Interpolation and scattered data fitting on manifolds using projected Powell–Sabin splines

O. Davydov, L.L. Schumaker

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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 languageEnglish
Pages (from-to)785-805
Number of pages21
JournalIMA Journal of Numerical Analysis
Issue number4
Publication statusPublished - Oct 2008


  • interpolation
  • scattered data fitting
  • data on surfaces and manifolds
  • Powell-Sabin spline

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