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＜電子ブック＞
Effective Computational Geometry for Curves and Surfaces / edited by Jean-Daniel Boissonnat, Monique Teillaud
(Mathematics and Visualization. ISSN:2197666X)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XII, 344 p : online resource
著者標目	Boissonnat, Jean-Daniel editor Teillaud, Monique editor SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Information visualization LCSH:Image processing -- Digital techniques  全ての件名で検索 LCSH:Computer vision LCSH:Numerical analysis LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Geometry FREE:Computational Mathematics and Numerical Analysis FREE:Data and Information Visualization FREE:Computer Imaging, Vision, Pattern Recognition and Graphics FREE:Numerical Analysis FREE:Mathematical and Computational Engineering Applications
一般注記	1 Arrangements - Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein, Nicola Wolpert -- 2 Curved Voronoi Diagrams - Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec -- 3 Algebraic Issues in Computational Geometry - Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Técourt, Elias Tsigaridas, Nicola Wolpert -- 4 Differential Geometry on Discrete Surfaces - David Cohen-Steiner, Jean-Marie Morvan -- 5 Meshing of Surfaces - Jean-Daniel Boissonnat, David Cohen-Steiner, Bernard Mourrain, Günter Rote, Gert Vegter -- 6 Delaunay Triangulation Based Surface Reconstruction - Frédéric Cazals, Joachim Giesen -- 7 Computational Topology: An Introduction - Günter Rote, Gert Vegter -- 8 Appendix - Generic Programming and the Cgal Library - Efi Fogel, Monique Teillaud -- References -- Index Computational geometry emerged as a discipline in the seventies and has had considerable success in improving the asymptotic complexity of the solutions tobasicgeometricproblemsincludingconstructionsofdatastructures,convex hulls, triangulations, Voronoi diagrams and geometric arrangements as well as geometric optimisation. However, in the mid-nineties, it was recognized that the computational geometry techniques were far from satisfactory in practice and a vigorous e?ort has been undertaken to make computational geometry more practical. This e?ort led to major advances in robustness, geometric software engineering and experimental studies, and to the development of a large library of computational geometry algorithms, Cgal. The goal of this book is to take into consideration the multidisciplinary nature of the problem and to provide solid mathematical and algorithmic foundationsfore?ectivecomputationalgeometryforcurvesandsurfaces. This book covers two main approaches. In a ?rst part, we discuss exact geometric algorithms for curves and s- faces. We revisit two prominent data structures of computational geometry, namely arrangements (Chap. 1) and Voronoi diagrams (Chap. 2) in order to understand how these structures, which are well-known for linear objects, behave when de?ned on curved objects. The mathematical properties of these structures are presented together with algorithms for their construction. To ensure the e?ectiveness of our algorithms, the basic numerical computations that need to be performed are precisely speci?ed, and tradeo?s are considered between the complexity of the algorithms (i. e. the number of primitive calls), and the complexity of the primitives and their numerical stability. Chap HTTP:URL=https://doi.org/10.1007/978-3-540-33259-6

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