在Ｈｅｒｍｉｔｅ样条和Ｂ样条的基础上提出了一种新基样条，并在此基础上推导出“快速递推插补算法”．该算法满足二阶连续，并具有实时性及无累积误差的特性．作为数控系统的核心，该算法已成功地应用于西安交通大学自行开发的五轴五联动数控系统，而且可以应用于任何以微机作为主控机的数控系统 Based on the Hermite spline and B-spline, a new base-line is proposed, and based on which a new fast recursive interpolation algorithm is derived. The algorithm satisfies the second order continuous and has the characteristics of real-time and non-cumulative error. As the core of numerical control system, the algorithm has been successfully applied to the five-axis five-linkage CNC system developed by Xi’an Jiaotong University and can be applied to any numerical control system