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Chordal Cubic Spline Quasi Interpolation

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Curves and Surfaces (Curves and Surfaces 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6920))

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Abstract

This paper studies cubic spline quasi-interpolation of parametric curves through sequences of points in any space dimension. We show that if the parameter values are chosen by chord length, the order of accuracy is four. We also use this chordal cubic spline quasi interpolant to approximate the arc length derivatives and the length of the parametric curve.

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References

  1. Ahlberg, J.H., Nilson, E.N., Walsh, J.L.: The theory of splines and their applications. Academic Press, New York (1967)

    MATH  Google Scholar 

  2. Barrera, D., Ibañez, M.J., Sbibih, D., Sablonnière, P.: Near best univariate discrete quasi-interpolants on non-uniform partitions. Constr. Approx. 28, 237–251 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, G., Chui, C.K., Lai, M.J.: Construction of real-time spline quasi-interpolation schemes. Approx. Theory Appl. 4, 61–75 (1988)

    MathSciNet  MATH  Google Scholar 

  4. DeVore, R.A., Lorentz, G.G.: Constructive approximation. Springer, Berlin (1993)

    Book  MATH  Google Scholar 

  5. Floater, M.S.: Arc length estimation and the convergence of parametric polynomial interpolation. BIT 45, 679–694 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Floater, M.S.: Chordal cubic spline interpolation is fourth order accurate. IMA J. Numer. Anal. 26(1), 25–33 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lee, B.G., Lyche, T., Schumaker, L.L.: Some examples of quasi-interpolants constructed from local spline projectors. In: Lyche, T., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces, Oslo 2000, pp. 243–252 (2000)

    Google Scholar 

  8. Lyche, T., Mørken, K.: A metric for parametric approximation. In: Laurent, P.J., Le Méhauté, A., Schumaker, L.L. (eds.) Curves and Surfaces, pp. 311–318. A. K. Peters, Wellesley (1994)

    Google Scholar 

  9. Rabut, C.: Higher level m-harmonic cardinal B-splines. Numer. Algorithms 2, 63–84 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sablonnière, P.: Univariate spline quasi-interpolants and applications to numerical analysis. Rend. Sem. Mat. Univ. Pol. Torino 63(2), 107–118 (2005)

    MathSciNet  MATH  Google Scholar 

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Authors
  1. P. Sablonnière
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  2. D. Sbibih
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  3. M. Tahrichi
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Editor information

Editors and Affiliations

  1. INRIA Sophia-Antipolis, 2004 Route des Lucioles, BP 93, 06902, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. Laboratoire LJK, University Joseph Fourier, BP 53, 38420, Grenoble Cedex 9, France

    Patrick Chenin

  3. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, 75005, Paris, France

    Albert Cohen

  4. Laboratoire de Mathématiques, INSA Rouen, Avenue de l’Université, 76800, St. Etienne du Rouvray, France

    Christian Gout

  5. University of Oslo, DMA, Blindern, P.O.Box 1053, 0316, Oslo, Norway

    Tom Lyche

  6. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

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

    Larry Schumaker

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Sablonnière, P., Sbibih, D., Tahrichi, M. (2012). Chordal Cubic Spline Quasi Interpolation. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_40

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  • DOI: https://doi.org/10.1007/978-3-642-27413-8_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27412-1

  • Online ISBN: 978-3-642-27413-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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