论文标题
Voronoi路径和SCAPES的平均和预期失真
Average and Expected Distortion of Voronoi Paths and Scapes
论文作者
论文摘要
圆的近似与细方网格的边缘的边缘扭曲了外围的因子约$ \ tfrac {4}π$。我们证明，该因子平均是相同的（从奇异的意义上），可以通过任何非出现的Delaunay Mosaic（称为Voronoi Path）的边缘进行任何整流曲线的近似值，并将结果扩展到所有维度，将Voronoi路径推广到Voronoi scapes。
The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about $\tfrac{4}π$. 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.
