Abstract: Through analyzing the de Boor-Cox formula of B-splines，a fast algorithm to compute B-spline functions is proposed based on vector extending operation.To calculate k degree B-spline function’s nonzero values，the new algorithm can improve the computing efficiency by 2k+1 times.As its application in CNC real-time interpolation of B-spline curves，to calculate k degree B-spline curve and its derivatives，the proposed algorithm can achieve much higher computing efficiency compares with de Boor algorithm.

Key words: B-spline functions, B-spline curve, de Boor algorithm, fast calculation, CNC interpolation

摘要： 通过对B样条的de Boor-Cox定义式分析，给出了一种基于向量扩展的B样条基函数快速求值算法。该算法能够将k次B样条非零值计算效率提高2k+1倍。该算法用于数控实时插补中的B样条曲线求值求导运算时，可获得比de Boor算法更高的计算效率。

关键词: B样条, B样条曲线, de Boor算法, 快速计算, 数控插补