Numerical Algorithms

, Volume 9, Issue 2, pp 263–276 | Cite as

Nonnegative surface fitting with Powell-Sabin splines

  • Karin Willemans
  • Paul Dierckx


Algorithms are presented for fitting a nonnegative Powell-Sabin spline to a set of scattered data. Existing necessary and sufficient nonnegativity conditions for a quadratic polynomial on a triangle are used to compose a set of necessary and sufficient nonnegativity constraints for the PS-spline. The PS-spline is expressed as a linear combination of locally supported basis functions, of which the Bernstein-Bézier representation is considered to improve the efficiency. Numerical examples illustrate the profit of nonnegative surface fitting with Powell-Sabin splines.


Conforming triangulations Bézier ordinates Powell-Sabin splines nonnegativity 

AMS(MOS) subject classification

41A15 41A29 65D07 


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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

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

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