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 C⁰-continuous. It has good numerical behavior and has an asymptotically optimal computational complexity.
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Chudy et al. (2024) studied this question.
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