### 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

Original language | English |
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Title of host publication | Proceedings of the 12th IMA international conference on Mathematics of surfaces XII |

Publisher | Springer-Verlag |

Pages | 138-153 |

Number of pages | 16 |

ISBN (Print) | 978-3-540-73842-8 |

Publication status | Published - 2007 |

### Keywords

- powell-sabine splines
- scattered data fitting
- statistics

## Cite this

Davydov, O., Schumaker, L. L., Martin, R. (Ed.), Sabin, M. (Ed.), & Winkler, J. (Ed.) (2007). Scattered data fitting on surfaces using projected Powell-Sabin splines. In

*Proceedings of the 12th IMA international conference on Mathematics of surfaces XII*(pp. 138-153). Springer-Verlag.