New differential-recurrence relations for B-spline basis functions are given. Using these relations, a recursive method for finding the Bernstein-B\'{e}zier coefficients of B-spline basis functions over a single knot span is proposed. The algorithm works for any knot sequence which guarantees that all B-spline functions are at least $C^0$-continuous. It has good numerical behavior and has an asymptotically optimal computational complexity.

翻译：本文给出了B样条基函数新的微分-递推关系。利用这些关系，提出了一种递归方法，用于计算单节点区间上B样条基函数的Bernstein-Bézier系数。该算法适用于所有保证B样条函数至少具有$C^0$连续性的节点序列。算法具有良好的数值稳定性，并具有渐近最优的计算复杂度。