Practical Conditions for Well-behaved-ness of Anisotropic Voronoi Diagrams

TL;DR

This paper introduces simple, efficiently evaluable conditions that ensure well-behaved anisotropic Voronoi diagrams, facilitating their practical use in approximation and optimization tasks, and highlighting their dual triangulations.

Contribution

The paper proposes new practical conditions for anisotropic Voronoi diagrams that are easier to evaluate and better suited for real-world approximation and optimization problems.

Findings

Proposed simple, efficient conditions for well-behaved anisotropic Voronoi diagrams.

Conditions are applicable in any dimension and improve practical utility.

Orphan-free diagrams have embedded triangulations as duals.

Abstract

Recently, simple conditions for well-behaved-ness of anisotropic Voronoi diagrams have been proposed. While these conditions ensure well-behaved-ness of two types of practical anisotropic Voronoi diagrams, as well as the geodesic-distance one, in any dimension, they are both prohibitively expensive to evaluate, and not well-suited for typical problems in approximation or optimization. We propose simple conditions that can be efficiently evaluated, and are better suited to practical problems of approximation and optimization. The practical utility of this analysis is enhanced by the fact that orphan-free anisotropic Voronoi diagrams have embedded triangulations as duals.