Geometric Modeling and Algebraic Geometry

1. Front Matter

   Pages I-VIII

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2. Survey of the European project GAIA II

   1. Front Matter

      Pages 2-3

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   2. The GAIA Project on Intersection and Implicitization

      • Tor Dokken

      Pages 5-25

3. Some special algebraic surfaces

   1. Front Matter

      Pages 28-29

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   2. Some Covariants Related to Steiner Surfaces

      • Franck Aries, Emmanuel Briand, Claude Bruchou

      Pages 31-46

   3. Real Line Arrangements and Surfaces with Many Real Nodes

      • Sonja Breske, Oliver Labs, Duco van Straten

      Pages 47-54

   4. Monoid Hypersurfaces

      • Pål Hermunn Johansen, Magnus Løberg, Ragni Piene

      Pages 55-77

   5. Canal Surfaces Defined by Quadratic Families of Spheres

      • Rimvydas Krasauskas, Severinas Zube

      Pages 79-92

   6. General Classification of (1,2) Parametric Surfaces in 葳3

      • Thi-Ha Lê, André Galligo

      Pages 93-113

4. Algorithms for geometric computing

   1. Front Matter

      Pages 116-117

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   2. Curve Parametrization over Optimal Field Extensions Exploiting the Newton Polygon

      • Tobias Beck, Josef Schicho

      Pages 119-140

   3. Ridges and Umbilics of Polynomial Parametric Surfaces

      • Frédéric Cazals, Jean-Charles Faugère, Marc Pouget, Fabrice Rouillier

      Pages 141-159

   4. Intersecting Biquadratic Bézier Surface Patches

      • Stéphane Chau, Margot Oberneder, André Galligo, Bert Jüttler

      Pages 161-180

   5. Cube Decompositions by Eigenvectors of Quadratic Multivariate Splines

      • Ioannis Ivrissimtzis, Hans-Peter Seidel

      Pages 181-197

   6. Subdivision Methods for the Topology of 2d and 3d Implicit Curves

      • Chen Liang, Bernard Mourrain, Jean-Pascal Pavone

      Pages 199-214

   7. Approximate Implicitization of Space Curves and of Surfaces of Revolution

      • Mohamed Shalaby, Bert Jüttler

      Pages 215-227

5. Back Matter

   Pages 229-231

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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) .

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

• Institute of Applied Geometry, Johannes Kepler University, Linz, Austria

  Bert Jüttler

• CMA and Department of Mathematics, University of Oslo, Oslo, Norway

  Ragni Piene

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