Shape-preserving interpolation of irregular data by bivariate curvature-based cubic \(L_1\) splines in spherical coordinates

DOI10.1016/j.cagd.2005.03.004zbMath1161.65314OpenAlexW2006783310MaRDI QIDQ2576042

John E. Lavery

Publication date: 8 December 2005

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2005.03.004

zbMATH Keywords

InterpolationCubic splineSpherical coordinatesCurvatureShape preservation\(L_1\)\(L_2\)BivariateIrregular

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical interpolation (65D05)

Related Items (4)

Univariate cubic \(L_1\) interpolating splines: analytical results for linearity, convexity and oscillation on 5-pointwindows ⋮ Scattered data interpolation based upon bivariate recursive polynomials ⋮ The convergence of three \(L_{1}\) spline methods for scattered data interpolation and fitting ⋮ Surface Reconstruction via L 1-Minimization

Cites Work

• A modification of Karmarkar's linear programming algorithm
• Improved accuracy of multiquadric interpolation using variable shape parameters
• The uniform convergence of thin plate spline interpolation in two dimensions
• Bernstein-Bézier polynomials on spheres and sphere-like surfaces
• Shape-preserving, multiscale interpolation by univariate curvature-based cubic \(L_{1}\) splines in Cartesian and polar coordinates
• Affine-scaling for linear programs with free variables
• Fitting scattered data on sphere-like surfaces using spherical splines
• The parameter \(R^ 2\) in multiquadric interpolation
• Spline Interpolation and Smoothing on the Sphere
• Erratum: Spline Interpolation and Smoothing on the Sphere
• Fitting Monotone Surfaces to Scattered Data Using C1 Piecewise Cubics
• A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere
• Shape-preserving, multiscale interpolation by bi- and multivariate cubic \(L_{1}\) splines
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