Developable Conditions for Ruled Surfaces and Design of Developable Surfaces

With the operator representation of Bezier curves, we first derive the sufficient and necessary conditions of a ruled surface being a developable surface, where the ruled surface is generated from two Bezier curves of degree m and n respectively as its boundary curves. Then we present a new method for designing the developable surface of degree (2, 3) with four corner points and one free control vertex. The experiment results indicate that the proposed method is simple to perform and can be easily used to control the shape of surface.