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On the Local Approximation Power of Quasi-Hierarchical Powell-Sabin Splines

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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))

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Abstract

Quasi-hierarchical Powell-Sabin (QHPS) splines are quadratic splines with a global C 1-continuity. They are defined on a locally refined hierarchical triangulation, and they admit a compact representation in a normalized B-spline basis. We show that sufficiently smooth functions and their derivatives can be approximated up to optimal order by a Hermite interpolating QHPS spline.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001, Leuven, Belgium

    Hendrik Speleers, Paul Dierckx & Stefan Vandewalle

Authors
  1. Hendrik Speleers
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  2. Paul Dierckx
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  3. Stefan Vandewalle
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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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Speleers, H., Dierckx, P., Vandewalle, S. (2010). On the Local Approximation Power of Quasi-Hierarchical Powell-Sabin Splines. 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_27

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_27

  • 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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