LR B-spline perspective for RM B-splines: construction and effortless refinements

TL;DR

This paper demonstrates that Reachable Minimally supported (RM) B-splines can be constructed as a special case of Locally Refined (LR) B-splines, enabling straightforward mesh refinement techniques for isogeometric analysis.

Contribution

It establishes a connection between RM B-splines and LR B-splines, facilitating automatic mesh refinement procedures.

Findings

RM B-splines are a special case of LR B-splines

Enables automatic mesh refinement for RM B-splines

Supports applications in isogeometric analysis

Abstract

Reachable Minimally supported (RM) B-splines have been recently introduced as a novel B-spline--like basis. They feature local linear independence and admit a fast de Boor--like evaluation algorithm. These properties make them particularly attractive for applications in isogeometric analysis. In this note, we show that automatic mesh refinement procedures can be readily established by observing that RM B-splines are a special case of Locally Refined (LR) B-splines.