Convexity preservation of the interpolating four-point \(C^{2}\) ternary stationary subdivision scheme

DOI10.1016/j.cagd.2009.02.004zbMath1205.65071OpenAlexW2069905492MaRDI QIDQ625272

Zhi-Jie Cai

Publication date: 15 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2009.02.004

zbMATH Keywords

subdivision schemeconvexity preservationinterpolating four-point ternary subdivision scheme

Mathematics Subject Classification ID

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

Related Items (15)

Convexity preservation of five-point binary subdivision scheme with a parameter ⋮ The four-point interpolation subdivision curve is neither convex nor concave in all but one case ⋮ 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 ⋮ Analysis of a 6-point binary subdivision scheme ⋮ The mask of odd points \(n\)-ary interpolating subdivision scheme ⋮ A new four-point shape-preserving \(C^3\) subdivision scheme ⋮ A nonstationary ternary 4-point shape-preserving subdivision scheme ⋮ Shape preservation of 4-point interpolating non-stationary subdivision scheme ⋮ Ternary shape-preserving subdivision schemes ⋮ On the interpolating 5-point ternary subdivision scheme: a revised proof of convexity-preservation and an application-oriented extension ⋮ Conditions on shape preserving of stationary polynomial reproducing subdivision schemes ⋮ A class of shape preserving 5-point n-ary approximating schemes ⋮ Level set shape analysis of binary 4-point non-stationary interpolating subdivision scheme ⋮ A new class of \(2m\)-point binary non-stationary subdivision schemes

Cites Work

• Convergence, error estimation and some properties of four-point interpolation subdivision scheme
• A 4-point interpolatory subdivision scheme for curve design
• Uniform refinement of curves
• Modified four-point scheme and its application
• Convexity preserving interpolatory subdivision schemes
• The refinability of the four point scheme
• Convexity preservation of the four-point interpolatory subdivision scheme
• An interpolating 4-point \(C^2\) ternary stationary subdivision scheme

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