In this paper, we propose a novel method for constructing developable surfaces using generalized C-Bézier bases with shape parameters. Based on the duality between points and planes in 3D projective space, the generalized developable C-Bézier surfaces, whose shape can be adjusted by changing multiple shape parameters, are designed using control planes with extensional C-Bézier basis functions. With the shape parameters taking different values, a family of developable surfaces can be constructed, which keeps most of characteristics of classic developable Bézier surfaces. Furthermore, some interesting properties of the new developable surfaces, as well as the geometric continuity conditions between two adjacent generalized developable C-Bézier surfaces, are investigated. Finally, we illustrate the convenience and efficiency of the proposed methods by several convictive and representative numerical examples.

在本文中，我们提出了一种使用具有形状参数的广义C-Bézier基来构造可展开曲面的新方法。基于3D投影空间中点和平面之间的对偶性，使用具有扩展C-Bézier基函数的控制平面设计了可通过更改多个形状参数来调整形状的广义可开发C-Bézier曲面。通过使用不同的形状参数值，可以构造一个可展开曲面族，其中保留了经典可展开贝塞尔曲面的大多数特征。此外，还研究了新的可展开曲面的一些有趣特性以及两个相邻的广义可展开C-Bézier曲面之间的几何连续性条件。最后，