A robust iterative method devoted to pole curve fitting

A Newton-type method for constrained least-squares data-fitting with easy-to-control rational curves

“…In this way, once a procedure for computing the optimal weight values has been designed, the control points turn out to be automatically defined and hence the best-fitting curve results completely determined. Therefore, differently from standard NURBS fitting procedures, which require a complicated and expensive iterative algorithm to minimize (with respect to knots, control points and weights) a sum of squared Euclidean norms measuring the distance between the point set and the curve to be generated [3,4,9,[11][12][13][14][15], the least-squares fitting method we are going to propose will be performed exclusively to identify the choice of weights that guarantees the best reconstruction of the original data. Moreover, while the output of existing algorithms cannot always guarantee a fitting curve with a fair shape (namely with a curvature plot consisting of only a small number of monotone pieces), due to the definition of the novel fitter this follows easily and, whenever the degree of the curve primitive is larger than three, a curvature-continuous approximation of the original data is also ensured.…”

Ανακατασκευή 3δ Μοντέλων Σχεδίασης Με Υπολογιστή Βασισμένη Σε Γεωμετρικά Προσδιορισμένες Τομές

“…Another iterative algorithm [13] minimizes the sum of squared Euclidean norms with respect to three types of unknowns: the control points, the node values, and the weights. The method uses the projection of the data points on the approximant to improve the node values, and a gradient based technique to update the control point positions and the weight values.…”