Least square geometric iterative fitting method for generalized B-spline curves with two different kinds of weights

Generalized B-spline bases are generated by monotone increasing and continuous “core” functions; thus generalized B-spline curves and surfaces not only hold almost the same perfect properties which classical B-splines hold but also show more flexibility in practical applications. Geometric iterative method (also known as progressive iterative approximation method) has good adaptability and stability and is popular due to its straight geometric meaning. However, in classical geometric iterative method, the number of control points is the same as that of data points. It is not suitable when large numbers of data points need to be fitted. In order to combine the advantages of generalized B-splines with those of geometric iterative method, a fresh least square geometric iterative fitting method for generalized B-splines is given, and two different kinds of weights are also introduced. The fitting method develops a series of fitting curves by adjusting control points iteratively, and the limit curve is weighted least square fitting result to the given large data points. Detailed discussion about choosing of core functions and two kinds of weights are also given. Plentiful numerical examples are also presented to show the effectiveness of the method.