A Rapid Hierarchical Radiosity Algorithm

Pat Hanrahan David Salzman Larry Aupperle Proceedings of SIGGRAPH 1991


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 $n^2$ 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.

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