In computational geometry, different ways of space partitioning have been developed, including the Voronoi diagram of points and the power diagram of balls. In this article, a generalized Voronoi partition of overlapping d-dimensional balls, called the boundary-partition-based diagram, is proposed. The definition, properties, and applications of this diagram are presented. Compared to the power diagram, this boundary-partition-based diagram is straightforward in the computation of the volume of overlapping balls, which avoids the possibly complicated construction of power cells. Furthermore, it can be applied to characterize singularities on molecular surfaces and to compute the medial axis that can potentially be used to classify molecular structures.

中文翻译：

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d维球的基于边界分区的Voronoi图：定义，属性和应用

在计算几何学中，已经开发出不同的空间分配方式，包括点的沃罗诺伊图和球的功率图。在本文中，提出了重叠的d维球的广义Voronoi分区，称为基于边界分区的图。给出了该图的定义，属性和应用。与功率图相比，此基于边界分区的图在重叠球的体积计算中非常简单，从而避免了可能复杂的功率单元构造。此外，它可用于表征分子表面上的奇异性并计算可潜在地用于对分子结构进行分类的中间轴。