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Ternary shape-preserving subdivision schemes

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  • Pitolli, Francesca

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.

Suggested Citation

  • Pitolli, Francesca, 2014. "Ternary shape-preserving subdivision schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 185-194.
    • Handle: RePEc:eee:matcom:v:106:y:2014:i:c:p:185-194
    DOI: 10.1016/j.matcom.2013.04.003
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    Cited by:

    1. Hameed, Rabia & Mustafa, Ghulam, 2017. "Family of a-point b-ary subdivision schemes with bell-shaped mask," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 289-302.
    2. Pakeeza Ashraf & Bushra Nawaz & Dumitru Baleanu & Kottakkaran Sooppy Nisar & Abdul Ghaffar & Muhammad Aqeel Ahmed Khan & Saima Akram, 2020. "Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme," Mathematics, MDPI, vol. 8(3), pages 1-19, March.

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