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P. DIERCKX, S. van LEEMPUT, T. VERMEIRE, Algorithms for surface fitting using Powell-Sabin splines, IMA Journal of Numerical Analysis, Volume 12, Issue 2, April 1992, Pages 271–299, https://doi.org/10.1093/imanum/12.2.271
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Abstract
Algorithms are presented for fitting a Powell-Sabin spline to a set of scattered data. Both the detemination of least-squares and smoothing splines are considered. For the latter we adopt the philosophy of an existing tensor product spline algorithm. The triangulation is determined in an automatic and adaptive way. The algorithm employs a single parameter to control the tradeoff between closeness of fit and smoothness of fit.
The Powell-Sabin splines are represented in terms of locally supported basis functions. The use of the Bernstein-Bézier ordinates of these B-splines results in efficient calculations. Numerical examples illustrate the usefulness of the given algorithms.