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Shape Interrogation

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Shape Analysis and Structuring

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

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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.

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Authors and Affiliations

  1. Laboratoire Jean Kuntzmann, Institut National Polytechnique de Grenoble, France

    Stefanie Hahmann

  2. MPII, Max Planck Institut für Informatik, Saarbrücken, Germany

    Alexander Belyaev

  3. INRIA Sophia-Antipolis, Germany

    Laurent Busé, Bernard Mourrain & Christian Rössl

  4. Technion - Israel Institute of Technology, Haifa, 32000, Israel

    Gershon Elber

Authors
  1. Stefanie Hahmann
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  2. Alexander Belyaev
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  3. Laurent Busé
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  4. Gershon Elber
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  5. Bernard Mourrain
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  6. Christian Rössl
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  1. Department of Computer and Information Sciences (DISI), University of Genova, Via Dodecaneso, 35, 16146, Genova, Italy

    Leila De Floriani

  2. Department of Computer Science, University of Maryland, College Park, MD 20740, USA

    Leila De Floriani

  3. Istituto per la Matematica Applicata e le Tecnologie Informatiche, Consiglio Nazionale delle Ricerche, Via De Marini, 6, 16149, Genova, Italy

    Michela Spagnuolo

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Hahmann, S., Belyaev, A., Busé, L., Elber, G., Mourrain, B., Rössl, C. (2008). Shape Interrogation. In: De Floriani, L., Spagnuolo, M. (eds) Shape Analysis and Structuring. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33265-7_1

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