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Quintic generalized Hermite interpolation curves: construction and shape optimization using an improved GWO algorithm

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Abstract

In the field of CAGD/CAD, interpolation curve plays an important role in shape representation and shape design. Based on the traditional quintic Hermite interpolation curve, this paper proposes a novel class of quintic generalized Hermite interpolation curve (QG-Hermite interpolation curve, for short) with local shape parameters, which can satisfy C2 continuity automatically. Since each segment of the constructed curve has independent shape parameters, and its shape can be adjusted locally or globally by modifying the shape parameters. First, to obtain an interpolation curve satisfying certain specific geometric requirements such as the approximate shortest arc length, the strain energy minimization or the curvature variation energy minimization, etc., three shape optimization models of the QG-Hermite interpolation curve are established. Second, an improved gray wolf optimization (I-GWO) algorithm is used to solve the shape optimization models so as to determine the optimal shape parameters. Finally, the modeling examples show that the proposed method is effective and applicable in shape designing.

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All data generated or analysed during this study are included in this published article (and its supplementary information files).

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Acknowledgements

We thank to the anonymous reviewers for their insightful suggestions and recommendations, which led to the improvements of presentation and content of the paper. This work is supported by the National Natural Science Foundation of China (Grant No. 51875454).

Funding

The funding has been received from National Natural Science Foundation of China with Grant No. 51875454.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xi’an University of Technology, Xi’an, 710054, People’s Republic of China

    Gang Hu & Xinqiang Qin

  2. School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, No. 5 South Jinhua Road, Xi’an, 710048, People’s Republic of China

    Jiaoyue Zheng, Gang Hu & Xiaomin Ji

Authors
  1. Jiaoyue Zheng
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  2. Gang Hu
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  3. Xiaomin Ji
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  4. Xinqiang Qin
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Correspondence to Gang Hu.

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Communicated by Margherita Porcelli.

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Zheng, J., Hu, G., Ji, X. et al. Quintic generalized Hermite interpolation curves: construction and shape optimization using an improved GWO algorithm. Comp. Appl. Math. 41, 115 (2022). https://doi.org/10.1007/s40314-022-01813-6

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  • DOI: https://doi.org/10.1007/s40314-022-01813-6

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