Construction of developable surfaces using generalized C-Bézier bases with shape parameters

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.