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
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)].