Local Progressive and Iterative Approximation for Least Squares B-spline Curve and Surface Fitting
Progressive and iterative approximation for least squares B-spline curve and surface fitting(LSPIA),as an effective method for fitting large data,has attracted the attention of many researchers.To address the problem that the LSPIA algorithm is less effective in fitting local data points,a local LSPIA algorithm,called LOCAL-LSPIA,is proposed.Firstly,the initial curve is given and some of the data points are selected from the given data points.Then,the control points to be adjusted are selected on the initial curve.Finally,LOCAL-LSPIA is used to generate a series of locally varying fitted curves(surfaces)by iteratively adjus-ting this part of the control points and ensuring that the limits of the generated curves(surfaces)are the least-squares results of fitting some of the data points while adjusting only this part of the control points.Experimental results on multiple curve-surface fitting show that the LOCAL-LSPIA algorithm requires fewer steps and shorter time than the LSPIA algorithm to achieve the same local fitting accuracy.Therefore,LOCAL-LSPIA is effective and has a faster convergence rate than LSPIA algorithm in the case of fitting local data.
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