A Unified Manifold Framework for Efficient BRDF Sampling based on Parametric Mixture Models

Virtually all existing analytic BRDF models are built from multiple functional components (e.g., Fresnel term, normal distribution function, etc.). This makes accurate importance sampling of the full model challenging, and so current solutions only cover a subset of the model's components. This leads to sub-optimal or even invalid proposed directional samples, which can negatively impact the efficiency of light transport solvers based on Monte Carlo integration. To overcome this problem, we propose a unified BRDF sampling strategy based on parametric mixture models (PMMs). We show that for a given BRDF, the parameters of the associated PMM can be defined in smooth manifold spaces, which can be compactly represented using multivariate B-Splines. These manifolds are defined in the parameter space of the BRDF and allow for arbitrary, continuous queries of the PMM representation for varying BRDF parameters, which further enables importance sampling for spatially varying BRDFs. Our representation is not limited to analytic BRDF models, but can also be used for sampling measured BRDF data. The resulting manifold framework enables accurate and efficient BRDF importance sampling with very small approximation errors.