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Shape Preserving Hermite Interpolation by Rational Biquadratic 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

We construct a rational biquadratic spline interpolating an arbitrary function and its gradient at vertices of a rectangular grid of a domain \({\it \Omega}=[a,b]\times[c,d]\). The introduction of the control net allows to give sufficient conditions ensuring the bimonotonicity or the biconvexity of the underlying surface.

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Author information

Authors and Affiliations

  1. INSA de Rennes, 20 avenue des Buttes de Coësmes, CS 14315, F-35043, Rennes Cédex, France

    Paul Sablonnière

Authors
  1. Paul Sablonnière
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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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Sablonnière, P. (2010). Shape Preserving Hermite Interpolation by Rational Biquadratic 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_24

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_24

  • 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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