Shape preserving HC2 interpolatory subdivision

A subdivision procedure is developed to solve a C2 Hermite interpolation problem with the further request of preserving the shape of the initial data. We consider a specific non-stationary and non-uniform variant of the Merrien HC2 subdivision family, and we provide a data dependent strategy to select the related parameters which ensures convergence and shape preservation for any set of initial monotone and/or convex data. Each step of the proposed subdivision procedure can be regarded as the midpoint evaluation of an interpolating function—and of its first and second derivatives—in a suitable space of C2 functions of dimension 6 which has tension properties. The limit function of the subdivision procedure is a C2 piecewise quintic polynomial interpolant.