A new three-point approximating \(C^{2}\) subdivision scheme

DOI10.1016/j.aml.2006.08.022zbMath1116.65019OpenAlexW1993590372MaRDI QIDQ879008

Nadeem Ahmad, Shahid S. Siddiqi

Publication date: 4 May 2007

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2006.08.022

zbMATH Keywords

convergencenumerical examplessmoothnesscontrol polygonLaurent polynomialmaskcurve designapproximating subdivision scheme

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (25)

A unified three point approximating subdivision scheme ⋮ Designing multi-parameter curve subdivision schemes with high continuity ⋮ Binary 3-point and 4-point non-stationary subdivision schemes using hyperbolic function ⋮ Ternary six-point interpolating subdivision scheme ⋮ Fractal behavior of ternary 4-point interpolatory subdivision scheme with tension parameter ⋮ A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes ⋮ Analysis of the Gibbs phenomenon in stationary subdivision schemes ⋮ Family of odd point non-stationary subdivision schemes and their applications ⋮ An approximating \(C^{2}\) non-stationary subdivision scheme ⋮ Analysis of a 6-point binary subdivision scheme ⋮ Fractal properties of the generalized chaikin corner-cutting subdivision scheme ⋮ A combined approximating and interpolating ternary 4-point subdivision scheme ⋮ Family of \(a\)-ary univariate subdivision schemes generated by Laurent polynomial ⋮ Fractal generation using ternary 5-point interpolatory subdivision scheme ⋮ Curve subdivision schemes for geometric modelling ⋮ A new non-stationary binary 6-point subdivision scheme ⋮ Modified form of binary and ternary 3-point subdivision schemes ⋮ A unified framework for interpolating and approximating univariate subdivision ⋮ A ternary three-point scheme for curve designing ⋮ Affine combination of B-spline subdivision masks and its non-stationary counterparts ⋮ A new five-point approximating subdivision scheme ⋮ Improved binary four point subdivision scheme and new corner cutting scheme ⋮ A \(C^6\) approximating subdivision scheme ⋮ Hyperbolic forms of ternary non-stationary subdivision schemes originated from hyperbolic B-splines ⋮ The \(m\)-point approximating subdivision scheme

Cites Work

• Sur une courbe plane
• A 4-point interpolatory subdivision scheme for curve design
• Symmetric iterative interpolation processes
• An interpolating 4-point \(C^2\) ternary stationary subdivision scheme
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