NURBS曲线拟合的最小二乘渐进迭代逼近优化算法

为了使NURBS曲线更精确地拟合散乱数据点,提出了一种基于最小二乘渐进迭代逼近(least square progressive and iterative approximation,LSPIA)的NURBS曲线拟合优化算法.首先,确定一条初始NURBS曲线,利用LSPIA算法优化控制顶点;然后,分别优化数据点参数,拟合曲线的节点和权因子,每优化好一个变量,重新优化控制顶点;最后,经多次优化迭代得到高精度的NURBS拟合曲线.在优化每类变量时,为了避免被其他变量影响,保持其他变量不变.基于LSPIA的NURBS曲线拟合优化算法充分利用了LSPIA算法的优点,在迭代过程中,可以重复使用前一迭代步骤得到的控制顶点等数据,从而节省了运算时间.算法实例表明,该算法能获得一定保形效果.

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.