Scattered data fitting on surfaces using projected Powell-Sabin splines

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Davydov, Oleg and Schumaker, L.L.; Martin, R. and Sabin, M. and Winkler, J., eds. (2007) Scattered data fitting on surfaces using projected Powell-Sabin splines. In: Proceedings of the 12th IMA international conference on Mathematics of surfaces XII. Springer-Verlag, pp. 138-153. ISBN 978-3-540-73842-8 (http://personal.strath.ac.uk/oleg.davydov/man1.pdf)

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Abstract

We present C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ω embedded into R3. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorithms with some numerical examples, which, in particular, confirm the O(h3) order of convergence as the data becomes dense

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