Rendering along a space-filling curve

Abstract

In photorealistic image synthesis by light transport simulation, the colors of each pixel are an integral of a high-dimensional function. However, the functions to integrate contain discontinuities that cannot be predicted efficiently. In practice, the pixel colors are estimated by using Monte Carlo and quasi-Monte Carlo methods to sample light transport paths that connect light sources and cameras and summing up the contributions to evaluate an integral. Because of the sampling, images appear noisy when the number of samples is insufficient. A low discrepancy sequence provides sample locations and these sample locations can be enumerated (assigned or distributed to pixels) according to a space-filling curve superimposed on a pixel grid. Correlations of such combinations of space-filling curves and low discrepancy sequences are analyzed, and the presented algorithms reduce correlations, are deterministic, and may be executed for each pixel in parallel.

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