We analyze the shape-preserving properties of ternary subdivision schemes generated by bell-shaped masks. We prove that any bell-shaped mask, satisfying the basic sum rules, gives rise to a convergent monotonicity preserving subdivision scheme, but convexity preservation is not guaranteed. We show that to reach convexity preservation the first order divided difference scheme needs to be bell-shaped, too. Finally, we show that ternary subdivision schemes associated with certain refinable functions with dilation 3 have shape-preserving properties of higher order.

Ternary shape-preserving subdivision schemes / Pitolli, Francesca. - In: MATHEMATICS AND COMPUTERS IN SIMULATION. - ISSN 0378-4754. - STAMPA. - 106:(2014), pp. 185-194. [10.1016/j.matcom.2013.04.003]

Ternary shape-preserving subdivision schemes

PITOLLI, Francesca
2014

Abstract

We analyze the shape-preserving properties of ternary subdivision schemes generated by bell-shaped masks. We prove that any bell-shaped mask, satisfying the basic sum rules, gives rise to a convergent monotonicity preserving subdivision scheme, but convexity preservation is not guaranteed. We show that to reach convexity preservation the first order divided difference scheme needs to be bell-shaped, too. Finally, we show that ternary subdivision schemes associated with certain refinable functions with dilation 3 have shape-preserving properties of higher order.
2014
shape-preserving; bell-shaped mask; subdivision scheme
01 Pubblicazione su rivista::01a Articolo in rivista
Ternary shape-preserving subdivision schemes / Pitolli, Francesca. - In: MATHEMATICS AND COMPUTERS IN SIMULATION. - ISSN 0378-4754. - STAMPA. - 106:(2014), pp. 185-194. [10.1016/j.matcom.2013.04.003]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/522787
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