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Effective Computational Geometry for Curves and Surfaces

  • Jean-Daniel Boissonnat
  • Monique Teillaud

Table of contents

  1. Front Matter
    Pages I-XII
  2. Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein, Nicola Wolpert
    Pages 1-66
  3. Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec
    Pages 67-116
  4. Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Técourt, Elias Tsigaridas, Nicola Wolpert
    Pages 117-155
  5. David Cohen-Steiner, Jean-Marie Morvan
    Pages 157-179
  6. Jean-Daniel Boissonnat, David Cohen-Steiner, Bernard Mourrain, Günter Rote, Gert Vegter
    Pages 181-229
  7. Frédéric Cazals, Joachim Giesen
    Pages 231-276
  8. Günter Rote, Gert Vegter
    Pages 277-312
  9. Efi Fogel, Monique Teillaud
    Pages 313-320
  10. Back Matter
    Pages 321-343

About this book

Introduction

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.

Keywords

CAGD Computational Geometry Computational topology Computer Algebra Computer-Aided Design (CAD) Computer-Aided Manufacturing (CAM) Differential geometry Surface approximation and meshing Triangulation algorithms construction linear optimization programming robotics topology

Editors and affiliations

  • Jean-Daniel Boissonnat
    • 1
  • Monique Teillaud
    • 2
  1. 1.INRIA Sophia-AntipolisFrance
  2. 2.INRIA Sophia-AntipolisFrance

Bibliographic information