English

Computation of multi-degree B-splines

Numerical Analysis 2021-10-19 v2

Abstract

Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar properties to standard B-splines. These basis functions are called multi-degree B-splines (or MDB-splines). The construction relies on an extraction operator that represents all MDB-splines as linear combinations of local B-splines of different degrees. This enables the use of existing efficient algorithms for B-spline evaluations and refinements in the context of multi-degree splines. A Matlab implementation is provided to illustrate the computation and use of MDB-splines.

Keywords

Cite

@article{arxiv.1809.01598,
  title  = {Computation of multi-degree B-splines},
  author = {Hendrik Speleers},
  journal= {arXiv preprint arXiv:1809.01598},
  year   = {2021}
}
R2 v1 2026-06-23T03:55:23.950Z