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.
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Notes
The monotone decreasing case can be addressed in a similar way.
The concave case can be addressed in a similar way.
The Maple worksheets with all the computations can be found at http://www.mat.uniroma2.it/~manni/Maple_HC2.html.
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Communicated by Tom Lyche.
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Lettieri, D., Manni, C., Pelosi, F. et al. Shape preserving \(HC^2\) interpolatory subdivision. Bit Numer Math 55, 751–779 (2015). https://doi.org/10.1007/s10543-014-0530-0
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DOI: https://doi.org/10.1007/s10543-014-0530-0