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}
}