Title: Fitting NURBS using separable least squares techniques

Authors: Per Bergström; Inge Söderkvist

Addresses: Department of Engineering Sciences and Mathematics, Division of Mathematical Sciences, Luleå University of Technology, SE-971 87 Luleå, Sweden. ' Department of Engineering Sciences and Mathematics, Division of Mathematical Sciences, Luleå University of Technology, SE-971 87 Luleå, Sweden

Abstract: We consider the problem of fitting a non-uniform rational B-spline (NURBS) curve to a set of data points by determining the control points and the weights using techniques aimed for solving separable least squares problems. The main technique under consideration is the variable projection method which utilises that the NURBS model depends linearly on its control points but non-linearly on the weights. The variable projection method can be used with the Gauss-Newton algorithm but also with Newton's algorithm. We investigate the efficiency of the different algorithms when fitting NURBS and observe that the variable projection methods do not perform as well as reported for its use on, e.g., exponential fitting problems.

Keywords: curve fitting; Gauss-Newton; Newton; non-uniform rational B-spline; NURBS; separable least squares; variable projection; numerical optimisation; exponential fitting.

DOI: 10.1504/IJMMNO.2012.049600

International Journal of Mathematical Modelling and Numerical Optimisation, 2012 Vol.3 No.4, pp.319 - 334

Received: 08 Sep 2011
Accepted: 23 Jan 2012

Published online: 30 Aug 2014 *

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