# A Rapid Hierarchical Radiosity Algorithm for Unoccluded
Environments

Pat Hanrahan and
David Salzman.
Eurographics 1990

### Abstract

This paper presents a linear-time radiosity algorithm for scenes containing
large mutually unoccluded polygonal patches. It subdivides pairs of
patches adaptively to build a hierarchical data structure with $n$ elements
at the leaves, and it encodes all the light transport between component
polygonal elements. Given a required numerical precision, determined here
by the specified bounds for maximum solid angle $F_\epsilon$ and minimum
area $A_\epsilon$, our algorithm reduces the number of form factor
calculations and interactions to $O(n)$ in the worst case and $O ( \sqrt n
)$ in the best case. Standard techniques for shooting and gathering can
then be used with the data structure. The best previous radiosity
algorithms represented the element-to-element transport interactions with
$n^2$ form factors.
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