Rmc. Bodduluri et B. Ravani, DESIGN OF DEVELOPABLE SURFACES USING DUALITY BETWEEN PLANE AND POINT GEOMETRIES, Computer Aided Design, 25(10), 1993, pp. 621-632
Citations number
18
Categorie Soggetti
Computer Sciences, Special Topics","Computer Applications & Cybernetics
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.