\(C^1\) and \(C^2\)-continuous polynomial parametric \(L_p\) splines (\(p\geq 1\))

DOI10.1016/j.cagd.2007.04.007zbMath1171.65323OpenAlexW1491924644MaRDI QIDQ733434

Eric Nyiri, Olivier Gibaru, Philippe Auquiert

Publication date: 16 October 2009

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2007.04.007

zbMATH Keywords

interpolation\(L_{1}\) polynomial parametric splines\(L_p\) polynomial parametric splines

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Numerical interpolation (65D05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (10)

On shape-preserving capability of cubic \(L^1\) spline fits ⋮ \(L_1\) spline fits via sliding window process: continuous and discrete cases ⋮ Univariate cubic \(L_1\) interpolating splines: analytical results for linearity, convexity and oscillation on 5-pointwindows ⋮ Univariate cubic \(L_1\) interpolating splines: spline functional, window size and analysis-based algorithm ⋮ Fast \(L_1^kC^k\) polynomial spline interpolation algorithm with shape-preserving properties ⋮ Univariate cubic \(L _{1}\) interpolating splines based on the first derivative and on 5-point windows: analysis, algorithm and shape-preserving properties ⋮ \(L_1C^1\) polynomial spline approximation algorithms for large data sets ⋮ On the cubic \(L_{1}\) spline interpolant to the Heaviside function ⋮ Curve construction based on five trigonometric blending functions ⋮ A class of general quartic spline curves with shape parameters

Cites Work

• A modification of Karmarkar's linear programming algorithm
• A practical guide to splines
• Convergence and Gibbs' phenomenon in the cubic spline interpolation of discontinuous functions
• Univariate cubic \(L_1\) splines -- a geometric programming approach
• Shape-preserving properties of univariate cubic \(L_{1}\) splines
• Univariate cubic \(L_{p}\) splines and shape-preserving, multiscale interpolation by univariate cubic \(L_{1}\) splines
• Shape-preserving, first-derivative-based parametric and nonparametric cubic \(L_{1}\) spline curves
• Shape-preserving, multiscale interpolation by bi- and multivariate cubic \(L_{1}\) splines
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