On 2-Site Voronoi Diagrams under Geometric Distance Functions

TL;DR

This paper explores the structure and complexity of 2-site Voronoi diagrams under various geometric distance functions, providing insights into their properties and potential applications.

Contribution

It introduces and analyzes new types of 2-site Voronoi diagrams based on geometric distance functions, expanding understanding of their structure and complexity.

Findings

Analyzed the structure of 2-site Voronoi diagrams for different distance functions

Determined the complexity bounds of these diagrams

Provided insights into their geometric properties

Abstract

We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, and analyze the structure and complexity of the nearest- and furthest-neighbor Voronoi diagrams of a point set with respect to these distance functions.