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Interpolation and scattered data fitting on manifolds using projected Powell–Sabin splines

Davydov, O. and Schumaker, L.L. (2008) Interpolation and scattered data fitting on manifolds using projected Powell–Sabin splines. IMA Journal of Numerical Analysis, 28 (4). pp. 785-805. ISSN 0272-4979

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Abstract

We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(Uξ , ξ)}ξ∈ satisfying certain conditions of smooth dependence on ξ. If is a C2-manifold embedded into R3, then projections into tangent planes can be employed. The data fitting method is a two-stage method. We prove that the resulting function on the manifold is continuously differentiable, and establish error bounds for both methods for the case when the data are generated by a smooth function.

Item type: Article
ID code: 15122
Keywords: interpolation, scattered data fitting, data on surfaces and manifolds, Powell-Sabin spline, Mathematics, Computational Mathematics, Applied Mathematics, Mathematics(all)
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Mrs Irene Spencer
Date deposited: 03 Feb 2010 19:05
Last modified: 19 Jan 2019 07:57
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URI: https://strathprints.strath.ac.uk/id/eprint/15122
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