Application Of Least Square Progressive Iterative Approximation In Fitting Scattered Data Points

Data fitting is a widely used modeling tool in data processing and geometric design.Generally speaking,data fitting is to get some unknown data through some method,and then find a function curve to express the relationship between the curves,and ensure that most data points can fall on the curve.Progressive iterative approximation(PIA),as an effective and intuitive data fitting method,has attracted wide attention in recent years.The algorithm is self-adaptive and stable convergence,simple and intuitive,and easy to program.The weighted progressive iterative approximation(WPIA)accelerates the iterative process of the traditional PIA method by weighting the adjustment vector.The curve fitted by the least square progressive iterative approximation is the least squares fitting result of the given data points.The research contents of this paper are as follows:In order to speed up the convergence of the progressive iterative approximation in the process of data fitting and overcome the defect that the general B-spline curve cannot represent curves such as circle or ellipse,this paper discusses the progressive-iterative approximation and the weighted progressive-iterative approximation of triangular ?-B curves(surfaces)with shape parameters.The shape parameter ? and the weight w with the fastest convergence speed are deduced according to the iterative matrix,and the convergence analysis of the method is carried out.In order to control some data points independently,adjust the shape of local curve and reduce least squares iteration error of local curve in the iterative process of B-spline fitting target curve,a least square progressive iterative approximation method with different weights is proposed in this paper.First,we assign a uniform initial weight to each data point,and use the least square progressive iterative approximation method to generate a B-spline fitting curve;secondly,we adjust the weights corresponding to some data points,and use the least squares asymptotic iterative method with different weights.The approximation method generates the B-spline fitting curve;finally,the fitting errors before and after adjustment are compared.In order to improve the shape control ability of cubic triangular B(?)zier surface,this paper uses the cubic triangular Bernstein basis with two shape parameters to explore the least squares progressive-iterative approximation of the triangular B(?)zier surface.In this paper,the convergence proof of LSPIA property of cubic triangular B(?)zier surface is given,and the weights of LSPIA when the convergence speed reaches the fastest are given.