沃罗诺伊路径和景观的平均失真和预期失真

Pub Date : 2024-06-04 DOI:10.1007/s00454-024-00660-y

Herbert Edelsbrunner, Anton Nikitenko

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引用次数: 0

摘要

用精细正方形网格的边缘近似一个圆时，其周长的扭曲系数约为\(\tfrac{4}{pi }\) 。我们证明，对于用任何非奇异的 Delaunay 马赛克（被称为 Voronoi 路径）的边缘逼近任何可整型曲线，这个因子的平均值是相同的（在遍历意义上），并将结果扩展到所有维度，将 Voronoi 路径推广到 Voronoi Scapes。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Average and Expected Distortion of Voronoi Paths and Scapes

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Average and Expected Distortion of Voronoi Paths and Scapes

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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