Implementation of Adjustably Developable Surfaces Using Duality Between Point and Plane Geometries

An explicit and efficient method of computer-aided design for adjustably developable surfaces is proposed. It is based on the important idea of duality between plane and point geometries. The shapes of developable surfaces can be adjusted using a control parameter. We show that the techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design. Further, we present a new method of displaying control planes and the generating plane at physically and geometrically meaningful location relative to the resulting surface. The new algorithm can not only overcome the difficulties in representation of developable surfaces utilizing traditional approaches, but also resolve the problems in adjusting and controlling the shape of developable surfaces that often faced in Engineering.