B-Spline Curve Fitting With Energy Term Based On LSPIA And Its Promotion

Using B-spline curves to fit scattered data points has always been an important research topic in computer-aided geometric design,progressive iterative approximation(PIA)is an important method in data fitting,and the energy of the curve is also a factor that needs to be considered in the fitting process.Therefore,it is of certain research significance to achieve B-spline fitting with energy terms by PIA method.In order to minimize the energy of B-spline curve under the fitting error accuracy,a B-spline fitting algorithm with energy term is proposed.Firstly,LSPIA is used to obtain a B-spline curve that meets the accuracy of fitting error as the initial fitting curve;then the energy term is added,and the energy coefficient proposed by M.S.Floater is used as the initial value;a new fitting curve is generated by the LSPIA method with energy term.Then,according to the fitting error,the energy coefficient is adjusted by dichotomy method,and continue to use the LSPIA method with energy term to obtain a new B-spline curve;until a B-spline curve with the largest possible energy coefficient is found that meets the precision of the fitting error.The example shoes that the algorithm has good robustness and can also reduce the energy of the fitting curve.In the above process,we first use the LSPIA method to fit the data points,use this method to obtain the fitting curve,and in the case of not meeting the fit error accuracy,by increasing the number of control points,meet the fit error accuracy requirements.This method is linear and easy to understand and calculate,but the fitting efficiency is not necessarily good.Therefore,according to another method,we gradually increase the B-spline node method,also known as the incremental LSPIA method,to achieve the fitting error accuracy requirements.First,the node vectors of the initial B-spline curve control vertex and the initial B-spline basis function are given,and then the node vector and the control vertex are gradually increased according to the given method according to the fitting error accuracy until the fitting error accuracy is met.This method can optimize the node vector and has a good fitting effect.We then add an energy term to the curve based on the curve that meets the accuracy of the fitting error using the incremental LSPIA method,and the energy matrix in this case is determined by the optimized node vector.The nodal vector of the B-spline curve has a greater influence on the shape of the curve,and the fitting curve after the node optimization is obtained before the energy term is added,which can efficiently improve the quality of the fitted curve after adding the energy term.