Microfacet BSDFs Generated from NDFs and Explicit Microgeometry

Microfacet distributions are considered nowadays as a reference for physically plausible BSDF representations. Many authors have focused on their physical and mathematical correctness, while introducing means to enlarge the range of possible appearances. This article is dedicated to Normal Distribution Functions (NDFs) and the influence of their shape on the rendered material aspect. We provide a complete framework for studying the impact of NDFs on the observed Bidirectional Scattering Distribution Functions (BSDFs). To explore very general NDFs, manually controlled by the user, and including anisotropic materials, we propose to use a piecewise continuous representation. It is derived with its associated Smith shadowing-masking function and importance sampling formulations for ensuring efficient global illumination computations. A new procedure is also proposed in this article for generating an explicit geometric micro-surface, used to evaluate the validity of analytic models and multiple scattering effects. The results are produced with a computer-generated process using path tracing. They show that this generation procedure is suitable with any NDF model, independently from its shape complexity.