Geodesic
Bending of a~Developable Surface That Preserves Its Edge and Generators
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 263-271

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We consider the problem of reconstructing a piecewise smooth developable surface with a curvilinear edge from its development on which the preimages of the curvilinear edge and all rectilinear generators of the surface that emanate from the points of this edge are given. The required developable surface admits a one-parameter bending in the ambient Euclidean 3-space, and this bending is presented explicitly by formulas. 
@article{TM_2009_266_a14,
     author = {M. I. Shtogrin},
     title = {Bending of {a~Developable} {Surface} {That} {Preserves} {Its} {Edge} and {Generators}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {263--271},
     publisher = {mathdoc},
     volume = {266},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_266_a14/}
}
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M. I. Shtogrin. Bending of a~Developable Surface That Preserves Its Edge and Generators. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 263-271. http://geodesic.mathdoc.fr/item/TM_2009_266_a14/