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Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/6509
Title: Voronoi Diagrams and Arrangements
Authors: Edelsbrunner, Herbert
Seidel, Raimund
Keywords: computer science
technical report
Issue Date: Mar-1985
Publisher: Cornell University
Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR85-669
Abstract: 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 domain $D$ induced by a finite number of real valued functions on $D$. Valuable insight can be gained when one considers how these real valued functions partition $D \times R$. With this view it turns out that the standard Euclidean Voronoi Diagram of point sets in $R^{d}$ along with its order-$k$ 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.
URI: http://hdl.handle.net/1813/6509
Appears in Collections:Computer Science Technical Reports

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