Scattered data fitting on surfaces using projected Powell-Sabin splines. (English) Zbl 1126.65012

Martin, Ralph (ed.) et al., Mathematics of surfaces XII. 12th IMA international conference, Sheffield, UK, September 4–6, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73842-8/pbk). Lecture Notes in Computer Science 4647, 138-153 (2007).
Summary: We present \(C ^1\) methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold \(\Omega \) embedded into \(\mathbb R^3\). 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 \({\mathcal O}(h^3)\) order of convergence as the data becomes dense.
For the entire collection see [Zbl 1122.68007].


65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines


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