A subdivision procedure is developed to solve a 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 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 functions of dimension which has tension properties. The limit function of the subdivision procedure is a piecewise quintic polynomial interpolant.
Lettieri, D., Manni, C., Pelosi, F., Speleers, H. (2015). Shape preserving HC2 interpolatory subdivision. BIT, 55(3), 751-779 [10.1007/s10543-014-0530-0].
Shape preserving HC2 interpolatory subdivision
Pelosi, Francesca;
2015-01-01
Abstract
A subdivision procedure is developed to solve a 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 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 functions of dimension which has tension properties. The limit function of the subdivision procedure is a piecewise quintic polynomial interpolant.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1261674