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arXiv · 2012.03350

Average and Expected Distortion of Voronoi Paths and Scapes

Herbert Edelsbrunner·Anton Nikitenko
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Abstract

The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about $\tfrac{4}{\pi}$. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes.

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Herbert Edelsbrunner, Anton Nikitenko. 2020-12-06. Average and Expected Distortion of Voronoi Paths and Scapes. https://arxiv.org/abs/2012.03350

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