A local simplex Spline basis for \(C^3\) quartic splines on arbitrary triangulations

DOI10.1016/j.amc.2023.128330OpenAlexW4386906370MaRDI QIDQ6068179

Carla Manni, Tom Lyche, Hendrik Speleers

Publication date: 13 November 2023

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2023.128330

zbMATH Keywords

triangulationsB-splinessimplex splines\(C^3\) quartic splinesWang-Shi macro-structure

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Approximations and expansions (41Axx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stable simplex spline bases for \(C^3\) quintics on the Powell-Sabin 12-split
• Multivariate spline spaces
• A normalized basis for quintic Powell-Sabin splines
• A normalized basis for reduced Clough-Tocher splines
• Simplex-splines on the Clough-Tocher element
• A normalized representation of super splines of arbitrary degree on Powell-Sabin triangulations
• Composite finite elements of class \(C^ k\)
• On calculating normalized Powell-Sabin B-splines
• Geometric interpretation of smoothness conditions of triangular polynomial patches
• Bézier and B-spline techniques
• A new B-spline representation for cubic splines over Powell-Sabin triangulations
• Construction and analysis of cubic Powell-Sabin B-splines
• Foundations of spline theory: B-splines, spline approximation, and hierarchical refinement
• Construction of normalized B-splines for a family of smooth spline spaces over Powell-Sabin triangulations
• Construction of \(C^2\) cubic splines on arbitrary triangulations
• Simplex-splines on the Clough-Tocher split with arbitrary smoothness
• Generalized \(C^1\) Clough-Tocher splines for CAGD and FEM
• Super-smooth cubic Powell-Sabin splines on three-directional triangulations: B-spline representation and subdivision
• A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines
• Smooth macro-elements on Powell-Sabin-12 splits
• Spline Functions on Triangulations
• Piecewise Quadratic Approximations on Triangles
• Isogeometric Analysis
• Smooth macro-elements based on Powell--Sabin triangle splits

This page was built for publication: A local simplex Spline basis for \(C^3\) quartic splines on arbitrary triangulations