English

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

Numerical Analysis 2024-07-22 v2 Graphics Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2404.10396,
  title  = {Efficient evaluation of Bernstein-B\'{e}zier coefficients of B-spline basis functions over one knot span},
  author = {Filip Chudy and Paweł Woźny},
  journal= {arXiv preprint arXiv:2404.10396},
  year   = {2024}
}