Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/6509
 Title: Voronoi Diagrams and Arrangements Authors: Edelsbrunner, HerbertSeidel, Raimund Keywords: computer sciencetechnical 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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