Optimizing NURBS Curves Fitting by Least Squares Progressive and Iterative Approximation

In order to make the NURBS curve fit scattered data points more accurately,a NURBS curve fitting optimization algorithm based on least square progressive iterative approximation(LSPIA)is proposed.Firstly,determine an initial NURBS and use the LSPIA algorithm to optimize the control vertices;then the data point parameters,the nodes and the weights of the fitting curve are optimized and improved;finally,the fitting NURBS curve with high precision is obtained by iterations.To avoid or reduce the impact of other variables,they are kept unchanged,when a type of variable is optimized.The NURBS curve fitting optimization algorithm based on LSPIA makes full use of the advantages of LSPIA algorithm.In the iterative process,the control points obtained from the previous iteration can be reused,so the operation time is saved.The example of the algorithm shows that the algorithm can obtain certain shape preservation effect.