Constructing foldable cylindrical surfaces via unfolded waterbomb origami units

Origami tessellations have shown the potential to be utilized for approximating curved target surfaces by folding a set of elemental units. As those units are in partially folded states, the origami approximation captures the outline of the target while demonstrating a corrugated surface. In this paper, we focus on the cylindrical surface and propose a method for constructing its discrete version via square or rectangular units with crease patterns inspired by the waterbomb tessellation. We unify the unit size through optimization to realize cost-efficient constructions. Three-dimensional curved structures are deployed by folding collinear creases between adjacent rows of units and the other creases in each row are remained unfolded. The deployed structure can still be folded to a compact state by folding all creases. To flexibly approximate the outline of the target surface, we analyse relationships between the width and height of the rectangular unit and utilize variations of the waterbomb tessellation to control the region of the origami structure when fully folded. The proposed method provides a novel solution to the so-called inverse-origami-design problem for generating foldable cylindrical surfaces using unfolded waterbomb origami units.Graphical Abstract