## 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].

### MSC:

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

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