|Preprint-No.:||< 438 >||Published in:||November 2015||PDF-File:||IGPM438.pdf|
|Title:||Fast Approximation Methods for Fitting Surfaces to Unorganized Point Clouds|
We present and analyze a novel fast method for scattered data approximation with curves / surfaces which have a representation as a linear combination of smooth basis functions associated with the control points. Our technique can be applied to standard Bezier and B-spline curves / surfaces as well as for subdivision schemes. The approach can be formulated in such way that for the iteration we have a standard least squares problem in each step. A regularization term that expresses the fairness of the intermediate and / or final result can be added. Adaptivity is easily integrated in our concept. Furthermore our approach is well suited for reparameterization occurring in grid generation.
|Keywords:||Splines, Multivariate Approximation, Fairing, Numerical Analysis, Numerical Linear Algebra|