Geometric design of developable composite Bézier surfaces

This paper studies geometric design of developable surfaces that consist of consecutive Bézier patches. It is shown that the number of degrees of freedom (DOF) for the surface design is independent of the degree of the surface. With a first boundary curve freely specified, (2m+3), (m+4), and five DOF's are available for a second boundary curve of a developable surface containing m patches, when the surface is G ⁰ , G ¹ , and G ² , respectively. There remain five and (7-2m) DOF's for C ¹ and C ² continuity. Four and three DOF's are left for the patch design when the end ruling vanishes on one and both sides. Design examples are presented that fully utilize the corresponding DOF's subject to various continuity conditions. This work provides the foundation for systematic implementation of a CAGD system for developable composite Bézier surfaces.