We develop a radiance formulation for discrete three point transport, and a new measure and description of reflectance: area reflectance.This formulation and associated reflectance allow an estimate of 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 computation is shown to beO(n+k 3 ) for sufficient refinement, where n is the number of elements at the finest level of subdivision over an environment consisting ofk input polygonal patches -this growth is exhibited in experimental trials.Naive application of three point transport would require computation over O(n 3 ) element-triple interactions.

This paper presents a rapid hierarchical radiosity algorithm for illuminating scenes containing large polygonal patches. The algorithm constructs a hierarchical representation of the form factor matrix by adaptively subdividing patches into subpatches according to a user-supplied error bound. The algorithm guarantees that all form factors are calculated to the same precision, removing many common image artifacts due to inaccurate form factors. More importantly, the algorithm decomposes the form factor matrix into at most O(n) blocks (where n is the number of elements). Previous radiosity algorithms represented the element-to-element transport interactions with n2 form factors. Visibility algorithms are given that work well with this approach. Standard techniques for shooting and gathering can be used with the hierarchical representation to solve for equilibrium radiosities, but we also discuss using a brightness-weighted error criteria, in conjunction with multigridding, to even more rapidly progressively refine the image.