Shape preserving $$HC^2$$ H C 2 interpolatory subdivision

Abstract

A subdivision procedure is developed to solve a C 2 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 HC 2 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 C 2 functions of dimension 6 which has tension properties. The limit function of the subdivision procedure is a C 2 piecewise quintic polynomial interpolant.