A Signal-Processing Framework for Reflection—Part 2: Analytic Formulae for Common Lighting and BRDF Models

The first part of this paper presented a signal-processing framework for analyzing the reflected light field from a homogeneous convex curved surface under distant illumination. The notion of reflection as convolution was formalized, with a quantitative analysis of the reflected light field as obtained by a spherical convolution of the incident illumination and the BRDF. In this part of the paper, we derive analytic formulae for spherical harmonic coefficients of many common lighting and BRDF models. In this way, we explore the implications of the theoretical analysis for many special cases of interest, determining the well-posedness and conditioning of many forward and inverse rendering problems, and explaining previous empirical results.