Scattered Data Fitting on Surfaces Using Projected Powell-Sabin Splines

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.

• Type: Conference
• Year: 2007
• Where: IMAMS
• Authors: Oleg Davydov, Larry L. Schumaker
• Keywords: Bivariate Powell-sabin Interpolation, Data fitting Method, IMAMS 2007, Mathematics, Two-dimensional Smooth Manifold