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

Abstract

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.

Keywords

• geometric modeling
• developable c-bézier surfaces
• c-bézier basis functions
• shape parameter
• continuity condition