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 parameterization 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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