A Hierarchical Illumination Algorithm for Surfaces with Glossy Reflection

Larry Aupperle and Pat Hanrahan. Proceedings of SIGGRAPH 1993


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 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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