An iterative method for rational pole curve fitting

Abstract

This paper adresses the problem of least-square fitting with rational pole curves. The issue is to minimize a sum of squared Euclidean norms with respect to three types of unknowns: the control points, the node values, and the weights. A new iterative algorithm is proposed to solve this problem. The method alternates between three steps to converge towards a solution. One step uses the projection of the data points on the approximant to improve the node values, the two others use a gradient based technique to update the control point positions and the weight values. Experimental results are proposed with rational Bézier and NURBS curves.