Degree Reduction of Q-Bézier Curves via Squirrel Search Algorithm

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-09, Vol.9 (18), p.2212
Main Authors: Liu, Xiaomin, Abbas, Muhammad, Hu, Gang, BiBi, Samia
Format: Article
Language:English
Subjects:
Approximation
control points
Curves
Degree reduction
Design
Food science
Methods
Optimization
Optimization algorithms
Optimization techniques
Q-Bernstein polynomials
Q-Bézier curves
Search algorithms
squirrel search algorithm
Squirrels
Swarm intelligence
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9182212