Visibility Silhouettes for Semi‐Analytic Spherical Integration

At each shade point, the spherical visibility function encodes occlusion from surrounding geometry, in all directions. Computing this function is difficult and point‐sampling approaches, such as ray‐tracing or hardware shadow mapping, are traditionally used to efficiently approximate it. We propose a semi‐analytic solution to the problem where the spherical silhouette of the visibility is computed using a search over a 4D dual mesh of the scene. Once computed, we are able to semi‐analytically integrate visibility‐masked spherical functions along the visibility silhouette, instead of over the entire hemisphere. In this way, we avoid the artefacts that arise from using point‐sampling strategies to integrate visibility, a function with unbounded frequency content. We demonstrate our approach on several applications, including direct illumination from realistic lighting and computation of pre‐computed radiance transfer data. Additionally, we present a new frequency‐space method for exactly computing all‐frequency shadows on diffuse surfaces. Our results match ground truth computed using importance‐sampled stratified Monte Carlo ray‐tracing, with comparable performance on scenes with low‐to‐moderate geometric complexity.