Abstract Precomputation and efficient approximate material models are well‐known approaches for achieving real‐time rendering with global illumination. Recent research in radiance fields and in particular 3D Gaussian Splatting has demonstrated the power of Gaussian primitives both to represent radiance and for fast optimization. Inspired by these advances, we propose a new representation to precompute global illumination, by using 3D Gaussians for the spatial and spherical Gaussians for the directional component of lighting. Critically, we precompute and store incoming radiance, thus requiring the optimization of a spatially smooth function, and we exploit the properties of anisotropic spherical Gaussians for very fast evaluation during rendering. We introduce a frequency‐aware sampling method, that guides both the placement of precomputed ground truth illumination samples and the placement of the Gaussians, both spatial and angular. Our approach provides very fast optimization, for a total precomputation time of less than 6 minutes for our test scenes, and better quality rendering than competing approaches at the same frame rates.

Abstract We introduce a discrete polydisperse micrograin BSDF model for the rendering of porous surface materials composed of microscopic elements of different size, shape and reflectance distributed on a bulk medium. Our approach generalizes the anisotropic monodisperse micrograin model We first reformulate it in a non‐axis‐aligned configuration, allowing for the later combination of different micrograin types elongated in arbitrary directions. We then extend the monodisperse model to the polydisperse case, deriving its three key components: (i) a general filling factor that controls the mix between micrograins and the bulk medium; (ii) an exact normal distribution function for surfaces composed of polydisperse micrograin distributions; and (iii) the corresponding fully‐correlated shadowing and masking term. This results in an analytical single‐scattering BSDF for discrete polydisperse surface materials, validated over ground truth simulations, for which we also derive a dedicated importance sampling procedure. Our model supports varying heights and anisotropy orientations of different micrograin types as input, giving additional control to simulate phenomena like retro‐reflection from mixed materials, color mixture depending on lighting and observation directions, multiple directions of anisotropy, etc.

Abstract Importance sampling of visible normal distribution functions (vNDF) is a required ingredient for the efficient rendering of microfacet‐based materials. In this paper, we explain how to sample the vNDF for the micrograin material model [LRPB23], which has been recently improved to handle height‐normal correlations through a new Geometric Attenuation Factor (GAF) [LRPB24], leading to a stronger impact on appearance compared to the earlier Smith approximation. To this end, we make two contributions: we derive analytic expressions for the marginal and conditional cumulative distribution functions (CDFs) of the vNDF; we provide efficient methods for inverting these CDFs based respectively on a 2D lookup table and on the triangle‐cut method [Hei20].

We introduce an improved version of the micrograin BSDF model [Lucas et al. 2023] for the rendering of anisotropic porous layers. Our approach leverages the properties of micrograins to take into account the correlation between their height and normal, as well as the correlation between the light and view directions. This allows us to derive an exact analytical expression for the Geometrical Attenuation Factor (GAF), summarizing shadowing and masking inside the porous layer. This fully-correlated GAF is then used to define appropriate mixing weights to blend the BSDFs of the porous and base layers. Furthermore, by generalizing the micrograins shape to anisotropy, combined with their fully-correlated GAF, our improved BSDF model produces effects specific to porous layers such as retro-reflection visible on dust layers at grazing angles or height and color correlation that can be found on rusty materials. Finally, we demonstrate very close matches between our BSDF model and light transport simulations realized with explicit instances of micrograins, thus validating our model.

We introduce a new BSDF model for the rendering of porous layers, as found on surfaces covered by dust, rust, dirt, or sprayed paint. Our approach is based on a distribution of elliptical opaque micrograins, extending the Trowbridge-Reitz (GGX) distribution [Trowbridge and Reitz 1975; Walter et al. 2007] to handle pores (i.e., spaces between micrograins). We use distance field statistics to derive the corresponding Normal Distribution Function (NDF) and Geometric Attenuation Factor (GAF), as well as a view- and light-dependent filling factor to blend between the porous and base layers. All the derived terms show excellent agreement when compared against numerical simulations.