Rmc. Bodduluri et B. Ravani, GEOMETRIC DESIGN AND FABRICATION OF DEVELOPABLE BEZIER AND B-SPLINE SURFACES, Journal of mechnical design, 116(4), 1994, pp. 1042-1048
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.