Algorithms for surface fitting using Powell-Sabin splines

Algorithms are presented for fitting a Powell-Sabin spline toa set of scattered data. Both the detemination of least-squaresand smoothing splines are considered. For the latter we adoptthe philosophy of an existing tensor product spline algorithm.The triangulation is determined in an automatic and adaptiveway. The algorithm employs a single parameter to control thetradeoff between closeness of fit and smoothness of fit. The Powell-Sabin splines are represented in terms of locallysupported basis functions. The use of the Bernstein-Bzier ordinatesof these B-splines results in efficient calculations. Numericalexamples illustrate the usefulness of the given algorithms.