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An improved black widow optimization algorithm for surfaces conversion

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Abstract

Bézier surfaces and Q-Bézier surfaces are effective modeling tools for shape design in computer-aided geometric design, computer vision, and computer graphics. The mutual conversion between these two kinds of surfaces is a pivotal and knotty technique in CAD/CAM. In this paper, the conversion between Q-Bézier surfaces and rectangular Bézier surfaces is investigated. However, due to the uncertain parameters of the Q-Bézier surfaces, the approximation conversion from rectangular Bézier surfaces to Q-Bézier surfaces can be regarded as an optimization problem, which is effectively dealt with by swarm intelligence algorithm. In this regard, an enhanced Black Widow Optimization called LDBWO is proposed to find more suitable shape parameters to obtain optimal approximation Q-Bézier surfaces, which are closer to the given Bézier surfaces. The LDBWO algorithm overcomes the shortcomings of standard BWO algorithm such as low accuracy, slow convergence, and is easy to fall into local optimum by introducing golden sine learning strategy and diffusion process. Furthermore, to confirm and validate the performance of the LDBWO, eight well-known intelligent algorithms are compared with the LDBWO on various benchmark functions and engineering examples. Finally, by minimizing the conversion error defined by the L2-norm, the optimization model of the approximation conversion from rectangular Bézier surfaces to Q-Bézier surfaces is established. Several representative numerical examples are provided to illustrate the accuracy and efficiency of the proposed methods.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 51875454).

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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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, Bo Du & Xiaofeng Wang

  2. School of Computer Science and Engineering, Xi’an University of Technology, |Xi’an, 710048, People’s Republic of China

    Gang Hu

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  1. Gang Hu
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Correspondence to Gang Hu.

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Hu, G., Du, B. & Wang, X. An improved black widow optimization algorithm for surfaces conversion. Appl Intell 53, 6629–6670 (2023). https://doi.org/10.1007/s10489-022-03715-w

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