Position-free multiple-scattering computations for micrograin BSDF model

Porous materials (e.g., weathered stone, industrial coatings) exhibit complex optical effects due to their micrograin and pore structures, posing challenges for photorealistic rendering. Explicit geometry models struggle to characterize their micrograin distributions at microscopic scales, while single-scattering microfacet model fails to accurately capture the multiple-scattering effects and causes energy non-conservation artifacts, manifesting as unrealistic luminance decay. We propose an enhanced micrograin BSDF model that accurately accounts for multiple scattering. First, we introduce a visible normal distribution function (VNDF) sampling method via rejection sampling. Building on VNDF sampling, we derive a position-free microsurface formulation incorporating both inter-micrograin and micrograin-to-base interactions. Furthermore, we propose a practical random walk method to simulate microsurface scattering, which accurately solves the derived formulation. Our micrograin BSDF model effectively eliminates the energy loss artifacts inherent in the previous model while significantly reducing noise, providing a physically accurate yet artistically controllable solution for rendering porous materials.