A Low-Distortion Map Between Triangle and Square

Eric Heitz

Technical Report 2019


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.