Voronoi diagrams and arrangements
 Herbert Edelsbrunner,
 Raimund Seidel
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We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inR ^{ d } along with its orderk generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.
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 Title
 Voronoi diagrams and arrangements
 Journal

Discrete & Computational Geometry
Volume 1, Issue 1 , pp 2544
 Cover Date
 19861201
 DOI
 10.1007/BF02187681
 Print ISSN
 01795376
 Online ISSN
 14320444
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Herbert Edelsbrunner ^{(1)}
 Raimund Seidel ^{(3)}
 Author Affiliations

 1. Institute f. Informationsverarbeitung, Technical University of Graz, Schießstattgasse 4A, A8010, Graz, Austria
 3. Computer Science Department, Cornell University, 14853, Ithaca, NY