Shape-preserving C1C1 Hermite interpolants generated by a Gori–Pitolli subdivision scheme

In this paper we present a method for the construction of C1C1 Hermite interpolants obtained from a particular family of refinable spline functions introduced by Gori and Pitolli. They constitute a one-parameter subfamily of the Hermite interpolants generated by the general Merrien's subdivision scheme. We compare this family to the other one-parameter subfamily studied by Merrien and Sablonnière and Lyche and Merrien on the solution of two-points Hermite interpolation problems with arbitrary monotonicity or convexity constraints.