Positivity of refinable functions defined by nonnegative finite masks

DOI10.1016/j.acha.2009.01.001zbMath1167.65012OpenAlexW2040847138MaRDI QIDQ837540

Xin-Long Zhou

Publication date: 20 August 2009

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2009.01.001

zbMATH Keywords

subdivision schemedilation equationcascade algorithmconnection of directed graphpositivity of refinable function

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items

Totally positive refinable functions with general dilation \(M\) ⋮ Convergent bivariate subdivision scheme with nonnegative mask whose support is non-convex ⋮ Lifespan in a primitive Boolean linear dynamical system ⋮ The Euler binary partition function and subdivision schemes ⋮ Necessary conditions for the convergence of subdivision schemes with finite masks ⋮ Some sufficient conditions for convergent multivariate subdivision schemes with nonnegative finite masks ⋮ SIA matrices and non-negative subdivision ⋮ Characterization of some convergent bivariate subdivision schemes with nonnegative masks

Cites Work

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• Uniform refinement of curves
• Descartes systems from corner cutting
• Subdivision algorithms with nonnegative masks generally converge
• A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
• Stationary subdivision
• Two-Scale Difference Equations. I. Existence and Global Regularity of Solutions
• Multivariate Refinement Equations and Convergence of Subdivision Schemes
• Subdivision schemes with nonnegative masks
• Convergence of Subdivision Schemes Associated with Nonnegative Masks
• Subdivision schemes and refinement equations with nonnegative masks