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Fat Arcs for Implicitly Defined Curves

  • Conference paper
Mathematical Methods for Curves and Surfaces (MMCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5862))

Abstract

We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein–Bézier representation. We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and rational parametric surfaces.

This work was supported by the Austrian Science Found (FWF) through the Doctoral Program in Computational Mathematics, subproject 3.

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Author information

Authors and Affiliations

  1. Doctoral Program in Computational Mathematics, Austria

    Szilvia Béla

  2. Institute of Applied Geometry, Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria

    Bert Jüttler

Authors
  1. Szilvia Béla
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  2. Bert Jüttler
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Norway

    Morten Dæhlen  & Tom Lyche  & 

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  3. INSA de Rennes, Rennes, France

    Jean-Louis Merrien

  4. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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Béla, S., Jüttler, B. (2010). Fat Arcs for Implicitly Defined Curves. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11619-3

  • Online ISBN: 978-3-642-11620-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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