Voronoi Diagrams of Semi-algebraic Sets
Delaunay Graphs of Semi-algebraic Sets
(Sprache: Englisch)
Most of the curves and surfaces encountered in geometricmodelling are defined as the set of solutions of a system ofalgebraic equations and inequalities (i.e., semi-algebraic sets).Many problems from different fields involve proximity queries likefinding...
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Most of the curves and surfaces encountered in geometricmodelling are defined as the set of solutions of a system ofalgebraic equations and inequalities (i.e., semi-algebraic sets).Many problems from different fields involve proximity queries likefinding the (nearest) neighbours. The Voronoi diagram of a set ofsites is a decomposition of space into proximal regions (pointshaving a generator as nearest neighbour). The dual graph of theVoronoi diagram is called the Delaunay graph. The book shows thebasic algebraic and geometric properties of offsets to algebraiccurves and introduces the concept of generalised Voronoi vertex, toreduces the semi-algebraic computation of the Delaunay graph to alinear algebra problem. Then, it presents the certified incrementalmaintenance of the Delaunay graph of conics and of semi-algebraicsets. The central idea of this book is that symbolicpre-computations can be integrated with interval analysis toaccelerate the certified incremental maintenance of the Delaunaygraph. The certified computation of the Delaunay graph relies ontheorems on the uniqueness of a root in given intervals(Kantorovitch, Moore-Krawczyk) and the ALIAS library.
Autoren-Porträt von François Anton
François Anton (Ph. D., U.B.C.) is Associate Professor at the Department of Informatics and Mathematical Modelling of the Technical University of Denmark. He has published 6 journal papers, 7 book chapters and 40+ conference papers. His interests include computational geometry and topology, computer graphics, interval analysis and databases.
Bibliographische Angaben
- Autor: François Anton
- 2008, 216 Seiten, Masse: 15 x 22 cm, Kartoniert (TB), Englisch
- Verlag: VDM Verlag Dr. Müller
- ISBN-10: 3639038479
- ISBN-13: 9783639038477
Sprache:
Englisch
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