Curve Fitting Based On Least Squares Asymptotic Iteration And Overrelaxation Iteration Algorithms

In the field of computer graphics,how to fit scattered data points efficiently and accurately has been the main research direction of many scholars.The fitting of scattered data points involves the sampling of data points.However,due to the irregular and uneven surfaces of many objects and the random errors generated in the sampling process of data points,the sampled data is usually discrete and needs to be processed.Therefore,choosing appropriate methods and basis functions to fit these random data points is the key to solve the problem.The least square asymptotic approximation algorithm(LSPIA algorithm)can handle large data sets and adjust the number of control points and node vector flexibly.Overrelaxation iterative algorithm is an effective method to solve linear equations because of the advantages of small storage space and simple program.B-spline and radial basis are the two most commonly used bases for data fitting.Therefore,in this paper,cubic uniform B-splines and truncated exponential radial basis(TERBF)are used as basis functions,and LSPIA algorithm and overrelaxation iterative algorithm are used to fit curves.The main research contents of this dissertation are as follows:First,in order to improve the convergence speed and adjust the local curve fitting effect,a compound LSPIA algorithm with different weight factors under cubic uniform B-spline curve is proposed based on the compound LSPIA algorithm,and it is proved that the algorithm is convergent when the weight factors in the weight matrix meet the given conditions.The experimental results show that the cubic uniform B-spline curve with different weight factors composite LSPIA algorithm can adjust the fitting shape of the local curve and reduce the fitting error of the local curve by adjusting the weight factors of some control points.On the other hand,it can also improve the overall convergence speed and accelerate the algorithm.Second,the truncated exponential radial basis function of positive definite compact support is used to interpolate the scattered data and construct the TERBF interpolation function.In order to improve the accuracy of interpolation function fitting curve,a data point weighted LSPIA(DW-LSPIA)algorithm based on TERBF interpolation function is proposed.The iterative format of interpolation function coefficients is given and the convergence of the algorithm is proved.The experimental results show that the DW-LSPIA algorithm based on TERBF interpolation function is easy to operate,flexible and controllable,and can adjust the error accuracy within a certain range,so that the curve fitting effect is better.Finally,In order to improve the accuracy of TERBF interpolation function and compare with DW-LSPIA algorithm,an overrelaxation iterative method based on TERBF interpolation function is proposed.When the relaxation factor satisfies the given conditions,the iterative convergence is achieved.The optimal relaxation factor was determined by golden section method.Experimental results show that under the same constraints,the overrelaxation iterative method based on TERBF interpolation function has fewer iterations,shorter time and higher curve fitting accuracy than the DW-LSPIA algorithm.Figure [15] table [13] reference [67]...