Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators

DOI10.1016/j.amc.2013.01.024zbMath1291.65053OpenAlexW1981310747MaRDI QIDQ2451330

Sergio Amat, Rosa Donat, J. Carlos Trillo

Publication date: 3 June 2014

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.01.024

zbMATH Keywords

subdivision schemesreconstruction operatorconvexity preservinginterpolatory

Mathematics Subject Classification ID

Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Approximation with constraints (41A29) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (10)

Convexity preservation of five-point binary subdivision scheme with a parameter ⋮ Generation of fractal curves and surfaces using ternary 4-point interpolatory subdivision scheme ⋮ A shape preserving \(C^2\) non-linear, non-uniform, subdivision scheme with fourth-order accuracy ⋮ Convexity preservation of six point \(C^{2}\) interpolating subdivision scheme ⋮ Improving the stability bound for the PPH nonlinear subdivision scheme for data coming from strictly convex functions ⋮ Shape preservation of 4-point interpolating non-stationary subdivision scheme ⋮ On the interpolating 5-point ternary subdivision scheme: a revised proof of convexity-preservation and an application-oriented extension ⋮ On certain inequalities associated to curvature properties of the nonlinear PPH reconstruction operator ⋮ The translation operator. Applications to nonlinear reconstruction operators on nonuniform grids ⋮ Level set shape analysis of binary 4-point non-stationary interpolating subdivision scheme

Cites Work

• A 4-point interpolatory subdivision scheme for curve design
• Convexity preserving interpolatory subdivision schemes
• Nonlinear multiscale decompositions: The approach of A. Harten
• Convexity preservation of the four-point interpolatory subdivision scheme
• Analysis of a new nonlinear subdivision scheme. Applications in image processing
• Shape Preserving Piecewise Rational Interpolation
• Shape Preserving Interpolation to Convex Data by Rational Functions with Quadratic Numerator and Linear Denominator
• Multiresolution Representation of Data: A General Framework

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