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

2025/11/28 by Patrizi, Francesco
#41A15 #65D07 #65N50 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2511.23412

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.

Citations

• Local spline refinement driven by fault jump estimates for scattered data approximation
• Effective grading refinement for locally linearly independent LR B-splines
• Scattered data approximation by LR B-spline surfaces. A study on refinement strategies for efficient approximation
• Approximation in FEM, DG and IGA: A Theoretical Comparison
• Deconfliction and Surface Generation from Bathymetry Data Using LR B-splines
• THB-splines: The truncated basis for hierarchical splines
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

Related

• Effective grading refinement for locally linearly independent LR B-splines
• Macro-element Refinement schemes for THB-Splines: Applications to Bézier Projection and Structure-Preserving Discretizations
• THU-Splines: Highly Localized Refinement on Smooth Unstructured Splines
• Unstructured spline spaces for isogeometric analysis based on spline manifolds
• Manifold-based B-splines on unstructured meshes