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Reparameterization of Curves and Surfaces with Respect to Their Convolution

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Mathematical Methods for Curves and Surfaces (MMCS 2008)

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

Abstract

Given two parametric planar curves or surfaces we find their new parameterizations (which we call coherent) permitting to compute their convolution by simply adding the points with the same parameter values. Several approaches based on rational reparameterization of one or both input objects or direct computation of new parameterizations are shown. Using the Gröbner basis theory we decide the simplest possible way for obtaining coherent parametrizations. We also show that coherent parameterizations exist whenever the convolution hypersurface is rational.

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Author information

Authors and Affiliations

  1. Faculty of Applied Sciences, Department of Mathematics, University of West Bohemia, Univerzitní 8, 301 00, Plzeň, Czech Republic

    Miroslav Lávička, Bohumír Bastl & Zbyněk Šír

Authors
  1. Miroslav Lávička
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  2. Bohumír Bastl
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  3. Zbyněk Šír
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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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Lávička, M., Bastl, B., Šír, Z. (2010). Reparameterization of Curves and Surfaces with Respect to Their Convolution. 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_19

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_19

  • 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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