A subdivision procedure is developed to solve a C2\documentclass[12pt]{minimal}
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\begin{document}$$C^2$$\end{document} 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\documentclass[12pt]{minimal}
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\begin{document}$$HC^2$$\end{document} 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\documentclass[12pt]{minimal}
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\begin{document}$$C^2$$\end{document} functions of dimension 6\documentclass[12pt]{minimal}
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\begin{document}$$6$$\end{document} which has tension properties. The limit function of the subdivision procedure is a C2\documentclass[12pt]{minimal}
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\begin{document}$$C^2$$\end{document} piecewise quintic polynomial interpolant.
