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On the interpolating 5-point ternary subdivision scheme: A revised proof of convexity-preservation and an application-oriented extension

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  • Novara, Paola
  • Romani, Lucia

Abstract

In this paper we provide the conditions that the free parameter of the interpolating 5-point ternary subdivision scheme and the vertices of a strictly convex initial polygon have to satisfy to guarantee the convexity preservation of the limit curve. Furthermore, we propose an application-oriented extension of the interpolating 5-point ternary subdivision scheme which allows one to construct C2 limit curves where locally convex segments as well as conic pieces can be incorporated simultaneously. The resulting subdivision scheme generalizes the non-stationary ternary interpolatory 4-point scheme and improves the quality of its limit curves by raising the smoothness order from 1 to 2 and by introducing the additional property of convexity preservation.

Suggested Citation

  • Novara, Paola & Romani, Lucia, 2018. "On the interpolating 5-point ternary subdivision scheme: A revised proof of convexity-preservation and an application-oriented extension," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 194-209.
    • Handle: RePEc:eee:matcom:v:147:y:2018:i:c:p:194-209
    DOI: 10.1016/j.matcom.2016.09.012
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    Cited by:

    1. 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.
    2. Baoxing Zhang & Hongchan Zheng, 2021. "A Variant Cubic Exponential B-Spline Scheme with Shape Control," Mathematics, MDPI, vol. 9(23), pages 1-11, December.

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