Skip to main content
SpringerLink
Log in

Scattered data interpolation by bivariate C1-piecewise quadratic functions

  • Published:
Approximation Theory and its Applications

Abstract

In this paper, we propose a completely local scheme based on continuously differentiable quadratic piecewise polynomials for interpolating scattered positional data in the plane, in such a way that quadratic polynomials are reproduced exactly. We present some numerical examples and applications to contour plotting.

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. Chui, C. K. and R. H. Wang, Multivariate Spline Spaces, J. Math. Analysis and Applications, 94 (1983), 197–221.

    Article  MATH  MathSciNet  Google Scholar 

  2. Dahmen, W., Subdivision algorithms-Recent Results, Some Extensions and Further Developments, Proc. Conf. Algorithms for the Approximation of Functions and data ed. J. C. Mason and M. G. Cox, Shrivenham, 1985, 21–49.

  3. Dahmen, W., DeVore, R. and K. Scherer, Multi-Dimensional Spline Approximation, SIAM J. Numer. Anal., 17 (1980), 380–402.

    Article  MATH  MathSciNet  Google Scholar 

  4. Dahmen, W., Goodman, T. N. T. and C. A. Micchelli, Compactly Supported Fundamental Functions for Spline Interpolation, Numer. Math. 52 (1988), 639–664.

    Article  MATH  MathSciNet  Google Scholar 

  5. Farin, G., Triangular Bernstein-Bézier patches, Computer Aided Geometric Design, 3 (1986), 83–127.

    Article  MathSciNet  Google Scholar 

  6. Franke, R., Scattered Data Interpolation: Tests of Some Methods, Math. Comp., 38 (1982), 181–200.

    Article  MATH  MathSciNet  Google Scholar 

  7. Gmeling Meyling, R. H. J. and P. R. Pfluger, On the Dimension of the Spline Space S 12 (Δ) in Special Cases, Multivariate Approximation Theory III, ed. W. Schempp and K. Zeller, Birkhäuser, Basel, 1985, 180–190.

    Google Scholar 

  8. Heindl, G., Interpolation and Approximation by Piecewise Quadratic C1-functions of two Variables, Multivariate Approximation Theory, ed. W. Schempp and Zeller, K. Birkäuser, Basel, 1979, 146–161.

    Google Scholar 

  9. Lawson, C. L., Software for C1-surface Interpolation, Mathematical Software III, ed. J. R. Rice, Academic Press, New York, 1977, 161–194.

    Google Scholar 

  10. Powell, M. J. D., Piecewise Quadratic Surface Fitting for Contour Plotting, Software for Numerical Mathematics, ed. D. J. Evans, Academic Press, New York, 1974, 253–271.

    Google Scholar 

  11. Powell, M. J. D. and M. A. Sabin, Piecewise Quadratic Approximations on Triangles, ACM TOMS, 3 (1977), 316–325.

    Article  MATH  MathSciNet  Google Scholar 

  12. Schumaker, L. L., Bounds on the Dimension of Spaces of Multivariate Piecewise Polynomials, Rocky Mountain J. of Math., 14 (1984), 251–264.

    Article  MATH  MathSciNet  Google Scholar 

  13. Ursem, J. H. M., Interpolation of Bivariate Functions by Quadratic C1-splines, masters thesis, University of Amsterdam, 1986.

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Freie Universitat Berlin, Berlin, Germany

    W. Dahmen

  2. Royal Duxch/Shell, Exploration and hoduction haloratory, Ryswyk, The Netherlands

    R. H. J. Gmelig Meyling

  3. Computer Science Department, University of Amsterdam, The Netherlands

    J. H. M. Ursem

Authors
  1. W. Dahmen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. H. J. Gmelig Meyling
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. H. M. Ursem
    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

Dahmen, W., Gmelig Meyling, R.H.J. & Ursem, J.H.M. Scattered data interpolation by bivariate C1-piecewise quadratic functions. Approx. Theory & its Appl. 6, 6–29 (1990). https://doi.org/10.1007/BF02836093

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02836093

Keywords

Search

Navigation