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.
Original language | English |
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Pages (from-to) | 785-805 |
Number of pages | 21 |
Journal | IMA Journal of Numerical Analysis |
Volume | 28 |
Issue number | 4 |
DOIs | |
Publication status | Published - Oct 2008 |
Keywords
- interpolation
- scattered data fitting
- data on surfaces and manifolds
- Powell-Sabin spline