Position-free Multiple-bounce Computations for Smith Microfacet BSDFs

TL;DR

This paper introduces a position-free formulation for multiple-bounce computations in Microfacet BSDFs, significantly reducing energy loss and noise in rendering by accurately modeling multiple light bounces.

Contribution

It presents a novel, position-free mathematical framework for multiple bounces in Microfacet BSDFs, improving energy conservation and rendering quality.

Findings

Reduces noise in multiple scattering computations

Achieves near noise-free results with 2-4 samples per pixel

Provides an unbiased Monte-Carlo estimator for multiple bounces

Abstract

Bidirectional Scattering Distribution Functions (BSDFs) encode how a material reflects or transmits the incoming light. The most commonly used model is the Microfacet BSDF. It computes material response from the micro-geometry of the surface assuming a single bounce on specular microfacets. The original model ignores multiple bounces on the micro-geometry, resulting in energy loss, especially with large roughness. In this paper, we present a position-free formulation of multiple bounces inside the micro-geometry, which eliminates this energy loss. We use an explicit mathematical definition of path space that describes single and multiple bounces in a uniform way. We then study the behavior of light on the different vertices and segments in path space, leading to an accurate and reciprocal multiple-bounce description of BSDFs. We also present practical, unbiased Monte-Carlo estimators to compute multiple scattering. Our method is less noisy than existing algorithms for computing multiple scattering. It is almost noise-free with a very-low sampling rate, from 2 to 4 samples per pixel.