A Hierarchical Illumination Algorithm for Surfaces with Glossy Reflection
Abstract:
We develop a radiance formulation for discrete three point transport, and
a new measure and description of reflectance: {em area reflectance}. This
formulation and associated reflectance allow an estimate of
% mn{This needs to be rephrased. Also probably toned down a tad.}
error in the computation of radiance across triples of surface elements,
and lead directly to a hierarchical refinement algorithm for global
illumination.
We have implemented and analyzed this algorithm over surfaces exhibiting
glossy specular and diffuse reflection. Theoretical growth in light
transport interactions is shown to be $O(n log n)$ for sufficient
refinement, where $n$ is the number of elements at the finest level of
subdivision within the environment --- in trials, this growth has been
nearly linear. Naive implementation of three point transport would
require $O(n^3)$ element-triple interactions.