A novel scheme of folding discretized surfaces of revolution inspired by waterbomb origami

Origami research is always devoted to exploring the transformation from a paper-like material into a three-dimensional (3D) object, which is widely used in the storage of planar structures. However, origami only has a two-dimensional crease map, so it performs limited effect on the storage of 3D surface. Inspired by waterbomb origami, this paper presents a scheme of folding discretized surfaces of revolution to create foldable 3D geometries. The geometries, which are the approximation of target surfaces of revolution, consist of discretizing surfaces of revolution and have 3D crease maps to guide folding. The discretized surfaces constructed by the approaching scheme can satisfy the error requirements and retain the features of original surfaces. The paper verifies the feasibility of the folding scheme by showing the formula of four typical surfaces, including convex shape, concave shape, concave-convex shape and capsule shape. This scheme of folding discretized surfaces of revolution shows the potential of origami to 3D deployable structures in the field of aerospace.