2024/04/16 by Filip Chudy, Chudy, Filip, Paweł Woźny +1
Engineering · #Advanced Numerical Analysis Techniques #Advanced machining processes and optimization #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2404.10396
openalex publication_date 2024/04/16 · openalex created_date 2024/04/18 · openalex updated_date 2026/07/28
New differential-recurrence relations for B-spline basis functions are given. Using these relations, a recursive method for finding the Bernstein-Bézier 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.