Binary space partitioning visibility tree for polygonal and environment light rendering

In this paper, we present a geometric approach to render shadows for physically based materials under polygonal light sources. Direct illumination calculation from a polygonal light source involves the triple product integral of the lighting, the bidirectional reflectance distribution function (BRDF), and the visibility function over the polygonal domain, which is computation intensive. To achieve real-time performance, work on polygonal light shading exploits analytical solutions of boundary integrals along the edges of the polygonal light at the cost of lacking shadowing effects. We introduce a hierarchical representation for the precomputed visibility function to retain the merits of closed-form solutions for boundary integrals. Our method subdivides the polygonal light into a set of polygons visible from a point to be shaded. Experimental results show that our method can render complex shadows with a GGX microfacet BRDF from polygonal light sources at interactive frame rates. In addition, our visibility representation can be easily incorporated into environment lighting.