Design of Developable Surfaces by Using Duality Between Plane and Point Geometries

Based on the idea of duality between plane and point geometries,we present an explicit representation for fourth degree developable surfaces.In our scheme,a developable surface is designed by utilizing control planes with Bézier or B-spline basis functions.In the paper,the properties and geometric construction algorithms for the developable surfaces designed are discussed,and furthermore,the method of representing control planes according to its center point is given.It shows that the techniques for the geometric design of developable surfaces in this paper fully possess the characteristics of existing methods for curve design.Our method provides a quite simple and intuitive way for designing developable surfaces.