Abstract: By utilizing the relationship between the knot intervals，a method for calculating the transform matrix between different B-spline basis functions is presented.Furthermore，an interval skipping algorithm is given to calculate B-spline functions multiplication.This algorithm is so-called just as only part of knot intervals need to be considered to calculate rapidly B-spline functions multiplication.This algorithm partially solves the multiplication of piecewise polynomial and B-spline curve；and it can be applied into smooth B-spline surfaces blending and elevation of B-spline.Some examples are given to illustrate the efficiency of the presented algorithm.

摘要： 利用B样条基函数节点区间的对应关系，首先给出了B样条基函数间的转换矩阵的计算方法，进而给出了计算B样条乘积的区间跳跃算法。该算法仅需计算部分节点区间上的转换矩阵，因此称其为区间跳跃算法。这一方法解决了分段多项式与B样条曲线乘积的计算问题，可应用到B样条曲线的升阶、曲面间光滑拼接等问题中。通过算例验证了该方法计算简捷、易于实现。