We determine shape-preserving regions and we describe a general setting to generate shape-preserving families for the 2-points Hermite subdivision scheme introduced by Merrien (Numer. Algorithms 2:187-200, [1992]). This general construction includes the shape-preserving families presented in Merrien and Sablonniere (Constr. Approx. 19:279-298, [2003]) and Pelosi and Sablonniere (C^1 GP Hermite Interpolants Generated by a Subdivision Scheme, Prepublication IRMAR 06-23, Rennes, [2006]). New special families are presented as particular examples. Nonstationary and nonuniform versions of such schemes, which produce smoother limits, are discussed.
Costantini, P., Manni, C. (2008). On Constrained Nonlinear Hermite Subdivision. CONSTRUCTIVE APPROXIMATION, 28(3), 291-331 [10.1007/s00365-007-9001-z].
On Constrained Nonlinear Hermite Subdivision
MANNI, CARLA
2008-01-01
Abstract
We determine shape-preserving regions and we describe a general setting to generate shape-preserving families for the 2-points Hermite subdivision scheme introduced by Merrien (Numer. Algorithms 2:187-200, [1992]). This general construction includes the shape-preserving families presented in Merrien and Sablonniere (Constr. Approx. 19:279-298, [2003]) and Pelosi and Sablonniere (C^1 GP Hermite Interpolants Generated by a Subdivision Scheme, Prepublication IRMAR 06-23, Rennes, [2006]). New special families are presented as particular examples. Nonstationary and nonuniform versions of such schemes, which produce smoother limits, are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
