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Shape Interrogation

  • Stefanie Hahmann
  • Alexander Belyaev
  • Laurent Busé
  • Gershon Elber
  • Bernard Mourrain
  • Christian Rössl
Chapter
Part of the Mathematics and Visualization book series (MATHVISUAL)

Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where “class A” surfaces are required and no surface imperfections are allowed, shape interrogation has become recently an important tool for various other types of surface representations such as triangulated or polygonal surfaces, subdivision surface, and algebraic surfaces. In this paper we present the state-of-the-art of shape interrogation methods including methods for detecting surface imperfections, surface analysis tools and methods for visualizing intrinsic surface properties. Furthermore we focus on stable numerical and symbolic solving of algebraic systems of equations, a problem that arises in most shape interrogation methods.

Keywords

Gaussian Curvature Principal Curvature Polynomial System Freeform Surface Geodesic Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Stefanie Hahmann
    • 1
  • Alexander Belyaev
    • 2
  • Laurent Busé
    • 3
  • Gershon Elber
    • 4
  • Bernard Mourrain
    • 3
  • Christian Rössl
    • 3
  1. 1.Laboratoire Jean KuntzmannInstitut National Polytechnique de GrenobleFrance
  2. 2.MPII, Max Planck Institut für InformatikSaarbrückenGermany
  3. 3.INRIA Sophia-AntipolisGermany
  4. 4.Technion - Israel Institute of TechnologyHaifaIsrael

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