A robust iterative method devoted to pole curve fitting

Applied to the general formulation of pole curves, least-square fining basically corresponds to minimize a quadratic error function d(P, t) (a sum of squared Euclidean norms) which depends on the set of control points P and nodes t linked to data points. We propose an iterative algorithm alternating between optimizing d(P, t) over t and P. Node corrections are achieved through the projection of data points on the approximation curve. Control points are updated relatively to the gradient of the error function. The method is convergent and directly applicable to every type of pole curve. Experimental results are proposed with Bezier and B-spline curves to emphasize the efficiency of this method.