当对非均匀有理B 样条( NURBS) 曲线进行高密度插值时，运用分段幂函数方法对基函数进行求值的效率远高于传统的de-Boor 算法． 为此，文中从NUＲBS 插补计算的特点出发，结合de-Boor 递推计算规律，设计了NURBS 插补快速求值算法． 首先采用该算法计算NURBS 在各节点区间的基函数显式方程，再运用显式方程进行NURBS 插补点求值，并设计相应的NUＲBS 曲线插补器． 复杂NURBS 曲线的铣削加工实验结果表明，该算法能够有效地缩减NUＲBS 曲线插补求值的计算耗时，提高插补计算的实时性．

In the high-density interpolation of non-uniform rational B-spline ( NURBS) curves,using the piecewise power function method to evaluate the B-spline basis function consumes much less computing time than the traditional de-Boor algorithm.Therefore,on the basis of the characteristic of the NURBS interpolation,an efficient evaluation algorithm for the NURBS interpolation is proposed by drawing on the recursive calculation laws of the de- Boor algorithm.First,the proposed algorithm is used to deduce the explicit equations of the B-spline basis function in each spline parameter knot interval.Then,NURBS interpolation points are evaluated by using explicit equations,and a corresponding NURBS curve interpolator is designed.The results of the milling experiment with complex NURBS curves show that the proposed algorithm can effectively reduce the computing time of the NURBS curve interpolation and can improve the real-time performance of NURBS interpolators.