Study on the optimal shape parameter of parametric curves based on PSO algorithm

Abstract

Although the curves with shape parameters has become one of the most popular topics in Computer Aided Geometric Design, but the values of shape parameters are always given as intervals, while in practice, we often need the optimal shape parameter values to ensure that the curves have good fairness and smoothness. This paper is motivated to solve the optimal shape parameters. Firstly, an automatic mathematical model is established to obtain the optimal parameters which is based on the fairing criterion, and then the particle swarm optimization (PSO) algorithm is introduced to solve the optimal model. At the end, Three classes of curves are used as examples to illustrate the effectiveness of our methods.