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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) can control the shape of the developable surface.