GEOMETRIC DESIGN AND FABRICATION OF DEVELOPABLE BEZIER AND B-SPLINE SURFACES

In this paper we study Computer Aided Geometric Design (CAGD) and Manu facturing (CAM) of developable surfaces. We develop a direct represent ation of developable surfaces in terms of plane geometry. It uses cont rol planes to determine a surface which is a Bezier or a B-spline inte rpolation of the control planes. In the Bezier case, a de Casteljau ty pe construction method is presented for geometric design of developabl e Bezier surfaces. In the B-spline case, de Boor type construction for the geometric design of the developable surface and Boehm type knot i nsertion algorithm are presented. In the area of manufacturing or fabr ication of developable surfaces, we present simple methods far both de velopment of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and li ne geometries and eliminates the need for solving differential equatio ns of Riccatti type used in previous methods. The results are illustra ted using an example generated by a CAD/CAM system implemented based o n the theory presented.