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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
Article

Abstract

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.

Keywords

Conforming triangulations Bézier ordinates Powell-Sabin splines shape preservation monotonicity 

AMS(MOS) subject classification

41A15 41A29 65D07 

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References

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    R.K. Beatson and Z. Ziegler, Monotonicity preserving surface interpolation, SIAM J. Numer. Anal. 22 (1985) 401–411.Google Scholar
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    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
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    R.E. Carlson and F.N. Fritsch, Monotone piecewise bicubic interpolation, SIAM J. Numer. Anal. 22 (1985) 386–400.Google Scholar
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    P. Costantini and F. Fontanella, Shape-preserving bivariate interpolation, SIAM J. Numer. Anal. 27 (1990) 488–506.Google Scholar
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    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

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