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The Resource Effective computational geometry for curves and surfaces, Jean-Daniel Boissonnat, Monique Teillaud, editors

Effective computational geometry for curves and surfaces, Jean-Daniel Boissonnat, Monique Teillaud, editors

Contributor
Summary
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
Language
eng
Work
Publication
Extent
1 online resource (xii, 343 pages)
Contents
  • 1. Arrangements / Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein and Nicola Wolpert
  • 2. Curved Voronoi diagrams / Jean-Daniel Boissonnat, Camille Wormser and Mariette Yvinec
  • 3. Algebraic issues in computational geometry / Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Tecourt and Elias Tsigaridas Nicola Wolpert
  • 4. Differential geometry on discrete surfaces / David Cohen-Steiner and Jean-Marie Morvan
  • 5. Meshing of surfaces / Jean-Daniel Biossonnat, David Cohen-Steiner, Bernard Mourrain, Gunter Rote and Gert Vegter
  • 6. Delaunay triangulation based surface reconstruction / Frederic Cazals and Joachim Giesen
  • 7. Computational topology : an introduction / Gunter Rote and Gert Vegter
  • 8. App.
  • Generic programming and the CGAL Library / Efi Fogel and Monique Teillaud
Isbn
9783540332596
Instance
Label
Effective computational geometry for curves and surfaces
Title
Effective computational geometry for curves and surfaces
Statement of responsibility
Jean-Daniel Boissonnat, Monique Teillaud, editors
Contributor
Subject
Language
eng
Summary
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
Member of
Cataloging source
GW5XE
Dewey number
516.3/6
Illustrations
illustrations
Index
index present
LC call number
QA643
LC item number
.E38 2007eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1953-
  • 1961-
http://library.link/vocab/relatedWorkOrContributorName
  • Boissonnat, J.-D.
  • Teillaud, Monique
Series statement
Mathematics and visualization
http://library.link/vocab/subjectName
  • Curves on surfaces
  • Geometry
  • Geometry, Differential
  • Courbes sur les surfaces
  • Géométrie
  • Géométrie différentielle
  • Curves on surfaces
  • Geometry
  • Geometry, Differential
  • Computational geometry
  • Krommen
  • Oppervlakken
  • Computergraphics
  • Visualisatie
Label
Effective computational geometry for curves and surfaces, Jean-Daniel Boissonnat, Monique Teillaud, editors
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 321]-340) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Arrangements / Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein and Nicola Wolpert -- 2. Curved Voronoi diagrams / Jean-Daniel Boissonnat, Camille Wormser and Mariette Yvinec -- 3. Algebraic issues in computational geometry / Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Tecourt and Elias Tsigaridas Nicola Wolpert -- 4. Differential geometry on discrete surfaces / David Cohen-Steiner and Jean-Marie Morvan -- 5. Meshing of surfaces / Jean-Daniel Biossonnat, David Cohen-Steiner, Bernard Mourrain, Gunter Rote and Gert Vegter -- 6. Delaunay triangulation based surface reconstruction / Frederic Cazals and Joachim Giesen -- 7. Computational topology : an introduction / Gunter Rote and Gert Vegter -- 8. App. -- Generic programming and the CGAL Library / Efi Fogel and Monique Teillaud
Control code
262692301
Dimensions
unknown
Extent
1 online resource (xii, 343 pages)
Form of item
online
Isbn
9783540332596
Lccn
2006931844
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
9786610700233
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-33258-9
Specific material designation
remote
System control number
(OCoLC)262692301
Label
Effective computational geometry for curves and surfaces, Jean-Daniel Boissonnat, Monique Teillaud, editors
Publication
Bibliography note
Includes bibliographical references (pages 321]-340) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Arrangements / Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein and Nicola Wolpert -- 2. Curved Voronoi diagrams / Jean-Daniel Boissonnat, Camille Wormser and Mariette Yvinec -- 3. Algebraic issues in computational geometry / Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Tecourt and Elias Tsigaridas Nicola Wolpert -- 4. Differential geometry on discrete surfaces / David Cohen-Steiner and Jean-Marie Morvan -- 5. Meshing of surfaces / Jean-Daniel Biossonnat, David Cohen-Steiner, Bernard Mourrain, Gunter Rote and Gert Vegter -- 6. Delaunay triangulation based surface reconstruction / Frederic Cazals and Joachim Giesen -- 7. Computational topology : an introduction / Gunter Rote and Gert Vegter -- 8. App. -- Generic programming and the CGAL Library / Efi Fogel and Monique Teillaud
Control code
262692301
Dimensions
unknown
Extent
1 online resource (xii, 343 pages)
Form of item
online
Isbn
9783540332596
Lccn
2006931844
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
9786610700233
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-33258-9
Specific material designation
remote
System control number
(OCoLC)262692301

Subject

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