Generalized B-splines’ geometric iterative fitting method with mutually different weights

Abstract

In this paper, a novel geometric iterative fitting method is presented which has a set of mutually different weights. It possesses the advantages of least square progressive iterative approximation method (abbr. LSPIA method) which can handle point sets of large sizes and adjust the number of control points and knot vector flexibly. The presenting method degrades into LSPIA method with appropriate choices of weights, and it illustrates better effects for the previous iteration steps comparing with the LSPIA method. Also, this method is further applied to generalized B-splines which have changing core functions (the mentioned generalized B-spline is a special generalization of classical B-spline with linear core function). Combining the advantages of generalized B-splines and choice of different weights, it can handle much more complicated practical problems. Detailed discussion about the choosing of core functions and weights is also given. Plentiful numerical examples are also presented to show the effectiveness of the method.