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Open AccessArticle

Approximate Multi-Degree Reduction of SG-Bézier Curves Using the Grey Wolf Optimizer Algorithm

by Gang Hu 1,*, Yu Qiao 1, Xinqiang Qin 1 and Guo Wei 2
1
Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China
2
Department of Mathematics & Computer Science, University of North Carolina at Pembroke, Pembroke, NC 28372, USA
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1242; https://doi.org/10.3390/sym11101242
Received: 26 July 2019 / Revised: 21 September 2019 / Accepted: 25 September 2019 / Published: 4 October 2019
SG-Bézier curves have become a useful tool for shape design and geometric representation in computer aided design (CAD), owed to their good geometric properties, e.g., symmetry and convex hull property. Aiming at the problem of approximate degree reduction of SG-Bézier curves, a method is proposed to reduce the n-th SG-Bézier curves to m-th (m < n) SG-Bézier curves. Starting from the idea of grey wolf optimizer (GWO) and combining the geometric properties of SG-Bézier curves, this method converts the problem of multi-degree reduction of SG-Bézier curves into solving an optimization problem. By choosing the fitness function, the approximate multi-degree reduction of SG-Bézier curves with adjustable shape parameters is realized under unrestricted and corner interpolation constraints. At the same time, some concrete examples of degree reduction and its errors are given. The results show that this method not only achieves good degree reduction effect, but is also easy to implement and has high accuracy. View Full-Text
Keywords: SG-Bézier curves; shape parameter; degree reduction; grey wolf optimizer algorithm SG-Bézier curves; shape parameter; degree reduction; grey wolf optimizer algorithm
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Hu, G.; Qiao, Y.; Qin, X.; Wei, G. Approximate Multi-Degree Reduction of SG-Bézier Curves Using the Grey Wolf Optimizer Algorithm. Symmetry 2019, 11, 1242.

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