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- catalog abstract ""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."--Publisher's website.".
- catalog contributor b2701637.
- catalog created "c1989.".
- catalog date "1989".
- catalog date "c1989.".
- catalog dateCopyrighted "c1989.".
- catalog description ""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."--Publisher's website.".
- catalog description "Includes bibliographical references.".
- catalog extent "iv, 167 p. :".
- catalog hasFormat "Concrete and abstract Voronoi diagrams.".
- catalog identifier "0387520554".
- catalog isFormatOf "Concrete and abstract Voronoi diagrams.".
- catalog isPartOf "Lecture notes in computer science ; 400".
- catalog issued "1989".
- catalog issued "c1989.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Concrete and abstract Voronoi diagrams.".
- catalog subject "516 20".
- catalog subject "Geometry Data processing.".
- catalog subject "QA278.2 .K554 1989".
- catalog subject "Spatial analysis (Statistics)".
- catalog subject "Voronoi polygons.".
- catalog title "Concrete and abstract Voronoi diagrams / Rolf Klein.".
- catalog type "text".