438 IGPM438.pdf        November 2015
TITLE Fast Approximation Methods for Fitting Surfaces to Unorganized Point Clouds
AUTHORS Karl-Heinz Brakhage
ABSTRACT 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
IMACS Series in Computational and Applied Mathematics (in press)