importance sample the BSSRDF SurfaceInteraction pi; Spectrum S = isect.bssrdf->Sample_S( scene, sampler.Get1D(), sampler.Get2D(), arena, &pi, &pdf); #ifndef NDEBUG Assert(std::isinf(alpha.y()) == false); #endif if (S.IsBlack() || pdf == 0) break; alpha *= S / pdf; // Account for the attenuated direct subsurface scattering // component L += alpha * UniformSampleOneLight(pi, scene, sampler, arena, true); // Account for the indirect subsurface scattering component Spectrum f = pi.bsdf->Sample_f(pi.wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0.f) break; alpha *= f * AbsDot(wi, pi.shading.n) / pdf; #ifndef NDEBUG Assert(std::isinf(alpha.y()) == false); #endif specularBounce = (flags & BSDF_SPECULAR) != 0; ray = pi.SpawnRay(wi); } } // Possibly terminate the path if (bounces > 3) { Float continueProbability = std::min((Float).5, alpha.y()); if (sampler.Get1D() > continueProbability) break; alpha /= continueProbability; Assert(std::isinf(alpha.y()) == false); } } return L; }
// PathIntegrator Method Definitions Spectrum PathIntegrator::Li(const RayDifferential &r, const Scene &scene, Sampler &sampler, MemoryArena &arena) const { Spectrum L(0.f); // Declare common path integration variables RayDifferential ray(r); Spectrum pathThroughput = Spectrum(1.f); bool specularBounce = false; for (int bounces = 0;; ++bounces) { // Store intersection into _isect_ SurfaceInteraction isect; bool foundIntersection = scene.Intersect(ray, &isect); // Possibly add emitted light and terminate if (bounces == 0 || specularBounce) { // Add emitted light at path vertex or from the environment if (foundIntersection) L += pathThroughput * isect.Le(-ray.d); else for (const auto &light : scene.lights) L += pathThroughput * light->Le(ray); } if (!foundIntersection || bounces >= maxDepth) break; // Compute scattering functions and skip over medium boundaries isect.ComputeScatteringFunctions(ray, arena, true); if (!isect.bsdf) { ray = isect.SpawnRay(ray.d); bounces--; continue; } // Sample illumination from lights to find path contribution L += pathThroughput * UniformSampleOneLight(isect, scene, sampler, arena); // Sample BSDF to get new path direction Vector3f wo = -ray.d, wi; Float pdf; BxDFType flags; Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0.f) break; pathThroughput *= f * AbsDot(wi, isect.shading.n) / pdf; #ifndef NDEBUG Assert(std::isinf(pathThroughput.y()) == false); #endif specularBounce = (flags & BSDF_SPECULAR) != 0; ray = isect.SpawnRay(wi); // Account for subsurface scattering, if applicable if (isect.bssrdf && (flags & BSDF_TRANSMISSION)) { // Importance sample the BSSRDF BSSRDFSample bssrdfSample; bssrdfSample.uDiscrete = sampler.Get1D(); bssrdfSample.pos = sampler.Get2D(); SurfaceInteraction isect_out = isect; pathThroughput *= isect.bssrdf->Sample_f( isect_out, scene, ray.time, bssrdfSample, arena, &isect, &pdf); #ifndef NDEBUG Assert(std::isinf(pathThroughput.y()) == false); #endif if (pathThroughput.IsBlack()) break; // Account for the direct subsurface scattering component isect.wo = Vector3f(isect.shading.n); // Sample illumination from lights to find path contribution L += pathThroughput * UniformSampleOneLight(isect, scene, sampler, arena); // Account for the indirect subsurface scattering component Spectrum f = isect.bsdf->Sample_f(isect.wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0.f) break; pathThroughput *= f * AbsDot(wi, isect.shading.n) / pdf; #ifndef NDEBUG Assert(std::isinf(pathThroughput.y()) == false); #endif specularBounce = (flags & BSDF_SPECULAR) != 0; ray = isect.SpawnRay(wi); } // Possibly terminate the path if (bounces > 3) { Float continueProbability = std::min((Float).5, pathThroughput.y()); if (sampler.Get1D() > continueProbability) break; pathThroughput /= continueProbability; Assert(std::isinf(pathThroughput.y()) == false); } } return L; }
Spectrum VolPathIntegrator::Li(const RayDifferential &r, const Scene &scene, Sampler &sampler, MemoryArena &arena, int depth) const { ProfilePhase p(Prof::SamplerIntegratorLi); Spectrum L(0.f), beta(1.f); RayDifferential ray(r); bool specularBounce = false; int bounces; // Added after book publication: etaScale tracks the accumulated effect // of radiance scaling due to rays passing through refractive // boundaries (see the derivation on p. 527 of the third edition). We // track this value in order to remove it from beta when we apply // Russian roulette; this is worthwhile, since it lets us sometimes // avoid terminating refracted rays that are about to be refracted back // out of a medium and thus have their beta value increased. Float etaScale = 1; for (bounces = 0;; ++bounces) { // Intersect _ray_ with scene and store intersection in _isect_ SurfaceInteraction isect; bool foundIntersection = scene.Intersect(ray, &isect); // Sample the participating medium, if present MediumInteraction mi; if (ray.medium) beta *= ray.medium->Sample(ray, sampler, arena, &mi); if (beta.IsBlack()) break; // Handle an interaction with a medium or a surface if (mi.IsValid()) { // Terminate path if ray escaped or _maxDepth_ was reached if (bounces >= maxDepth) break; ++volumeInteractions; // Handle scattering at point in medium for volumetric path tracer const Distribution1D *lightDistrib = lightDistribution->Lookup(mi.p); L += beta * UniformSampleOneLight(mi, scene, arena, sampler, true, lightDistrib); Vector3f wo = -ray.d, wi; mi.phase->Sample_p(wo, &wi, sampler.Get2D()); ray = mi.SpawnRay(wi); } else { ++surfaceInteractions; // Handle scattering at point on surface for volumetric path tracer // Possibly add emitted light at intersection if (bounces == 0 || specularBounce) { // Add emitted light at path vertex or from the environment if (foundIntersection) L += beta * isect.Le(-ray.d); else for (const auto &light : scene.infiniteLights) L += beta * light->Le(ray); } // Terminate path if ray escaped or _maxDepth_ was reached if (!foundIntersection || bounces >= maxDepth) break; // Compute scattering functions and skip over medium boundaries isect.ComputeScatteringFunctions(ray, arena, true); if (!isect.bsdf) { ray = isect.SpawnRay(ray.d); bounces--; continue; } // Sample illumination from lights to find attenuated path // contribution const Distribution1D *lightDistrib = lightDistribution->Lookup(isect.p); L += beta * UniformSampleOneLight(isect, scene, arena, sampler, true, lightDistrib); // Sample BSDF to get new path direction Vector3f wo = -ray.d, wi; Float pdf; BxDFType flags; Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0.f) break; beta *= f * AbsDot(wi, isect.shading.n) / pdf; DCHECK(std::isinf(beta.y()) == false); specularBounce = (flags & BSDF_SPECULAR) != 0; if ((flags & BSDF_SPECULAR) && (flags & BSDF_TRANSMISSION)) { Float eta = isect.bsdf->eta; // Update the term that tracks radiance scaling for refraction // depending on whether the ray is entering or leaving the // medium. etaScale *= (Dot(wo, isect.n) > 0) ? (eta * eta) : 1 / (eta * eta); } ray = isect.SpawnRay(ray, wi, flags, isect.bsdf->eta); // Account for attenuated subsurface scattering, if applicable if (isect.bssrdf && (flags & BSDF_TRANSMISSION)) { // Importance sample the BSSRDF SurfaceInteraction pi; Spectrum S = isect.bssrdf->Sample_S( scene, sampler.Get1D(), sampler.Get2D(), arena, &pi, &pdf); DCHECK(std::isinf(beta.y()) == false); if (S.IsBlack() || pdf == 0) break; beta *= S / pdf; // Account for the attenuated direct subsurface scattering // component L += beta * UniformSampleOneLight(pi, scene, arena, sampler, true, lightDistribution->Lookup(pi.p)); // Account for the indirect subsurface scattering component Spectrum f = pi.bsdf->Sample_f(pi.wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0) break; beta *= f * AbsDot(wi, pi.shading.n) / pdf; DCHECK(std::isinf(beta.y()) == false); specularBounce = (flags & BSDF_SPECULAR) != 0; ray = pi.SpawnRay(wi); } } // Possibly terminate the path with Russian roulette // Factor out radiance scaling due to refraction in rrBeta. Spectrum rrBeta = beta * etaScale; if (rrBeta.MaxComponentValue() < rrThreshold && bounces > 3) { Float q = std::max((Float).05, 1 - rrBeta.MaxComponentValue()); if (sampler.Get1D() < q) break; beta /= 1 - q; DCHECK(std::isinf(beta.y()) == false); } } ReportValue(pathLength, bounces); return L; }
Spectrum ConnectBDPT(const Scene &scene, Vertex *lightSubpath, Vertex *cameraSubpath, int s, int t, const Distribution1D &lightDistr, const Camera &camera, Sampler &sampler, Point2f *rasterPos, Float *misWeight) { Spectrum weight(0.f); // Ignore invalid connections related to infinite area lights if (t > 1 && s != 0 && cameraSubpath[t - 1].type == VertexType::Light) return Spectrum(0.f); // Perform connection and write contribution to _weight_ Vertex sampled; if (s == 0) { // Interpret the camera subpath as a complete path const Vertex &pt = cameraSubpath[t - 1]; if (pt.IsLight()) { const Vertex &ptMinus = cameraSubpath[t - 2]; weight = pt.Le(scene, ptMinus) * pt.weight; } } else if (t == 1) { // Sample a point on the camera and connect it to the light subpath const Vertex &qs = lightSubpath[s - 1]; if (qs.IsConnectible()) { VisibilityTester vis; Vector3f wi; Float pdf; Spectrum cameraWeight = camera.Sample_We(qs.GetInteraction(), sampler.Get2D(), &wi, &pdf, rasterPos, &vis); if (pdf > 0 && !cameraWeight.IsBlack()) { // Initialize dynamically sampled vertex and _weight_ sampled = Vertex(VertexType::Camera, EndpointInteraction(vis.P1(), &camera), cameraWeight); weight = qs.weight * qs.f(sampled) * vis.T(scene, sampler) * sampled.weight; if (qs.IsOnSurface()) weight *= AbsDot(wi, qs.GetShadingNormal()); } } } else if (s == 1) { // Sample a point on a light and connect it to the camera subpath const Vertex &pt = cameraSubpath[t - 1]; if (pt.IsConnectible()) { Float lightPdf; VisibilityTester vis; Vector3f wi; Float pdf; int lightNum = lightDistr.SampleDiscrete(sampler.Get1D(), &lightPdf); const std::shared_ptr<Light> &light = scene.lights[lightNum]; Spectrum lightWeight = light->Sample_L( pt.GetInteraction(), sampler.Get2D(), &wi, &pdf, &vis); if (pdf > 0 && !lightWeight.IsBlack()) { sampled = Vertex(VertexType::Light, EndpointInteraction(vis.P1(), light.get()), lightWeight / (pdf * lightPdf)); sampled.pdfFwd = sampled.PdfLightOrigin(scene, pt, lightDistr); weight = pt.weight * pt.f(sampled) * vis.T(scene, sampler) * sampled.weight; if (pt.IsOnSurface()) weight *= AbsDot(wi, pt.GetShadingNormal()); } } } else { // Handle all other cases const Vertex &qs = lightSubpath[s - 1], &pt = cameraSubpath[t - 1]; if (qs.IsConnectible() && pt.IsConnectible()) { weight = qs.weight * qs.f(pt) * GeometryTerm(scene, sampler, qs, pt) * pt.f(qs) * pt.weight; } } // Compute MIS weight for connection strategy *misWeight = weight.IsBlack() ? 0.f : MISWeight(scene, lightSubpath, cameraSubpath, sampled, s, t, lightDistr); return weight; }
Spectrum ConnectBDPT( const Scene &scene, Vertex *lightVertices, Vertex *cameraVertices, int s, int t, const Distribution1D &lightDistr, const std::unordered_map<const Light *, size_t> &lightToIndex, const Camera &camera, Sampler &sampler, Point2f *pRaster, Float *misWeightPtr) { Spectrum L(0.f); // Ignore invalid connections related to infinite area lights if (t > 1 && s != 0 && cameraVertices[t - 1].type == VertexType::Light) return Spectrum(0.f); // Perform connection and write contribution to _L_ Vertex sampled; if (s == 0) { // Interpret the camera subpath as a complete path const Vertex &pt = cameraVertices[t - 1]; if (pt.IsLight()) L = pt.Le(scene, cameraVertices[t - 2]) * pt.beta; DCHECK(!L.HasNaNs()); } else if (t == 1) { // Sample a point on the camera and connect it to the light subpath const Vertex &qs = lightVertices[s - 1]; if (qs.IsConnectible()) { VisibilityTester vis; Vector3f wi; Float pdf; Spectrum Wi = camera.Sample_Wi(qs.GetInteraction(), sampler.Get2D(), &wi, &pdf, pRaster, &vis); if (pdf > 0 && !Wi.IsBlack()) { // Initialize dynamically sampled vertex and _L_ for $t=1$ case sampled = Vertex::CreateCamera(&camera, vis.P1(), Wi / pdf); L = qs.beta * qs.f(sampled, TransportMode::Importance) * sampled.beta; if (qs.IsOnSurface()) L *= AbsDot(wi, qs.ns()); DCHECK(!L.HasNaNs()); // Only check visibility after we know that the path would // make a non-zero contribution. if (!L.IsBlack()) L *= vis.Tr(scene, sampler); } } } else if (s == 1) { // Sample a point on a light and connect it to the camera subpath const Vertex &pt = cameraVertices[t - 1]; if (pt.IsConnectible()) { Float lightPdf; VisibilityTester vis; Vector3f wi; Float pdf; int lightNum = lightDistr.SampleDiscrete(sampler.Get1D(), &lightPdf); const std::shared_ptr<Light> &light = scene.lights[lightNum]; Spectrum lightWeight = light->Sample_Li( pt.GetInteraction(), sampler.Get2D(), &wi, &pdf, &vis); if (pdf > 0 && !lightWeight.IsBlack()) { EndpointInteraction ei(vis.P1(), light.get()); sampled = Vertex::CreateLight(ei, lightWeight / (pdf * lightPdf), 0); sampled.pdfFwd = sampled.PdfLightOrigin(scene, pt, lightDistr, lightToIndex); L = pt.beta * pt.f(sampled, TransportMode::Radiance) * sampled.beta; if (pt.IsOnSurface()) L *= AbsDot(wi, pt.ns()); // Only check visibility if the path would carry radiance. if (!L.IsBlack()) L *= vis.Tr(scene, sampler); } } } else { // Handle all other bidirectional connection cases const Vertex &qs = lightVertices[s - 1], &pt = cameraVertices[t - 1]; if (qs.IsConnectible() && pt.IsConnectible()) { L = qs.beta * qs.f(pt, TransportMode::Importance) * pt.f(qs, TransportMode::Radiance) * pt.beta; VLOG(2) << "General connect s: " << s << ", t: " << t << " qs: " << qs << ", pt: " << pt << ", qs.f(pt): " << qs.f(pt, TransportMode::Importance) << ", pt.f(qs): " << pt.f(qs, TransportMode::Radiance) << ", G: " << G(scene, sampler, qs, pt) << ", dist^2: " << DistanceSquared(qs.p(), pt.p()); if (!L.IsBlack()) L *= G(scene, sampler, qs, pt); } } ++totalPaths; if (L.IsBlack()) ++zeroRadiancePaths; ReportValue(pathLength, s + t - 2); // Compute MIS weight for connection strategy Float misWeight = L.IsBlack() ? 0.f : MISWeight(scene, lightVertices, cameraVertices, sampled, s, t, lightDistr, lightToIndex); VLOG(2) << "MIS weight for (s,t) = (" << s << ", " << t << ") connection: " << misWeight; DCHECK(!std::isnan(misWeight)); L *= misWeight; if (misWeightPtr) *misWeightPtr = misWeight; return L; }
int RandomWalk(const Scene &scene, RayDifferential ray, Sampler &sampler, MemoryArena &arena, Spectrum beta, Float pdf, int maxDepth, TransportMode mode, Vertex *path) { if (maxDepth == 0) return 0; int bounces = 0; // Declare variables for forward and reverse probability densities Float pdfFwd = pdf, pdfRev = 0; while (true) { // Attempt to create the next subpath vertex in _path_ MediumInteraction mi; VLOG(2) << "Random walk. Bounces " << bounces << ", beta " << beta << ", pdfFwd " << pdfFwd << ", pdfRev " << pdfRev; // Trace a ray and sample the medium, if any SurfaceInteraction isect; bool foundIntersection = scene.Intersect(ray, &isect); if (ray.medium) beta *= ray.medium->Sample(ray, sampler, arena, &mi); if (beta.IsBlack()) break; Vertex &vertex = path[bounces], &prev = path[bounces - 1]; if (mi.IsValid()) { // Record medium interaction in _path_ and compute forward density vertex = Vertex::CreateMedium(mi, beta, pdfFwd, prev); if (++bounces >= maxDepth) break; // Sample direction and compute reverse density at preceding vertex Vector3f wi; pdfFwd = pdfRev = mi.phase->Sample_p(-ray.d, &wi, sampler.Get2D()); ray = mi.SpawnRay(wi); } else { // Handle surface interaction for path generation if (!foundIntersection) { // Capture escaped rays when tracing from the camera if (mode == TransportMode::Radiance) { vertex = Vertex::CreateLight(EndpointInteraction(ray), beta, pdfFwd); ++bounces; } break; } // Compute scattering functions for _mode_ and skip over medium // boundaries isect.ComputeScatteringFunctions(ray, arena, true, mode); if (!isect.bsdf) { ray = isect.SpawnRay(ray.d); continue; } // Initialize _vertex_ with surface intersection information vertex = Vertex::CreateSurface(isect, beta, pdfFwd, prev); if (++bounces >= maxDepth) break; // Sample BSDF at current vertex and compute reverse probability Vector3f wi, wo = isect.wo; BxDFType type; Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdfFwd, BSDF_ALL, &type); VLOG(2) << "Random walk sampled dir " << wi << " f: " << f << ", pdfFwd: " << pdfFwd; if (f.IsBlack() || pdfFwd == 0.f) break; beta *= f * AbsDot(wi, isect.shading.n) / pdfFwd; VLOG(2) << "Random walk beta now " << beta; pdfRev = isect.bsdf->Pdf(wi, wo, BSDF_ALL); if (type & BSDF_SPECULAR) { vertex.delta = true; pdfRev = pdfFwd = 0; } beta *= CorrectShadingNormal(isect, wo, wi, mode); VLOG(2) << "Random walk beta after shading normal correction " << beta; ray = isect.SpawnRay(wi); } // Compute reverse area density at preceding vertex prev.pdfRev = vertex.ConvertDensity(pdfRev, prev); } return bounces; }
// PathIntegrator Method Definitions Spectrum PathIntegrator::Li(const RayDifferential &r, const Scene &scene, Sampler &sampler, MemoryArena &arena, int depth) const { ProfilePhase p(Prof::SamplerIntegratorLi); Spectrum L(0.f), beta(1.f); RayDifferential ray(r); bool specularBounce = false; for (int bounces = 0;; ++bounces) { // Find next path vertex and accumulate contribution // Intersect _ray_ with scene and store intersection in _isect_ SurfaceInteraction isect; bool foundIntersection = scene.Intersect(ray, &isect); // Possibly add emitted light at intersection if (bounces == 0 || specularBounce) { // Add emitted light at path vertex or from the environment if (foundIntersection) L += beta * isect.Le(-ray.d); else for (const auto &light : scene.lights) L += beta * light->Le(ray); } // Terminate path if ray escaped or _maxDepth_ was reached if (!foundIntersection || bounces >= maxDepth) break; // Compute scattering functions and skip over medium boundaries isect.ComputeScatteringFunctions(ray, arena, true); if (!isect.bsdf) { ray = isect.SpawnRay(ray.d); bounces--; continue; } // Sample illumination from lights to find path contribution L += beta * UniformSampleOneLight(isect, scene, arena, sampler); // Sample BSDF to get new path direction Vector3f wo = -ray.d, wi; Float pdf; BxDFType flags; Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0.f) break; beta *= f * AbsDot(wi, isect.shading.n) / pdf; Assert(std::isinf(beta.y()) == false); specularBounce = (flags & BSDF_SPECULAR) != 0; ray = isect.SpawnRay(wi); // Account for subsurface scattering, if applicable if (isect.bssrdf && (flags & BSDF_TRANSMISSION)) { // Importance sample the BSSRDF SurfaceInteraction pi; Spectrum S = isect.bssrdf->Sample_S( scene, sampler.Get1D(), sampler.Get2D(), arena, &pi, &pdf); #ifndef NDEBUG Assert(std::isinf(beta.y()) == false); #endif if (S.IsBlack() || pdf == 0) break; beta *= S / pdf; // Account for the direct subsurface scattering component L += beta * UniformSampleOneLight(pi, scene, arena, sampler); // Account for the indirect subsurface scattering component Spectrum f = pi.bsdf->Sample_f(pi.wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0) break; beta *= f * AbsDot(wi, pi.shading.n) / pdf; #ifndef NDEBUG Assert(std::isinf(beta.y()) == false); #endif specularBounce = (flags & BSDF_SPECULAR) != 0; ray = pi.SpawnRay(wi); } // Possibly terminate the path with Russian roulette if (bounces > 3) { Float continueProbability = std::min((Float).95, beta.y()); if (sampler.Get1D() > continueProbability) break; beta /= continueProbability; Assert(std::isinf(beta.y()) == false); } } return L; }
int RandomWalk(const Scene &scene, RayDifferential ray, Sampler &sampler, MemoryArena &arena, Spectrum weight, Float pdfFwd, int maxdepth, TransportMode mode, Vertex *path) { int bounces = 0; if (maxdepth == 0) return 0; SurfaceInteraction isect; MediumInteraction mi; while (true) { // Trace a ray and sample the medium, if any bool foundIntersection = scene.Intersect(ray, &isect); if (ray.medium) weight *= ray.medium->Sample(ray, sampler, arena, &mi); if (weight.IsBlack()) break; Vertex &vertex = path[bounces], &prev = path[bounces - 1]; Float pdfRev; if (mi.IsValid()) { // Handle the medium case // Record medium interaction in _path_ and compute forward density vertex = Vertex(mi, weight); vertex.pdfFwd = ConvertDensity(prev, pdfFwd, vertex); if (++bounces >= maxdepth) break; // Sample direction and compute reverse density at preceding vertex Vector3f wi; pdfFwd = pdfRev = mi.phase->Sample_p(-ray.d, &wi, sampler.Get2D()); ray = mi.SpawnRay(wi); } else { // Handle the surface case if (!foundIntersection) { // Capture escaped rays when tracing from the camera if (mode == TransportMode::Radiance) { vertex = Vertex(VertexType::Light, EndpointInteraction(ray), weight); vertex.pdfFwd = pdfFwd; ++bounces; } break; } // Compute scattering functions for _mode_ and skip over medium // boundaries isect.ComputeScatteringFunctions(ray, arena, true, mode); if (!isect.bsdf) { ray = isect.SpawnRay(ray.d); continue; } // Fill _vertex_ with intersection information vertex = Vertex(isect, weight); vertex.pdfFwd = ConvertDensity(prev, pdfFwd, vertex); if (++bounces >= maxdepth) break; // Sample BSDF at current vertex and compute reverse probability Vector3f wi, wo = isect.wo; BxDFType flags; Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdfFwd, BSDF_ALL, &flags); if (f.IsBlack() || pdfFwd == 0.f) break; weight *= f * AbsDot(wi, isect.shading.n) / pdfFwd; pdfRev = isect.bsdf->Pdf(wi, wo, BSDF_ALL); if (flags & BSDF_SPECULAR) { vertex.delta = true; pdfRev = pdfFwd = 0; } weight *= ShadingNormalCorrection(isect, wo, wi, mode); ray = isect.SpawnRay(wi); } // Compute reverse area density at preceding vertex prev.pdfRev = ConvertDensity(vertex, pdfRev, prev); } return bounces; }
Spectrum ConnectBDPT(const Scene &scene, Vertex *lightVertices, Vertex *cameraVertices, int s, int t, const Distribution1D &lightDistr, const Camera &camera, Sampler &sampler, Point2f *pRaster, Float *misWeightPtr) { Spectrum L(0.f); // Ignore invalid connections related to infinite area lights if (t > 1 && s != 0 && cameraVertices[t - 1].type == VertexType::Light) return Spectrum(0.f); // Perform connection and write contribution to _L_ Vertex sampled; if (s == 0) { // Interpret the camera subpath as a complete path const Vertex &pt = cameraVertices[t - 1]; if (pt.IsLight()) L = pt.Le(scene, cameraVertices[t - 2]) * pt.beta; } else if (t == 1) { // Sample a point on the camera and connect it to the light subpath const Vertex &qs = lightVertices[s - 1]; if (qs.IsConnectible()) { VisibilityTester vis; Vector3f wi; Float pdf; Spectrum Wi = camera.Sample_Wi(qs.GetInteraction(), sampler.Get2D(), &wi, &pdf, pRaster, &vis); if (pdf > 0 && !Wi.IsBlack()) { // Initialize dynamically sampled vertex and _L_ for $t=1$ case sampled = Vertex::CreateCamera(&camera, vis.P1(), Wi / pdf); L = qs.beta * qs.f(sampled) * vis.Tr(scene, sampler) * sampled.beta; if (qs.IsOnSurface()) L *= AbsDot(wi, qs.ns()); } } } else if (s == 1) { // Sample a point on a light and connect it to the camera subpath const Vertex &pt = cameraVertices[t - 1]; if (pt.IsConnectible()) { Float lightPdf; VisibilityTester vis; Vector3f wi; Float pdf; int lightNum = lightDistr.SampleDiscrete(sampler.Get1D(), &lightPdf); const std::shared_ptr<Light> &light = scene.lights[lightNum]; Spectrum lightWeight = light->Sample_Li( pt.GetInteraction(), sampler.Get2D(), &wi, &pdf, &vis); if (pdf > 0 && !lightWeight.IsBlack()) { EndpointInteraction ei(vis.P1(), light.get()); sampled = Vertex::CreateLight(ei, lightWeight / (pdf * lightPdf), 0); sampled.pdfFwd = sampled.PdfLightOrigin(scene, pt, lightDistr); L = pt.beta * pt.f(sampled) * vis.Tr(scene, sampler) * sampled.beta; if (pt.IsOnSurface()) L *= AbsDot(wi, pt.ns()); } } } else { // Handle all other bidirectional connection cases const Vertex &qs = lightVertices[s - 1], &pt = cameraVertices[t - 1]; if (qs.IsConnectible() && pt.IsConnectible()) { L = qs.beta * qs.f(pt) * pt.f(qs) * pt.beta; if (!L.IsBlack()) L *= G(scene, sampler, qs, pt); } } // Compute MIS weight for connection strategy Float misWeight = L.IsBlack() ? 0.f : MISWeight(scene, lightVertices, cameraVertices, sampled, s, t, lightDistr); L *= misWeight; if (misWeightPtr) *misWeightPtr = misWeight; return L; }
Spectrum PathIntegrator::Li(const RayDifferential &r, const Scene &scene, Sampler &sampler, MemoryArena &arena, int depth) const { ProfilePhase p(Prof::SamplerIntegratorLi); Spectrum L(0.f), beta(1.f); RayDifferential ray(r); bool specularBounce = false; int bounces; for (bounces = 0;; ++bounces) { // Find next path vertex and accumulate contribution VLOG(2) << "Path tracer bounce " << bounces << ", current L = " << L << ", beta = " << beta; // Intersect _ray_ with scene and store intersection in _isect_ SurfaceInteraction isect; bool foundIntersection = scene.Intersect(ray, &isect); // Possibly add emitted light at intersection if (bounces == 0 || specularBounce) { // Add emitted light at path vertex or from the environment if (foundIntersection) { L += beta * isect.Le(-ray.d); VLOG(2) << "Added Le -> L = " << L; } else { for (const auto &light : scene.infiniteLights) L += beta * light->Le(ray); VLOG(2) << "Added infinite area lights -> L = " << L; } } // Terminate path if ray escaped or _maxDepth_ was reached if (!foundIntersection || bounces >= maxDepth) break; // Compute scattering functions and skip over medium boundaries isect.ComputeScatteringFunctions(ray, arena, true); if (!isect.bsdf) { VLOG(2) << "Skipping intersection due to null bsdf"; ray = isect.SpawnRay(ray.d); bounces--; continue; } const Distribution1D *distrib = lightDistribution->Lookup(isect.p); // Sample illumination from lights to find path contribution. // (But skip this for perfectly specular BSDFs.) if (isect.bsdf->NumComponents(BxDFType(BSDF_ALL & ~BSDF_SPECULAR)) > 0) { ++totalPaths; Spectrum Ld = beta * UniformSampleOneLight(isect, scene, arena, sampler, false, distrib); VLOG(2) << "Sampled direct lighting Ld = " << Ld; if (Ld.IsBlack()) ++zeroRadiancePaths; CHECK_GE(Ld.y(), 0.f); L += Ld; } // Sample BSDF to get new path direction Vector3f wo = -ray.d, wi; Float pdf; BxDFType flags; Spectrum f = isect.bsdf->Sample_f(wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); VLOG(2) << "Sampled BSDF, f = " << f << ", pdf = " << pdf; if (f.IsBlack() || pdf == 0.f) break; beta *= f * AbsDot(wi, isect.shading.n) / pdf; VLOG(2) << "Updated beta = " << beta; CHECK_GE(beta.y(), 0.f); DCHECK(!std::isinf(beta.y())); specularBounce = (flags & BSDF_SPECULAR) != 0; ray = isect.SpawnRay(wi); // Account for subsurface scattering, if applicable if (isect.bssrdf && (flags & BSDF_TRANSMISSION)) { // Importance sample the BSSRDF SurfaceInteraction pi; Spectrum S = isect.bssrdf->Sample_S( scene, sampler.Get1D(), sampler.Get2D(), arena, &pi, &pdf); DCHECK(!std::isinf(beta.y())); if (S.IsBlack() || pdf == 0) break; beta *= S / pdf; // Account for the direct subsurface scattering component L += beta * UniformSampleOneLight(pi, scene, arena, sampler, false, lightDistribution->Lookup(pi.p)); // Account for the indirect subsurface scattering component Spectrum f = pi.bsdf->Sample_f(pi.wo, &wi, sampler.Get2D(), &pdf, BSDF_ALL, &flags); if (f.IsBlack() || pdf == 0) break; beta *= f * AbsDot(wi, pi.shading.n) / pdf; DCHECK(!std::isinf(beta.y())); specularBounce = (flags & BSDF_SPECULAR) != 0; ray = pi.SpawnRay(wi); } // Possibly terminate the path with Russian roulette if (beta.y() < rrThreshold && bounces > 3) { Float q = std::max((Float).05, 1 - beta.MaxComponentValue()); VLOG(2) << "RR termination probability q = " << q; if (sampler.Get1D() < q) break; beta /= 1 - q; VLOG(2) << "After RR survival, beta = " << beta; DCHECK(!std::isinf(beta.y())); } } ReportValue(pathLength, bounces); return L; }