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Geometric Modeling and Algebraic Geometry

  • Bert Jüttler
  • Ragni Piene

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Survey of the European project GAIA II

    1. Front Matter
      Pages 2-3
  3. Some special algebraic surfaces

    1. Front Matter
      Pages 28-29
    2. Franck Aries, Emmanuel Briand, Claude Bruchou
      Pages 31-46
    3. Sonja Breske, Oliver Labs, Duco van Straten
      Pages 47-54
    4. Pål Hermunn Johansen, Magnus Løberg, Ragni Piene
      Pages 55-77
    5. Rimvydas Krasauskas, Severinas Zube
      Pages 79-92
    6. Thi-Ha Lê, André Galligo
      Pages 93-113
  4. Algorithms for geometric computing

    1. Front Matter
      Pages 116-117
    2. Frédéric Cazals, Jean-Charles Faugère, Marc Pouget, Fabrice Rouillier
      Pages 141-159
    3. Stéphane Chau, Margot Oberneder, André Galligo, Bert Jüttler
      Pages 161-180
    4. Ioannis Ivrissimtzis, Hans-Peter Seidel
      Pages 181-197
    5. Chen Liang, Bernard Mourrain, Jean-Pascal Pavone
      Pages 199-214
  5. Back Matter
    Pages 229-231

About this book

Introduction

The two ?elds of Geometric Modeling and Algebraic Geometry, though closely - lated, are traditionally represented by two almost disjoint scienti?c communities. Both ?elds deal with objects de?ned by algebraic equations, but the objects are studied in different ways. While algebraic geometry has developed impressive - sults for understanding the theoretical nature of these objects, geometric modeling focuses on practical applications of virtual shapes de?ned by algebraic equations. Recently, however, interaction between the two ?elds has stimulated new research. For instance, algorithms for solving intersection problems have bene?ted from c- tributions from the algebraic side. The workshop series on Algebraic Geometry and Geometric Modeling (Vilnius 1 2 2002 , Nice 2004 ) and on Computational Methods for Algebraic Spline Surfaces 3 (Kefermarkt 2003 , Oslo 2005) have provided a forum for the interaction between the two ?elds. The present volume presents revised papers which have grown out of the 2005 Oslo workshop, which was aligned with the ?nal review of the European project GAIA II, entitled Intersection algorithms for geometry based IT-applications 4 using approximate algebraic methods (IST 2001-35512) .

Keywords

Algebraic Geometry Classification Computer Aided Geometric Design Geometric Algorithms Geometric Modeling algorithm algorithms geometry modeling topology

Editors and affiliations

  • Bert Jüttler
    • 1
  • Ragni Piene
    • 2
  1. 1.Institute of Applied GeometryJohannes Kepler UniversityLinzAustria
  2. 2.CMA and Department of MathematicsUniversity of OsloOsloNorway

Bibliographic information