Generation of quasi‐developable Q‐Bézier strip via PSO‐based shape parameters optimization

Abstract

The generation of quasi‐developable from two boundary curves finds extensive application in manufacturing system. In this paper, we present a new method to generate a quasi‐developable from two Bézier boundary curves via particle swarm optimization (PSO)‐based shape parameters optimization. Owing to the powerful and flexible shape adjustment ability of Q‐Bézier curves, we introduce the multiple shape parameters of Q‐Bézier model into original boundary curves for developability optimization. We formulate the generation of quasi‐developable as a geometric optimization problem in which the objective function is defined as the developability degree of the strip and search within the value range of the shape parameters for the set of optimal shape parameters by PSO to achieve a higher‐accuracy developability. Modeling examples demonstrate that the proposed method is effective, easy to implement, which provides users with the overall shape control of the output strip. With the control points keeping unchanged, the fairness of the surface and its approximation to the original surface can be guaranteed naturally, and the number of optimization variables is greatly reduced compared with previous methods.