中文摘要：

为了改进传统的插值样条曲线算法不易于后期处理和实时局部修改、B样条算法不能满足精度要求的缺点，提出了一种基于三次B样条的曲线逼近算法。该算法以三次B样条为基础对曲线的逼近领域进行了研究，通过大量的数值实验证明了该算法的可行性及高效性。该算法通过结合插值样条与B样条的各种优点，有效避免了传统算法的不足。同时，对该算法的收敛性进行了理论证明。数值实验表明了该算法具有收敛速度快、精度高且编程易实现等优点，为曲线研究提供了可供参考的有效算法。

英文摘要：

In order to improve the shortcomings of the traditional interpolation spline that is not easy to solve the problems at the post-processing and to do the local modification in time, and to improve the disadvantage of the approximate spline which can not meet the accuracy requirements, the approximate algorithm based on the cubic B-Spline is put forward. The algorithm is based on the cubic B-Spline and makes some research on the area of the curve approximate. A large number of numerical experiments are made to illustrate the feasibility and the efficiency of the algorithm, The algrithm combines the advantages of the interpola- tion spline and the B-Spline. The shortcomings of the traditional algrithm are prevented effectively. At the same time, the theoretical proof is put forward to demonstrate the convergence of the algorithm. And the numerical experiments show that this algorithm has fast convergence speed and high precision. And its programming is easy to implement. A effective algorithm is put forward for the curve research which can be use as a reference.