Design of developable surfaces using duality between plane and point geometries

Spacelike developable surfaces through a common line of curvature in Minkowski 3-space

“…Another approach to design developable surfaces is a direct surface represented in terms of geometric duality between points and planes in 3D projective space by Chu and Séquin (Chu and Séquin, 2002). In paper (Bodduluri and Ravani, 1993), the concept of duality between points and planes in 3D projective space was used to develop a new representation for developable surfaces in terms of plane geometry.…”

Non-degenerate Developable Triangular Bézier Patches

“…-Projective geometry methods: planes and points are exchanged using duality: Bodduluri and Ravani [8], Pottmann and Farin [9], Pottmann and Wallner [10]. -Based on the de Casteljau algorithm: Chu and Séquin [11], Aumann [12], [13] and Fernández-J ambrina [14].…”

A survey on CAD methods in 3D garment design

“…A developable surface can also be viewed as the envelope of a oneparameter family of tangent planes, and thus can be treated as a curve in a dual projective 3-space. Given this dual representation, some interpolation and approximation algorithms can be computed efficiently [12,78].…”