Monte Carlo light transport simulations often lack robustness in scenes containing specular or near-specular materials. Widely used uni- and bidirectional sampling strategies tend to find light paths involving such materials with insufficient probability, producing unusable images that are contaminated by significant variance. This article addresses the problem of sampling a light path connecting two given scene points via a single specular reflection or refraction, extending the range of scenes that can be robustly handled by unbiased path sampling techniques. Our technique enables efficient rendering of challenging transport phenomena caused by such paths, such as underwater caustics or caustics involving glossy metallic objects. We derive analytic expressions that predict the total radiance due to a single reflective or refractive triangle with a microfacet BSDF and we show that this reduces to the well known Lambert boundary integral for irradiance. We subsequently show how this can be leveraged to efficiently sample connections on meshes comprised of vast numbers of triangles. Our derivation builds on the theory of off-center microfacets and involves integrals in the space of surface slopes. Our approach straightforwardly applies to the related problem of rendering glints with high-resolution normal maps describing specular microstructure. Our formulation alleviates problems raised by singularities in filtering integrals and enables a generalization of previous work to perfectly specular materials. We also extend previous work to the case of GGX distributions and introduce new techniques to improve accuracy and performance.

Differentiable rendering has recently opened the door to a number of challenging inverse problems involving photorealistic images, such as computational material design and scattering-aware reconstruction of geometry and materials from photographs. Differentiable rendering algorithms strive to estimate partial derivatives of pixels in a rendered image with respect to scene parameters, which is difficult because visibility changes are inherently non-differentiable. We propose a new technique for differentiating path-traced images with respect to scene parameters that affect visibility, including the position of cameras, light sources, and vertices in triangle meshes. Our algorithm computes the gradients of illumination integrals by applying changes of variables that remove or strongly reduce the dependence of the position of discontinuities on differentiable scene parameters. The underlying parameterization is created on the fly for each integral and enables accurate gradient estimates using standard Monte Carlo sampling in conjunction with automatic differentiation. Importantly, our approach does not rely on sampling silhouette edges, which has been a bottleneck in previous work and tends to produce high-variance gradients when important edges are found with insufficient probability in scenes with complex visibility and high-resolution geometry. We show that our method only requires a few samples to produce gradients with low bias and variance for challenging cases such as glossy reflections and shadows. Finally, we use our differentiable path tracer to reconstruct the 3D geometry and materials of several real-world objects from a set of reference photographs.

Abstract Naïve linear methods for downsampling high‐resolution microflake volumes often produce inaccurate appearance, especially when input voxels are very opaque. Preserving correct appearance at all resolutions requires taking into account maskingshadowing effects that occur between and inside dense input voxels. We introduce a new microflake model whose additional parameters characterize self‐shadowing effects at a microscopic scale. We provide an anisotropic self‐shadowing function and microflake distributions for which the scattering coefficients and the phase functions of our model have closed‐form expressions. We use this model in a new downsampling approach in which scattering parameters are computed from local estimations of self‐shadowing probabilities in the input volume. Unlike previous work, our method handles datasets with spatially varying scattering parameters, semi‐transparent volumes and datasets with intricate silhouettes. We show that our method generates LoDs with correct transparency and consistent appearance through scales for a wide range of challenging datasets, allowing for huge memory savings and efficient distant rendering without loss of quality.

We address the problem of constructing appearance-preserving level of details (LoDs) of complex 3D models such as trees. We propose a hybrid method that combines the strengths of mesh and volume representations. Our main idea is to separate macroscopic (i.e. larger than the target spatial resolution) and microscopic (sub-resolution) surfaces at each scale and to treat them differently, because meshes are very efficient at representing macroscopic surfaces while sub-resolution geometry benefits from volumetric approximations. We introduce a new algorithm that detects the macroscopic surfaces of a mesh for a given resolution. We simplify these surfaces with edge collapses and we provide a method for pre-filtering their normal distributions and albedos. To approximate microscopic details, we use a heterogeneous microflake participating medium and we introduce a new artifact-free voxelization algorithm that preserves local occlusion. Thanks to our macroscopic surface analysis, our algorithm is fully automatic and it generates seamless LoDs at arbitrarily coarse resolutions for a wide range of 3D models.