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A family of non-uniform subdivision schemes with variable parameters for curve design

Author

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  • Fang, Mei-e
  • Jeong, Byeongseon
  • Yoon, Jungho

Abstract

In this paper, we present non-uniform subdivision schemes with variable parameter sequences. A locally different tension parameter is set at each edge of the initial control polygon to control locally the shape of the resulting curve such that the scheme becomes non-uniform. Due to the variable parameters, the scheme can reproduce locally different analytic curves such as conics, Lissajous, trigonometric and catenary curves. Hence blending curves including such analytic components can be successfully generated. We discuss the convergence and smoothness of the proposed non-uniform schemes and present some numerical results to demonstrate their advantages in geometric modeling. Furthermore, as an application, we propose a chamfering algorithm which can be used in designing automobile and mechanical products.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:1-11
    DOI: 10.1016/j.amc.2017.05.063
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    Cited by:

    1. Conti, Costanza & Dyn, Nira & Romani, Lucia, 2020. "Convergence analysis of corner cutting algorithms refining nets of functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 134-146.
    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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