Proximal Vorono\"i Regions
J.F. Peters
TL;DR
This paper proves that proximal Voronoi regions are convex polygons and that collections of such regions have a Leader uniform topology, contributing to the geometric and topological understanding of Voronoi diagrams.
Contribution
It introduces the proof that proximal Voronoi regions are convex polygons and establishes the topological structure of their collections.
Findings
Proximal Voronoi regions are convex polygons.
Collections of proximal Voronoi regions have a Leader uniform topology.
Provides foundational geometric and topological insights into Voronoi diagrams.
Abstract
A main result in this paper is the proof that proximal Vorono\"{i} regions are convex polygons. In addition, it is proved that every collection of proximal Vorono\"{i} regions has a Leader uniform topology.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Mathematical Modeling in Engineering · Point processes and geometric inequalities