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A ternary 4-point approximating subdivision scheme. (English) Zbl 1144.65012
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.

65D18Computer graphics, image analysis, and computational geometry
Full Text: DOI
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