Ternary shape-preserving subdivision schemes

Francesca Pitolli

Mathematics and Computers in Simulation (MATCOM), 2014, vol. 106, issue C, 185-194

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.

Keywords: Subdivision scheme; Bell-shaped mask; Shape-preserving (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:106:y:2014:i:c:p:185-194

DOI: 10.1016/j.matcom.2013.04.003

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