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Item Discrepancy as a Quality Measure for Sample Distributions(Eurographics Association, 1991) Shirley, PeterDiscrepancy, a scalar measure of sample point equidistribution, is discussed in the context of Computer Graphics sampling problems. Several sampling strategies and their discrepancy characteristics are examined. The relationship between image error and the discrepancy of the sampling patterns used to generate the image is established. The definition of discrepancy is extended to non-uniform sampling patterns.Item Time Complexity of Monte Carlo Radiosity(Eurographics Association, 1991) Shirley, PeterThe time complexity of Monte Carlo radiosity is discussed, and a proof is given that the expected number of rays required to produce a satisfactory radiosity solution for N zones is O(N). A satisfactory solution is defined to be one in which the variance of radiance estimates for each zone is below a predefined threshold. The proof assumes that the radiance is bounded, and the area ratio of the largest to smallest zone is bounded.