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A Variant Cubic Exponential B-Spline Scheme with Shape Control

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  • Baoxing Zhang

    (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China)

  • Hongchan Zheng

    (School of Mathematics and Statistics, Nothwestern Polytechnical University, Xi’an 710072, China)

Abstract

This paper presents a variant scheme of the cubic exponential B-spline scheme, which, with two parameters, can generate curves with different shapes. This variant scheme is obtained based on the iteration from the generation of exponentials and a suitably chosen function. For such a scheme, we show its C 2 -convergence and analyze the effect of the parameters on the shape of the generated curves and also discuss its convexity preservation. In addition, a non-uniform version of this variant scheme is derived in order to locally control the shape of the generated curves. Numerical examples are given to illustrate the performance of the new schemes in this paper.

Suggested Citation

  • Baoxing Zhang & Hongchan Zheng, 2021. "A Variant Cubic Exponential B-Spline Scheme with Shape Control," Mathematics, MDPI, vol. 9(23), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3116-:d:694118
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Tan, Jieqing & Sun, Jiaze & Tong, Guangyue, 2016. "A non-stationary binary three-point approximating subdivision scheme," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 37-43.
    4. Fang, Mei-e & Jeong, Byeongseon & Yoon, Jungho, 2017. "A family of non-uniform subdivision schemes with variable parameters for curve design," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 1-11.
    5. Jeong, Byeongseon & Yoon, Jungho, 2020. "A new family of non-stationary hermite subdivision schemes reproducing exponential polynomials," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    6. 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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