On mathematical folding of curved crease origami: Sliding developables and parametrizations of folds into cylinders and cones.

Motivated by the art of curved crease origami we study mathematical models for folding ideal paper along curved creases. We approach the problem of finding mathematical descriptions in terms of developable surfaces of those shapes which can be folded from real paper but where its rigorous description is very often unknown. For that we investigate a particular one-parameter family of surfaces isometric to a given planar surface patch. For each such surface we parametrize the crease curves which fold those surfaces into cylinders and cones. We apply our methods to explore curved crease origami designs, such as tessellations of the plane and cylinders. • We compute explicit isometric deformations of developable surfaces that are guided by sliding on planes. • We give explicit parametrizations of crease curves between developable surfaces and cylinders and cones. • We illustrate our methods on examples such as curved crease tessellations of cylinders and planes. [ABSTRACT FROM AUTHOR]