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.
Highlights
Mathematics 2021, 9, 2212. https://In the representation of a curve or surface, it is crucial which bases are used if the shape and characteristics of the curve or surface are wished to be preserved
Due to the extensive application of Q-Bézier curves and the significant function that degree reduction plays in data conversion between different CAD/CAM systems, as well as the superiorities and potential possessed by intelligent optimizers in solving optimization problems, this paper propose a new method for the degree reduction of Q-Bézier by incorporating the high-efficient swarm intelligence-based squirrel search algorithm
Is an absolute error, and its value is affected by the coordinate value of the control points of the curves, which brings inconvenience to the objective evaluation of the approximation effect
Summary
In the representation of a curve or surface, it is crucial which bases are used if the shape and characteristics of the curve or surface are wished to be preserved. Compared with the first two methods, the third kind of method in [31,32,33,34] is more convenient to be used for the multiple-degree reduction of different types of curves These methods based on intelligent optimization algorithms seem simpler, by which global optimal degree reduced curves can be obtained intelligently, avoiding complicated theoretical derivation. Due to the extensive application of Q-Bézier curves and the significant function that degree reduction plays in data conversion between different CAD/CAM systems, as well as the superiorities and potential possessed by intelligent optimizers in solving optimization problems, this paper propose a new method for the degree reduction of Q-Bézier by incorporating the high-efficient swarm intelligence-based squirrel search algorithm.
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