Scattered data fitting on surfaces using projected Powell-Sabin splines

Authors:
Oleg Davydov;Larry L. Schumaker
Affiliations:
Department of Mathematics, University of Strathclyde, Glasgow, UK;Department of Mathematics, Vanderbilt University, Nashville, TN
Venue:
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Year:
2007

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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.