An approach for designing a developable surface through a given line of curvature

Developable surface and line of curvature play an important role in geometric design and surface analysis. This paper proposes a new method to construct a developable surface possessing a given curve as the line of curvature of it. We analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Finally, we illustrate the convenience and efficiency of this method by some representative examples.

► We construct a developable surface possessing a given curve as the line of curvature.
► We derive the conditions when the developable surface is cylinder, cone or tangent surface.
► The function θ(s)θ(s) can control the shape of the developable surface.