Skip to main content
SpringerLink
Log in

Approximation of Surfaces by Fairness Bicubic Splines

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

In this paper we present an approximation method of surfaces by a new type of splines, which we call fairness bicubic splines, from a given Lagrangian data set. An approximating problem of surface is obtained by minimizing a quadratic functional in a parametric space of bicubic splines. The existence and uniqueness of this problem are shown as long as a convergence result of the method is established. We analyze some numerical and graphical examples in order to prove the validity of our method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Attéia, Fonctions splines definies sur un ensemble convexe, Numer. Math. 12 (1968) 192–210.

    Google Scholar 

  2. P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amsterdam, 1978).

    Google Scholar 

  3. J. Duchon, Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces, RAIRO 10(12) (1976) 5–12.

    Google Scholar 

  4. G. Greiner, Surface construction based on variational principles, in: Wavelets Images and Surfaces Fitting, eds. P.J. Laurent, A. Le Méhauté and L.L. Shumaker (1994) pp. 277–286.

  5. A. Kouibia, M. Pasadas and J.J. Torrens, Fairness approximation by modified discrete smoothing Dmsplines, in: Mathematical Methods for Curves and Surfaces, Vol. II, eds. M. Daehlen, T. Lyche and L.L. Schumaker (Vanderbilt Univ. Press, Nashville, 1998) pp. 295–302.

    Google Scholar 

  6. A. Kouibia and M. Pasadas, Smoothing variational splines, Appl. Math. Lett. 13 (2000) 71–75.

    Google Scholar 

  7. A. Kouibia and M. Pasadas, Approximation by discrete variational splines, J. Comput. Appl.Math. 116 (2000) 145–156.

    Google Scholar 

  8. M.C. López de Silanes and R. Arcangéli, Sur la convergence des D m-splines d'ajustement pour des données exactes ou bruitées, Revista Matemática Universidad Complutense Madrid 4(2/3) (1991) 279–284.

  9. P.M. Prenter, Splines and Variational Methods (Wiley-Interscience, New York, 1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Sciences, University of Granada, Granada, Spain

    A. Kouibia & M. Pasadas

Authors
  1. A. Kouibia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Pasadas
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kouibia, A., Pasadas, M. Approximation of Surfaces by Fairness Bicubic Splines. Advances in Computational Mathematics 20, 87–103 (2004). https://doi.org/10.1023/A:1025805701726

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025805701726

Search

Navigation