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.
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
Manni C.;Pelosi F.;Speleers H.
2015-09-01
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
Lettieri_BIT_2015_shape.pdf
solo utenti autorizzati
Tipologia:
Versione Editoriale (PDF)
Licenza:
Copyright dell'editore
Dimensione
796.49 kB
Formato
Adobe PDF
|
796.49 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.