Browsing by Author "Heitz, Eric"

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    Can't Invert the CDF? The Triangle-Cut Parameterization of the Region under the Curve
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Heitz, Eric; Dachsbacher, Carsten and Pharr, Matt
    We present an exact, analytic and deterministic method for sampling densities whose Cumulative Distribution Functions (CDFs) cannot be inverted analytically. Indeed, the inverse-CDF method is often considered the way to go for sampling non-uniform densities. If the CDF is not analytically invertible, the typical fallback solutions are either approximate, numerical, or nondeterministic such as acceptance-rejection. To overcome this problem, we show how to compute an analytic area-preserving parameterization of the region under the curve of the target density. We use it to generate random points uniformly distributed under the curve of the target density and their abscissae are thus distributed with the target density. Technically, our idea is to use an approximate analytic parameterization whose error can be represented geometrically as a triangle that is simple to cut out. This triangle-cut parameterization yields exact and analytic solutions to sampling problems that were presumably not analytically resolvable.
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    Distributing Monte Carlo Errors as a Blue Noise in Screen Space by Permuting Pixel Seeds Between Frames
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Heitz, Eric; Belcour, Laurent; Boubekeur, Tamy and Sen, Pradeep
    Recent work has shown that distributing Monte Carlo errors as a blue noise in screen space improves the perceptual quality of rendered images. However, obtaining such distributions remains an open problem with high sample counts and highdimensional rendering integrals. In this paper, we introduce a temporal algorithm that aims at overcoming these limitations. Our algorithm is applicable whenever multiple frames are rendered, typically for animated sequences or interactive applications. Our algorithm locally permutes the pixel sequences (represented by their seeds) to improve the error distribution across frames. Our approach works regardless of the sample count or the dimensionality and significantly improves the images in low-varying screen-space regions under coherent motion. Furthermore, it adds negligible overhead compared to the rendering times.