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Concrete and Abstract Voronoi Diagrams

Author: Rolf Klein

Publisher: Springer Science & Business Media

ISBN: 3540520554

Category: Computers

Page: 167

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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.
Concrete and Abstract Voronoi Diagrams
Language: en
Pages: 167
Authors: Rolf Klein
Categories: Computers
Type: BOOK - Published: 1989-12-20 - Publisher: Springer Science & Business Media

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
Concrete and Abstract Voronoi Diagrams
Language: en
Pages: 176
Authors: Rolf Klein
Categories: Computers
Type: BOOK - Published: 2014-09-11 - Publisher:

Books about Concrete and Abstract Voronoi Diagrams
Randomized Incremental Construction of Abstract Voronoi Diagrams
Language: en
Pages: 29
Authors: Rolf Klein, Kurt Mehlhorn, Stefan Meiser, Max-Planck-Institut für Informatik
Categories: Computational geometry
Type: BOOK - Published: 1993 - Publisher:

Abstract: "Abstract Voronoi diagrams were introduced by R. Klein [Kle89b, Kle88a, Kle88b] as an axiomatic basis of Voronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(n log n) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique [CS89]. The new
Computational Geometry
Language: en
Pages: 386
Authors: Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars
Categories: Computers
Type: BOOK - Published: 2008-03-07 - Publisher: Springer Science & Business Media

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and
Algorithms - ESA 2002
Language: en
Pages: 919
Authors: Rolf Möhring, Rajeev Raman
Categories: Computers
Type: BOOK - Published: 2003-08-02 - Publisher: Springer

This volume contains the 74 contributed papers and abstracts of 4 of the 5 invited talks presented at the 10th Annual European Symposium on Algorithms (ESA 2002), held at the University of Rome “La Sapienza”, Rome, Italy, 17-21 September, 2002. For the ?rst time, ESA had two tracks, with separate