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Improving smoothness and accuracy of Modified Butterfly subdivision scheme

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  • Novara, Paola
  • Romani, Lucia
  • Yoon, Jungho

Abstract

Motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications, we construct a non-stationary subdivision scheme for regular 3-directional grids, which enjoys the following properties: (i) interpolation, (ii) affine invariance, (iii) C2 smoothness, (iv) approximation order 6 and (v) the capability of reproducing several trigonometric surfaces, especially ellipsoids. To study the smoothness properties of this new scheme via existing analysis tools, we also construct an auxiliary stationary subdivision scheme enjoying properties (i)–(iv). Taking into account that, when applied on regular 3-directional grids, the Modified Butterfly scheme is C1 and has approximation order 4, the subdivision schemes derived in this paper can be considered improved variants of the Modified Butterfly scheme.

Suggested Citation

  • Novara, Paola & Romani, Lucia & Yoon, Jungho, 2016. "Improving smoothness and accuracy of Modified Butterfly subdivision scheme," Applied Mathematics and Computation, Elsevier, vol. 272(P1), pages 64-79.
    • Handle: RePEc:eee:apmaco:v:272:y:2016:i:p1:p:64-79
    DOI: 10.1016/j.amc.2015.07.065
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    Cited by:

    1. Zhang, Baoxing & Zheng, Hongchan & Song, Weijie & Lin, Zengyao & Zhou, Jie, 2019. "Interpolatory subdivision schemes with the optimal approximation order," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 1-14.
    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.
    3. Zheng, Hongchan & Zhang, Baoxing, 2017. "A non-stationary combined subdivision scheme generating exponential polynomials," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 209-221.

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