Aligned plane drawings of the generalized Delaunay-graphs for pseudo-disks

TL;DR

This paper demonstrates that for any finite family of pseudo-disks and a point set, the Delaunay-graph can be drawn in the plane so that each edge is contained within all pseudo-disks containing its endpoints, generalizing Delaunay triangulations.

Contribution

It introduces a method to produce aligned plane drawings of generalized Delaunay-graphs for pseudo-disks, extending classical results to more complex geometric families.

Findings

Existence of aligned plane drawings for Delaunay-graphs of pseudo-disks

Edges lie inside all pseudo-disks containing their endpoints

Generalization of Delaunay triangulations to pseudo-disk families

Abstract

We study general Delaunay-graphs, which are natural generalizations of Delaunay triangulations to arbitrary families, in particular to pseudo-disks. We prove that for any finite pseudo-disk family and point set, there is a plane drawing of their Delaunay-graph such that every edge lies inside every pseudo-disk that contains its endpoints.