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A Hierarchical Illumination Algorithm for Surfaces with Glossy Reflection

Report ID:
December 1992
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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
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.

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