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Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration pp 109–125Cite as

Stability and Computation of Medial Axes - a State-of-the-Art Report

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

Summary

The medial axis of a geometric shape captures its connectivity. In spite of its inherent instability, it has found applications in a number of areas that deal with shapes. In this survey paper, we focus on results that shed light on this instability and use the new insights to generate simplified and stable modifications of the medial axis.

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Author information

Authors and Affiliations

  1. Gipsa-lab, ENSE 3, Domaine Universitaire, BP 46, 38402, Saint Martin d’Hères, France

    Dominique Attali

  2. INRIA, 2004 Route des Lucioles, BP 93, 06904, Sophia-Antipolis, France

    Jean-Daniel Boissonnat

  3. Department of Computer Science, Duke University, Durham, and Raindrop Geomagic, Research Triangle Park, NC, USA

    Herbert Edelsbrunner

  4. Department of Computer Science, Duke University, Raindrop Geomagic, Research Triangle Park, NC, USA

    Herbert Edelsbrunner

Authors
  1. Dominique Attali
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  2. Jean-Daniel Boissonnat
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  3. Herbert Edelsbrunner
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Editor information

Editors and Affiliations

  1. School of Computing Science, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    Torsten Möller  & Robert D. Russell  & 

  2. Department of Computer Science, University of California, Davis, 1 Shields Avenue, Davis, CA, 95616-8562, USA

    Bernd Hamann

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Attali, D., Boissonnat, JD., Edelsbrunner, H. (2009). Stability and Computation of Medial Axes - a State-of-the-Art Report. In: Möller, T., Hamann, B., Russell, R.D. (eds) Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b106657_6

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