Two order C2 Hermite interpolatory subdivision

Based on the linear spaces spanned respectively by the functions {1, x, x², x³, x⁴, x⁵}, {1,x, x², x³, e^sx, e^-sx} and {1, x, x², x³, e^isx, e^-isx}, a non-stationary two order Hermite interpolatory subdivision scheme with one parameter is constructed for the given function values and the first and second order derivatives at two sequential points. Also, the convergence, C² continuity and geometric properties are analyzed. Finally, some examples which contain the hyperbola, ellipse and other conical curves are given.