Efficient rendering of layered materials using an atomic decomposition with statistical operators

Abstract

Fig. 1. We introduce a BSDF model to render plane-parallel layered materials using an analysis of the directional statistics of light interaction with microfacet geometry and participating media. Our model closely matches the reference and supports an arbitrary number of textured layers while being energy conserving, free from heavy per-material precomputation, and compatible with real-time constraints.We derive a novel framework for the e cient analysis and computation of light transport within layered materials. Our derivation consists of two steps. First, we decompose light transport into a set of atomic operators that act on its directional statistics. Speci cally, our operators consist of re ection, refraction, sca ering, and absorption, whose combinations are su cient to describe the statistics of light sca ering multiple times within layered structures. We show that the rst three directional moments (energy, mean and variance) already provide an accurate summary. Second, we extend the adding-doubling method to support arbitrary combinations of such operators e ciently. During shading, we map the directional moments to BSDF lobes. We validate that the resulting BSDF closely matches the ground truth in a lightweight and e cient form. Unlike previous methods, we support an arbitrary number of textured layers, and demonstrate a practical and accurate rendering of layered materials with both an o ine and real-time implementation that are free from per-material precomputation.

Real-time rendering of layered materials with anisotropic normal distributions

“…However, the vMF distributions cannot capture the heavy tails of directional distributions, which is often required for modeling metallic materials. Recently, Belcour [7] considered directional statistics of light rays by projecting the directional distribution on a base plane. The reflection or refraction property of each layer is then defined as an operator of changing the projected distribution.…”

“…In the original method [7], a behavior of light interaction with layered materials was represented by energy of light e and two statistical parameters, that is, the mean μ ∈ [−1, 1] 2 and variance σ ∈ [0, ∞] of the distribution of light directions. The symbol σ represents variance rather than standard deviation following the original paper [7]. The property of a surface between two neighboring layers is defined by three functions each of which modifies one of the three parameters above.…”

“…where ω i ∈ S 2 denotes an incident direction; ω t ∈ S 2 refers to a refracted direction; n ∈ S 2 denotes a surface normal; (e i , μ i , σ i ) refer to the parameters of incident light; (e {R,T } , μ {R,T } , σ {R,T } ) denote the parameters of reflected or transmitted light; α ∈ [0, 1] and η refer to the roughness parameter and relative refractive index on a boundary surface between layers, respectively. F GD ∞ represents an integral of the product of Fresnel term F , shadowingmasking function G, and NDF D. In the original method, Belcour [7] precomputed the F GD ∞ values while considering multiple scattering effects [11] and stored them in a lookup table. On the other hand, another implementation in Unity [10] ignored multiple scattering effects and approximated the integral using a simple product of F and G for a direction of perfect reflection or refraction.…”

Gaussian Product Sampling for Rendering Layered Materials

“…It is accurate and general, but it requires a precomputation that depends on the parameters of all the layers, so it is unworkable for textured materials. Belcour [Bel18] proposed a simpler approach for interactive rendering that composes layers by estimating the statistics of the combined BSDF and representing the result as a sum of GGX lobes. This model is efficient, but approximate, and is not general enough to be a complete solution.…”

“…It is accurate and general, but it requires a precomputation that depends on the parameters of all the layers, so it is unworkable for textured materials. Belcour [Bel18] proposed a simpler approach for interactive rendering that [GHZ18] and our pair-product sampling method. All the objects in this scene are characterized using Microfacet BSDF layers.…”