A novel geometric modeling approach for cubic developable C-Bézier surfaces

抄録

In this paper, a novel geometric modeling method is proposed to construct generalized cubic developable C-Bézier (GCDC-Bézier, for short) surfaces with shape parameters. By using the control plane with generalized cubic C-Bézier basis function, the GCDC-Bézier surfaces are designed, and the shape of the surfaces are adjusted by changing its shape parameters. In addition, the necessary and sufficient conditions of G¹ continuity and G² Beta smooth continuity between two adjacent GCDC-Bézier surfaces are derived. Finally, we also discuss some properties of the GCDC-Bézier surfaces. The approach proposed in this paper provides a valuable alternative to the existing geometric modeling methods of developable surfaces.