“Wavelet radiosity” by Gortler, Schröder, Cohen and Hanrahan

  • ©Steven J. Gortler, Peter Schröder, Michael F. Cohen, and Patrick (Pat) Hanrahan




    Wavelet radiosity



    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 n2
    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 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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