Abstract: 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.

Key words: NURBS, spline function, efficient algorithm, parametric interpolation