Multi-degree B-splines: Algorithmic computation and properties

Deepesh Toshniwal*, Hendrik Speleers, René R. Hiemstra, Carla Manni, Thomas J.R. Hughes

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

23 Citations (Scopus)


This paper addresses theoretical considerations behind the algorithmic computation of polynomial multi-degree spline basis functions as presented in Toshniwal et al. (2017). The approach in Toshniwal et al. (2017) breaks from the reliance on computation of integrals recursively for building B-spline-like basis functions that span a given multi-degree spline space. The gains in efficiency are indisputable; however, the theoretical robustness needs to be examined. In this paper, we show that the construction of Toshniwal et al. (2017) yields linearly independent functions with the minimal support property that span the entire multi-degree spline space and form a convex partition of unity.

Original languageEnglish
Article number101792
Pages (from-to)1-16
Number of pages16
JournalComputer Aided Geometric Design
Publication statusPublished - 2020


  • Algorithmic computation
  • B-splines
  • Convex partition of unity
  • Linear independence
  • Non-uniform degrees
  • Smooth splines


Dive into the research topics of 'Multi-degree B-splines: Algorithmic computation and properties'. Together they form a unique fingerprint.

Cite this