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
|Title of host publication||Proceedings of the 12th IMA international conference on Mathematics of surfaces XII|
|Number of pages||16|
|Publication status||Published - 2007|
- powell-sabine splines
- scattered data fitting
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.