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arXiv · 2404.10396

Efficient evaluation of Bernstein-B\'{e}zier coefficients of B-spline basis functions over one knot span

Filip Chudy·Paweł Woźny
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Abstract

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 and has an asymptotically optimal computational complexity. Numerical experiments show that the new method gives results which preserve a high number of digits when compared to an approach which uses the well-known de Boor-Cox formula.

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Filip Chudy, Paweł Woźny. 2024-04-16. Efficient evaluation of Bernstein-B\'{e}zier coefficients of B-spline basis functions over one knot span. https://arxiv.org/abs/2404.10396

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