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Ternary six-point interpolating subdivision scheme. (English) Zbl 1221.65045
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 [C. Beccari, G. Casciola and 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 [A. Weissman, A six-point interpolation scheme for curve design. M.Sc. Thesis. Tel Aviv University (1990)].
65D17Computer aided design (modeling of curves and surfaces)