Numerical Algorithms

, Volume 12, Issue 1, pp 215–231 | Cite as

Smoothing scattered data with a monotone Powell-Sabin spline surface

  • Karin Willemans
  • Paul Dierckx


An algorithm is presented for smoothing arbitrarily distributed noisy measurement data with a Powell-Sabin spline surface that satisfies necessary and sufficient monotonicity conditions. The Powell-Sabin spline is expressed as a linear combination of locally supported basis functions used in their Bernstein-Bézier representation. Numerical examples are given to illustrate the performance of the algorithm.


Conforming triangulations Bézier ordinates Powell-Sabin splines shape preservation monotonicity 

AMS(MOS) subject classification

41A15 41A29 65D07 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R.K. Beatson and Z. Ziegler, Monotonicity preserving surface interpolation, SIAM J. Numer. Anal. 22 (1985) 401–411.Google Scholar
  2. [2]
    R.E. Carlson, Shape preserving interpolation, inAlgorithms for Approximation, eds. J.C. Mason and M.G. Cox (Clarendon Press, Oxford, 1987) pp. 97–113.Google Scholar
  3. [3]
    R.E. Carlson and F.N. Fritsch, Monotone piecewise bicubic interpolation, SIAM J. Numer. Anal. 22 (1985) 386–400.Google Scholar
  4. [4]
    P. Costantini and F. Fontanella, Shape-preserving bivariate interpolation, SIAM J. Numer. Anal. 27 (1990) 488–506.Google Scholar
  5. [5]
    P. Dierckx,Curve and Surface Fitting with Splines, Monographs on Numerical Analysis (Clarendon Press, Oxford, 1993).Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Karin Willemans
    • 1
  • Paul Dierckx
    • 1
  1. 1.Department of Computer ScienceKatholieke Universiteit LeuvenLeuvenBelgium

Personalised recommendations