Computer-aided design of developable surfaces

Abstract

It order to overcome the difficulties in representation of developable surfaces utilizing traditional approaches, based the concept of duality between points and planes in 3D projective space, a direct explicit method of computer-aided design for developable surfaces was presented. In this manner, a developable surface was designed using control planes with Bezier and B-spline basis functions. Techniques for the geometric design of developable surfaces herein had all the characteristics of existing approaches for curves design. Meanwhile, the properties of Bezier and B-spline representation were discussed respectively, and the method of representing control planes according to its center point was given. It shows that some of the geometric construction algorithms that exist for curves can be also generalized to the design of developable surfaces. Furthermore, by the design method that a developable surface is an envelope surface, we give detail analysis of examples about using the same control planes to design developable surfaces. The algorithms were explained in detail, and the examples demonstrate efficiency of the method.