Concrete and Abstract Voronoi Diagrams by Rolf KleinConcrete and Abstract Voronoi Diagrams by Rolf Klein

Concrete and Abstract Voronoi Diagrams

byRolf Klein

Paperback | December 20, 1989

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The Voronoi diagram of a set of sites is a partition of the plane into regions, one to each site, such that the region of each site contains all points of the plane that are closer to this site than to the other ones. Such partitions are of great importance to computer science and many other fields. The challenge is to compute Voronoi diagrams quickly. The problem is that their structure depends on the notion of distance and the sort of site. In this book the author proposes a unifying approach by introducing abstract Voronoi diagrams. These are based on the concept of bisecting curves, which are required to have some simple properties that are actually possessed by most bisectors of concrete Voronoi diagrams. Abstract Voronoi diagrams can be computed efficiently and there exists a worst-case efficient algorithm of divide-and-conquer type that applies to all abstract Voronoi diagrams satisfying a certain constraint. The author shows that this constraint is fulfilled by the concrete diagrams based on large classes of metrics in the plane.
Title:Concrete and Abstract Voronoi DiagramsFormat:PaperbackDimensions:171 pagesPublished:December 20, 1989Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540520554

ISBN - 13:9783540520559

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Table of Contents

Voronoi diagrams in nice metrics.- Abstract Voronoi diagrams.- Computing abstract Voronoi diagrams.- Acyclic partitions.- Concluding remarks.