Wavelet Radiosity

Peter Schröder, Steven J. Gortler, Michael Cohen, and Pat Hanrahan, Proceedings of SIGGRAPH 93

Abstract

Radiosity methods have been shown to be an effective means to solve the global illumination problem in Lambertian diffuse environments. These methods approximate the radiosity integral equation by projecting the unknown radiosity function into a set of basis functions with limited support resulting in a set of $n$ linear equations where $n$ is the number of discrete elements in the scene. Classical radiosity methods required the evaluation of $n^2$ interaction coefficients. Efforts to reduce the number of required coefficients without compromising error bounds have focused on raising the order of the basis functions, meshing, accounting for discontinuities, and on developing hierarchical approaches, which have been shown to reduce the required interactions to $O(n)$.

In this paper we show that the hierarchical radiosity formulation is an instance of a more general set of methods based on {\em wavelet\/} theory. This general framework offers a unified view of both higher order element approaches to radiosity and the hierarchical radiosity methods. After a discussion of the relevant theory, we discuss a new set of linear time hierarchical algorithms based on wavelets such as the multiwavelet family and a flatlet basis which we introduce. Initial results of experimentation with these basis sets are demonstrated and discussed.

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