Geometric Design of Developable Bezier and B-spline Parametric Surfaces

Using the concept of duality between points and planes in 3D projective space, an explicit and efficient method of computer-aided design for developable surfaces based on Bezier and B-spline basis functions is proposed. By the result that a developable surface is the envelope of a single-parameter family of planes, we give the parametric equation of a Bezier and B-spline developable surface, and discuss respectively properties of Bezier and B-spline representations. Meanwhile, we also present a simplified geometric-construction for developable surfaces, that is, G² Beta restraint condition algorithm for G² continuity between two developable surfaces. It is shown that the geometric construction technique that exists for curves also can be generalized to the design of developable surfaces.