基于四次B样条的曲线逼近算法

An approximate algorithm based on quartic B-spline curves

考虑到插值算法增减节点困难,传统逼近算法精度不够等缺点,有文献提出一种基于三次B样条的曲线逼近算法。该算法通过迭代逼近,提高了计算速度与精度。在系统研究此算法的基础上,将该算法推广到四次B样条,使其具有三阶可导性,并给出该算法收敛性的理论证明。最后用该算法对常用函数进行逼近效果实验。结果表明,所提出的四次B样条的曲线逼近算法收敛速度更快,且能够满足更高精度的实际工业生产需要。

To overcome the shortcomings of the traditional interpolation spline that is difficult to add or delete points and the inaccuracy of the traditional approximate spline, we propose an approximate algorithm based on the cubic B-spline. The algorithm, which is based on the approximation and the iteration, improves the calculation speed and precision. Based on the periodic cubic B-spline curves, the algorithm extends to quartic B-spline, which is third derivative. Besides, the theoretical proof of the conver- gence of the algorithm is given out. Finally, the numerical approximation experiments on common functions show that the algorithm has a faster convergence speed and can meet higher practical industrial needs.