Data-weighted Least Square Progressive And Iterative Approximation And Related B-spline Curve And Surface Fitting

The problem of curve and surface fitting has always been a key research topic in computer-aided geometric design,and many curve and surface fitting methods already exist.The progressive iterative approximation algorithm has been widely used in the computer-aided geometric design field.The Progressive and Iterative Approximation algorithm is used to continuously adjust the control vertices of the mixed curve and surface to obtain a good approximation curve and surface.The Progressive and Iterative Approximation algorithm has good adaptability and convergence stability,and it avoids the problem of solving equations in reverse engineering.Therefore,in industrial production,the use of B-spline to deal with the problem of fitting given data points has been widely used,and has a certain research significance so far.In this paper,we mainly present the method of making the fitting curves interpolate some data points and approximate others.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 present the iterative format and prove its convergence and extend method for surfaces.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.We present the proof of convergence properties,local properties,conformal analysis of DW-LSPIA algorithm in theory.Examples showed that the B-spline fitting algorithm is robust,efficient and can obtain shape-preserving fitting curves.