438	RWTH Publication No: 560962        2015        IGPM438.pdf
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
PUBLICATION	MASCOT15 Proceedings IMACS Series in Computational and Applied Mathematics (in press)