A geometric characterization of Powell-Sabin triangulations allowing the construction of \(C^2\) quartic splines

DOI10.1016/j.camwa.2021.08.028OpenAlexW3200247886MaRDI QIDQ2234850

Publication date: 19 October 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2021.08.028

zbMATH Keywords

blending functions Bernstein basis Powell-Sabin triangulation quartic splines

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (1)

On \(C^2\) cubic quasi-interpolating splines and their computation by subdivision via blossoming

Cites Work

Unnamed Item
\(C^1\) quadratic and \(C^2\) quartic macro-elements on a modified Morgan-Scott triangulation
Interpolation with quintic Powell-Sabin splines
Cubic spline quasi-interpolants on powell-sabin partitions
A normalized basis for quintic Powell-Sabin splines
\(\mathcal{C}^1\) cubic splines on Powell-Sabin triangulations
A normalized representation of super splines of arbitrary degree on Powell-Sabin triangulations
Superconvergent \(C^1\) cubic spline quasi-interpolants on Powell-Sabin partitions
Quadratic spline quasi-interpolants on Powell-Sabin partitions
A bivariate \(C^1\) cubic super spline space on Powell-Sabin triangulation
Polar forms and quadratic spline quasi-interpolants on Powell-Sabin partitions
On calculating normalized Powell-Sabin B-splines
A new B-spline representation for cubic splines over Powell-Sabin triangulations
A B-spline basis for \(C^1\) quadratic splines on triangulations with a 10-split
Construction and analysis of cubic Powell-Sabin B-splines
On numerical quadrature for \(C^1\) quadratic Powell-Sabin 6-split macro-triangles
Gaussian quadrature for \(C^1\) cubic Clough-Tocher macro-triangles
Construction of normalized B-splines for a family of smooth spline spaces over Powell-Sabin triangulations
A normalized basis for \(\mathcal{C}^1\) cubic super spline space on Powell-Sabin triangulation
Interpolation with \(C^2\) quartic macro-elements based on \(10\)-splits
A family of smooth quasi-interpolants defined over Powell-Sabin triangulations
Quartic splines on Powell-Sabin triangulations
Construction of quintic Powell-Sabin spline quasi-interpolants based on blossoming
Spline Functions on Triangulations
On Cubic and Quartic Clough–Tocher Finite Elements
Piecewise Quadratic Approximations on Triangles

This page was built for publication: A geometric characterization of Powell-Sabin triangulations allowing the construction of \(C^2\) quartic splines