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there's my question:

Given 2 regular plane curves (let's say $\mathcal{C}^1$) in the 3D space, is there always a developable surface which contains both curves ?

Thanks, anders

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    Sure. If you have parametric equations for both your curves, and the parameter ranges for both curves are the same, you can then consider the surface drawn out by a moving straight line whose endpoints are at the two curves.2012-07-26
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    Do you really want the surface to *contain* the curves, or to have them as parts of the boundary? Are the curves disjoint? Is the surface required to be embedded (without self-intersections)?2012-07-26
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    @J.M.: It seems to me you are proving that you can build a ruled surface from two curves, but nothing proves such built surface is developable.2013-10-13

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