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.File | Dimensione | Formato | |
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