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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.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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