A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines

DOI10.1090/S0025-5718-2013-02664-6zbMath1278.41005OpenAlexW2039317544MaRDI QIDQ2840627

Tom Lyche, Richard F. Riesenfeld, Elaine Cohen

Publication date: 23 July 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02664-6

zbMATH Keywords

subdivisionquasi-interpolationMarsden identitysimplex splinesPowell-Sabin split

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical interpolation (65D05) Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items

Quartic splines on Powell-Sabin triangulations, Continuity and convergence in rational triangular Bézier spline based isogeometric analysis, A B-spline basis for \(C^1\) quadratic splines on triangulations with a 10-split, A Hermite interpolatory subdivision scheme for \(C^2\)-quintics on the Powell-Sabin 12-split, Constructing B-spline representation of quadratic Sibson-Thomson splines, A normalized basis for condensed \(\mathcal{C}^1\) Powell-Sabin-12 splines, B-spline-like bases for \(C^2\) cubics on the Powell-Sabin 12-split, Argyris type quasi-interpolation of optimal approximation order, Construction and analysis of cubic Powell-Sabin B-splines, A local simplex Spline basis for \(C^3\) quartic splines on arbitrary triangulations, Simplex-splines on the Clough-Tocher element, Stable simplex spline bases for \(C^3\) quintics on the Powell-Sabin 12-split, Mathematical analysis of variational isogeometric methods, \(C^1\) piecewise quadratic hierarchical bases, Construction of \(C^2\) cubic splines on arbitrary triangulations, Simplex-splines on the Clough-Tocher split with arbitrary smoothness, U-splines: splines over unstructured meshes

Cites Work

• On the stability of normalized Powell--Sabin B-splines
• A normalized basis for quintic Powell-Sabin splines
• The dimension of bivariate spline spaces of smoothness r for degree \(d\geq 4r+1\)
• Box splines
• On calculating normalized Powell-Sabin B-splines
• On the \(p\)-norm condition number of the multivariate triangular Bernstein basis
• Smooth macro-elements on Powell-Sabin-12 splits
• Delaunay configurations and multivariate splines: A generalization of a result of B. N. Delaunay
• Spline Functions on Triangulations
• The Computational Cost of Simplex Spline Functions
• The Stable Evaluation of Multivariate Simplex Splines
• On Multivariate B-Splines
• A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
• Multivariate Splines
• On the Linear Independence of Multivariate B-Splines, I. Triangulations of Simploids
• Blossoming Begets B-Spline Bases Built Better by B-Patches
• Piecewise Quadratic Approximations on Triangles
• On the Local Approximation Power of Quasi-Hierarchical Powell-Sabin Splines
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item