The shape optimization design of developable surface is a critical and intractable technique in CAD/CAM and used in many manufacturing planning operations. In this paper, we study shape optimization by using a new cuckoo search (CS) algorithm to promote the development of generalized developable H-Bézier surfaces (or GDHBS, for short). According to the duality between points and planes in 3D projective space, the GDHBS shape optimization problem is formulated as an arc length, energy and curvature variation minimization problem of dual curve, respectively. Then, an adaptive CS optimization algorithm is applied to the solutions of those GDHBS shape optimization models. Finally, we illustrate the effectiveness and performance of the proposed methods by some representative and convictive examples.

可展表面的形状优化设计是CAD / CAM中的一项关键且棘手的技术，并用于许多制造计划操作中。在本文中，我们通过使用新的布谷鸟搜索（CS）算法研究形状优化，以促进广义可发展H-Bézier曲面（或简称GDHBS）的发展。根据3D投影空间中点和平面之间的对偶性，将GDHBS形状优化问题分别表述为对偶曲线的弧长，能量和曲率变化最小化问题。然后，将自适应CS优化算法应用于这些GDHBS形状优化模型的解。最后，我们通过一些有代表性和有说服力的例子来说明所提出方法的有效性和性能。