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Zbl 1221.65045
Faheem, K.; Mustafa, G.
Ternary six-point interpolating subdivision scheme. (English)
[J] Lobachevskii J. Math. 29, No. 3, 153-163 (2008). ISSN 1995-0802; ISSN 1818-9962/e

A ternary six-point interpolating subdivision scheme for a closed polygon is constructed first. Then it is extended to an open polygon. The scheme is analyzed by using the Laurent polynomial method. It is shown that the scheme is $C^2$ continuous over a certain fairly small parametric open interval. It is shown that the scheme has approximation order 4. Finally, using the techniques in [{\it C. Beccari}, {\it G. Casciola} and {\it L. Romani}, Comput. Aided Geom. Des. 24, No.~4, 210--219 (2007; Zbl 1171.65326)] it is shown that the support of the scheme is smaller than the support of the corresponding scheme in [{\it A. Weissman}, A six-point interpolation scheme for curve design. M.Sc. Thesis. Tel Aviv University (1990)].
[H. P. Dikshit (Bhopal)]

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)

Keywords: interpolating subdivision scheme; smoothness; shape parameter; Laurent polynomial

Citations: Zbl 1171.65326

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