Orphan-Free Anisotropic Voronoi Diagrams

TL;DR

This paper establishes conditions ensuring that anisotropic Voronoi diagrams have connected cells in any dimension, which is useful for optimization and approximation problems, supported by existing algorithms.

Contribution

It introduces natural conditions guaranteeing connected cells in anisotropic Voronoi diagrams and relates them to existing algorithms that produce suitable site sets.

Findings

Connected cells in anisotropic Voronoi diagrams are guaranteed under certain conditions.

Conditions are natural for optimization and approximation applications.

Algorithms exist to generate site sets satisfying these conditions.

Abstract

We describe conditions under which an appropriately-defined anisotropic Voronoi diagram of a set of sites in Euclidean space is guaranteed to be composed of connected cells in any number of dimensions. These conditions are natural for problems in optimization and approximation, and algorithms already exist to produce sets of sites that satisfy them.