A bivariate \(C^1\) cubic super spline space on Powell-Sabin triangulation

DOI10.1016/j.camwa.2008.02.044zbMath1155.65310OpenAlexW2024838316MaRDI QIDQ1004822

Sun-Kang Chen, Huan-Wen Liu

Publication date: 12 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2008.02.044

zbMATH Keywords

Hermite interpolationsuper splinemacro-elementnodal parametersPowell-Sabin type-1 split

Mathematics Subject Classification ID

Spline approximation (41A15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (11)

Quartic splines on Powell-Sabin triangulations ⋮ A new B-spline representation for cubic splines over Powell-Sabin triangulations ⋮ Construction and analysis of cubic Powell-Sabin B-splines ⋮ Super-smooth cubic Powell-Sabin splines on three-directional triangulations: B-spline representation and subdivision ⋮ A normalized basis for \(\mathcal{C}^1\) cubic super spline space on Powell-Sabin triangulation ⋮ Cubic spline quasi-interpolants on powell-sabin partitions ⋮ \(\mathcal{C}^1\) cubic splines on Powell-Sabin triangulations ⋮ Three recipes for quasi-interpolation with cubic Powell-Sabin splines ⋮ A geometric characterization of Powell-Sabin triangulations allowing the construction of \(C^2\) quartic splines ⋮ A normalized representation of super splines of arbitrary degree on Powell-Sabin triangulations ⋮ Superconvergent \(C^1\) cubic spline quasi-interpolants on Powell-Sabin partitions

Cites Work

• Scattered data interpolation and approximation using bivariate \(C^{1}\) piecewise cubic polynomials
• \(C^ r\)-finite elements of Powell-Sabin type on the three direction mesh
• Composite finite elements of class \(C^ k\)
• The dimension of bivariate spline spaces of smoothness r for degree \(d\geq 4r+1\)
• On dual functionals of polynomials in B-form
• Smooth macro-elements based on Clough-Tocher triangle splits
• On \(C^ 2\) quintic spline functions over triangulations of Powell-Sabin's type
• Smooth macro-elements on Powell-Sabin-12 splits
• On Cubic and Quartic Clough–Tocher Finite Elements
• Macro-elements and stable local bases for splines on Powell-Sabin triangulations
• Macro-elements and stable local bases for splines on Clough-Tocher triangulations
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