Data-Weighted Least Square Progressive and Iterative Approximation and Related B-Spline Curve Fitting

In order to make the fitting curves interpolate some data points and approximate others,we propose the data-weighted least square progressive and iterative approximation(DW-LSPIA)algorithm and prove its convergence.Based on DW-LSPIA,we present a B-spline curve fitting scheme.First,we define initial weights for all data points to be interpolated and get a B-spline fitting curve by DW-LSPIA.Then we update all weights according to the errors between data points to be interpolated and their corresponding points on the fitting curve and update the B-spline fitting curve by DW-LSPIA again.We update the weights and fitting curves iteratively until the interpolation accuracy is satisfied.Examples showed that the B-spline fitting algorithm is robust,efficient and can obtain shape-preserving fitting curves.