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Combined SGC-Ball Interpolation Curves: Construction and IGEO-Based Shape Optimization

Author

Listed:
  • Jiaoyue Zheng

    (School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China)

  • Gang Hu

    (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China)

  • Liuxin Chen

    (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China)

  • Xiaomin Ji

    (School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China)

Abstract

With the swift advancement of the geometric modeling industry and computer technology, traditional generalized Ball curves and surfaces are challenging to achieve the geometric modeling of various complex curves and surfaces. Constructing an interpolation curve for the given discrete data points and optimizing its shape have important research value in engineering applications. This article uses an improved golden eagle optimizer to design the shape-adjustable combined generalized cubic Ball interpolation curves with ideal shape. Firstly, the combined generalized cubic Ball interpolation curves are constructed, which have global and local shape parameters. Secondly, an improved golden eagle optimizer is presented by integrating Lévy flight, sine cosine algorithm, and differential evolution into the original golden eagle optimizer; the three mechanisms work together to increase the precision and convergence rate of the original golden eagle optimizer. Finally, in view of the criterion of minimizing curve energy, the shape optimization models of combined generalized cubic Ball interpolation curves that meet the C 1 and C 2 smooth continuity are instituted. The improved golden eagle optimizer is employed to deal with the shape optimization models, and the combined generalized cubic Ball interpolation curves with minimum energy are attained. The superiority and competitiveness of improved golden eagle optimizer in solving the optimization models are verified through three representative numerical experiments.

Suggested Citation

  • Jiaoyue Zheng & Gang Hu & Liuxin Chen & Xiaomin Ji, 2023. "Combined SGC-Ball Interpolation Curves: Construction and IGEO-Based Shape Optimization," Mathematics, MDPI, vol. 11(16), pages 1-25, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3496-:d:1216362
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    References listed on IDEAS

    as
    1. Lu, Lizheng, 2015. "A note on curvature variation minimizing cubic Hermite interpolants," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 596-599.
    2. Nicholas Zaranis & George M. Exarchakos, 2018. "How ICT Affects the Understanding of Stereometry Among University Students," International Journal of Web-Based Learning and Teaching Technologies (IJWLTT), IGI Global, vol. 13(1), pages 37-49, January.
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