By bidirectionally linking the dimensions of a flat and a folded version of the mesh, it is possible to manipulate either one and see its effects on the other, and always maintain developability.

Generally if we start with a 3d model of a folded shape, such as a piece of origami, and move its vertices around arbitrarily, we destroy this condition of developability, and it can no longer be unfolded to a flat sheet.

In the plane, angles around each vertex obviously always add to 360°, so if we triangulate the mesh and make sure the folded and flat versions always have the same edge lengths, we can ensure it is always unfoldable.

Made using Kangaroo/Grasshopper

Thanks to Tomohiro Tachi, whose work was a great inspiration.

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