Zone Theorem for Arrangements in three dimensions

TL;DR

This paper presents a straightforward description of the zone theorem in three dimensions, highlighting its utility in constructing higher-order Voronoi diagrams and providing an intuitive explanation.

Contribution

It offers a simple, elementary, and intuitive treatment of the three-dimensional zone theorem, enhancing understanding and application in computational geometry.

Findings

Provides a clear description of the 3D zone theorem

Demonstrates the theorem's use in higher-order Voronoi diagram construction

Offers an accessible, elementary explanation

Abstract

In this note, a simple description of zone theorem in three dimensions is given.Arrangements in three dimensions are useful for constructing higher-order Voronoi diagrams in plane. An elementary and very intuitive treatment of this result is also given.