Interpolation and Scattered Data Fitting on Manifolds using Projected Powell-Sabin Splines

Abstract

We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold Ω. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(Uξ , φξ)}ξ∈Ω satisfying certain conditions of smooth dependence on ξ. If Ω 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.

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Cite this paper

@inproceedings{Davydov2007InterpolationAS, title={Interpolation and Scattered Data Fitting on Manifolds using Projected Powell-Sabin Splines}, author={Oleg Davydov and Larry L. Schumaker}, year={2007} }