DESIGN OF DEVELOPABLE SURFACES USING DUALITY BETWEEN PLANE AND POINT GEOMETRIES

The concept of duality between points and planes in 3D projective spac e is used to develop a new representation for developable surfaces in terms of plane geometry. In this manner, a developable surface is desi gned using control planes with appropriate basis functions. The use of rational Bezier and B-spline bases is focused on, and a technique for the geometric design of developable surfaces is developed that has al l the characteristics of existing methods for curve design. It is show n that some of the geometric constructions that exist for curves also generalize to the design of developable surfaces. In particular, de Ca steljau- and Farin-Boehm-type construction algorithms are developed fo r Bezier developable surfaces.