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A Low-Distortion Map Between Triangle and Square

Abstract : We introduce a low-distortion map between triangle and square. This mapping yields an area-preserving parameterization that can be used for sampling random points with a uniform density in arbitrary triangles. This parameterization presents two advantages compared to the square-root param-eterization typically used for triangle sampling. First, it has lower distortions and better preserves the blue-noise properties of the input samples. Second, its computation relies only on arithmetic operations (+, *), which makes it faster to evaluate.
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https://hal.archives-ouvertes.fr/hal-02073696
Contributor : Eric Heitz <>
Submitted on : Wednesday, June 12, 2019 - 1:51:09 PM
Last modification on : Friday, July 5, 2019 - 5:15:09 PM

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square2triangle.pdf
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  • HAL Id : hal-02073696, version 2

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Eric Heitz. A Low-Distortion Map Between Triangle and Square. 2019. ⟨hal-02073696v2⟩

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