Reflected and Transmitted Irradiance from Area Sources Using Vertex Tracing

Computing irradiance analytically from polygonal luminaires in polygonal environments has proven effective for direct lighting applications in diffuse radiosity environments. Methods for analytic integration have traditionally used edge-based solutions to the irradiance integral; our previous work presented a vertex-based analytic solution, allowing irradiance to be computed incrementally by ray tracing the apparent vertices of the luminaire. In this work we extend the vertex tracing technique to the analytic computation of irradiance from a polygonal luminaire in other indirect lighting applications: transmission through non-refractive transparent polygons, and reflection off perfectly specular polygons. Furthermore we propose an approximate method for computing transmitted irradiance through refractive polyhedra. The method remains effective in the presence of blockers.