Degeneracy of Angular Voronoi Diagram

TL;DR

This paper investigates the degeneracy and singularities of edges in Angular Voronoi diagrams, essential for improving computational robustness in mesh generation.

Contribution

It enumerates all possible curve types of diagram edges, highlighting degeneracies and the need to handle singularities.

Findings

Identifies all edge curve types in Angular Voronoi diagrams

Classifies potential degeneracies and singularities

Provides insights for robust computational implementations

Abstract

Angular Voronoi diagram was introduced by Asano et al. as fundamental research for a mesh generation. In an angular Voronoi diagram, the edges are curves of degree three. From view of computational robustness we need to treat the curves carefully, because they might have a singularity. We enumerate all the possible types of curves that appear as an edge of an angular Voronoi diagram, which tells us what kind of degeneracy is possible and tells us necessity of considering a singularity for computational robustness.