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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.

Origami tessellations are geometric pieces folded from a single sheet of paper with flatly overlapped facets. Most existing origami tessellations are constructed by first marking a grid of crease lines on the paper and then arranging repeating patterns along the grid. However, this design method is limited because it cannot design origami tessellations with patterns that cannot be represented on a grid, such as a regular pentagon. This paper proposes a new construction method for origami tessellations that solves this problem and enriches these varieties. In the proposed method, a boundary of an origami tessellation is determined first, and then patterns called triangle twist fold patterns are placed inside the boundary. A similar approach is known as a hole problem, although in this paper, the problem is redefined and discussed in a form suitable for origami tessellations. As a result, a grid-independent construction method was proposed, and new origami tessellations were obtained by using software that implements the method.

Folding a thin sheet material such as paper along curves creates a developable surface composed of ruled surface patches. When using such surfaces in design, designers often repeat a process of folding along curves drawn on a sheet and checking the folded shape. Although several methods for constructing such shapes on a computer have been proposed, it is still difficult to check the folded shapes instantly from the crease patterns. In this paper, we propose a simple method that approximately realizes a simulation of curved folds with a triangular mesh from its crease pattern. The proposed method first approximates curves in a crease pattern with polylines and then generates a triangular mesh. In order to construct the discretized developable surface, the edges in the mesh are rearranged so that they align with the estimated rulings. The proposed method is characterized by its simplicity and is implemented on an existing origami simulator that runs in a web browser.

Origami techniques, as folding and unfolding, can be utilized in shrinkable structures. Especially when the crease pattern is rigid foldable, it can be treated as a mechanical linkage of rigid panels connected by hinges. Since rigid foldable crease patterns have the strong geometrical constraint of the facets not being able to stretch or bend, it is difficult to design new crease patterns, and variations of existing patterns are limited. However, it is known that there are cases where crease patterns can be made rigid foldable by adding some slits. This paper proposes a mechanical linkage that folds into a similar flat shape by adding slits. A method is presented of generating rigid foldable crease patterns in arbitrary polygons that fold smaller, and it is confirmed that structures that have a mechanism for shrinking can be generated from these crease patterns using rigid thick panels and hinges.

Origami techniques, as folding and unfolding, can be utilized in shrinkable structures. Especially when the crease pattern is rigid foldable, it can be treated as a mechanical linkage of rigid panels connected by hinges. Since rigid foldable crease patterns have the strong geometrical constraint of the facets not being able to stretch or bend, it is difficult to design new crease patterns, and variations of existing patterns are limited. However, it is known that there are cases where crease patterns can be made rigid foldable by adding some slits. This paper proposes a mechanical linkage that folds into a similar flat shape by adding slits. A method is presented of generating rigid foldable crease patterns in arbitrary polygons that fold smaller, and it is confirmed that structures that have a mechanism for shrinking can be generated from these crease patterns by using rigid thick panels and hinges.