Degree Reduction of Q-Bézier Curves via Squirrel Search Algorithm

Xiaomin Liu, Muhammad Abbas, Gang Hu and Samia BiBi
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Xiaomin Liu: College of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China
Muhammad Abbas: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Gang Hu: Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China
Samia BiBi: School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia

Mathematics, 2021, vol. 9, issue 18, 1-20

Abstract: Q-Bézier curves find extensive applications in shape design owing to their excellent geometric properties and good shape adjustability. In this article, a new method for the multiple-degree reduction of Q-Bézier curves by incorporating the swarm intelligence-based squirrel search algorithm (SSA) is proposed. We formulate the degree reduction as an optimization problem, in which the objective function is defined as the distance between the original curve and the approximate curve. By using the squirrel search algorithm, we search within a reasonable range for the optimal set of control points of the approximate curve to minimize the objective function. As a result, the optimal approximating Q-Bézier curve of lower degree can be found. The feasibility of the method is verified by several examples, which show that the method is easy to implement, and good degree reduction effect can be achieved using it.

Keywords: Q-Bernstein polynomials; Q-Bézier curves; degree reduction; squirrel search algorithm; control points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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