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A New Class of Interpolatory L-Splines with Adjoint End Conditions

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Curves and Surfaces (Curves and Surfaces 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9213))

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Abstract

A thin plate spline for interpolation of smooth transfinite data prescribed along concentric circles was recently proposed by Bejancu, using Kounchev’s polyspline method. The construction of the new ‘Beppo Levi polyspline’ surface reduces, via separation of variables, to that of a countable family of univariate L-splines, indexed by the frequency integer k. This paper establishes the existence, uniqueness and variational properties of the ‘Beppo Levi L-spline’ schemes corresponding to non-zero frequencies k. In this case, the resulting L-spline end conditions are formulated in terms of adjoint differential operators, unlike the usual ‘natural’ L-spline end conditions, which employ identical operators at both ends. Our L-spline error analysis leads to an \(L^{2}\)-error bound for transfinite surface interpolation with Beppo Levi polysplines.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Kuwait University, PO Box 5969, Safat 13060, Kuwait, Kuwait

    Aurelian Bejancu & Reyouf S. Al-Sahli

Authors
  1. Aurelian Bejancu
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  2. Reyouf S. Al-Sahli
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Corresponding author

Correspondence to Aurelian Bejancu .

Editor information

Editors and Affiliations

  1. INRIA, Sophia Antipolis, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. École Normale Supérieure, Paris, France

    Albert Cohen

  3. Arts Et Metiers ParisTech Lab de Sciences de l'Information, Paris, France

    Olivier Gibaru

  4. INSA de Rouen, LMI, Saint-Étienne-du-Rouvray, France

    Christian Gout

  5. Department of Mathematics, University of Oslo, Oslo, Norway

    Tom Lyche

  6. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Bejancu, A., Al-Sahli, R.S. (2015). A New Class of Interpolatory L-Splines with Adjoint End Conditions. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2014. Lecture Notes in Computer Science(), vol 9213. Springer, Cham. https://doi.org/10.1007/978-3-319-22804-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-22804-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22803-7

  • Online ISBN: 978-3-319-22804-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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