# A Rapid Hierarchical Radiosity Algorithm

Pat Hanrahan
David Salzman
Larry Aupperle
Proceedings of SIGGRAPH 1991

## Abstract

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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