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Zbl 1144.65012
Ko, Kwan Pyo; Lee, Byung-Gook; Yoon, Gang Joon
A ternary 4-point approximating subdivision scheme. (English)
[J] Appl. Math. Comput. 190, No. 2, 1563-1573 (2007). ISSN 0096-3003

The authors provide a new ternary 4-point approximating subdivision scheme. This new scheme is based on the evaluation at some points of the interpolating Lagrange polynomials of node points $-1,0,1,2$. This subdivision scheme has smoothness $C^2$, an approximation order of four and its support has size 5.5. The authors provide a table with comparisons of these characteristics with other known subdivision schemes. As pointed in the article, this idea of using values of Lagrange interpolating polynomials can be extended to ternary $(2n+2)$-point approximation subdivision schemes, using Lagrange interpolation polynomials of higher degree.
[Luis Felipe Tabera Alonso (Madrid)]

MSC 2000:: *65D18 Computer graphics and computational geometry

Keywords: ternary subdivision scheme; support; mask; approximation order; convergence; smoothness; Lagrange interpolating polynomials

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