Scattered data fitting on surfaces using projected Powell-Sabin splines

Oleg Davydov, L.L. Schumaker, R. Martin (Editor), M. Sabin (Editor), J. Winkler (Editor)

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

9 Citations (Scopus)
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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 languageEnglish
Title of host publicationProceedings of the 12th IMA international conference on Mathematics of surfaces XII
PublisherSpringer-Verlag
Pages138-153
Number of pages16
ISBN (Print)978-3-540-73842-8
Publication statusPublished - 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.