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Traditional origami structures can be continuously deformed back to a flat sheet of paper, while traditional kirigami requires glue or seams in order to maintain its rigidity. In the former, non-trivial geometry can be created through…
Over the past decade, we have designed six typefaces based on mathematical theorems and open problems, specifically computational geometry. These typefaces expose the general public in a unique way to intriguing results and hard problems in…
We reviewed 43 papers to understand the fabrication of dynamic paper-based interactions. We used a design space to classify tool selection, technique choice, and exploration of paper as a material. We classified 9 dimensions for the design…
Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve…
This paper shows a cut along a crease on an origami sheet makes simple modeling of popular traditional basic folds such as a squash fold in computational origami. The cut operation can be applied to other classical folds and significantly…
Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design and self-folding structures, it is essential to understand the interplay between the set of folds in…
Creating complex spatial objects from a flat sheet of material using origami folding techniques has attracted attention in science and engineering. In the present work, we employ geometric properties of partially folded zigzag strips to…
Origami-inspired mechanisms can transform flat sheets into functional three-dimensional dynamic structures that are lightweight, compact, and capable of complex motion. These properties make origami increasingly valuable in robotic and…
Flat-foldability problem of origami is the problem to determine whether a given crease pattern drawn on a piece of paper is possible to fold without any penetration or intrusion of a polygon into any connections among them. It is known from…
Soft robots employing compliant materials and deformable structures offer great potential for wearable devices that are comfortable and safe for human interaction. However, achieving both structural integrity and compliance for comfort…
This paper presents the designing and testing of PizzaBox, a 3D printed, interactive food ordering system that aims to differ from conventional food ordering systems and provide an entertaining and unique experience when ordering a pizza by…
Curves are essential concepts that enable compounded aesthetic curves, e.g., to assemble complex silhouettes, match a specific curvature profile in industrial design, and construct smooth, comfortable, and safe trajectories in vehicle-robot…
Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer…
We introduce a simple and concrete way of visualizing in three dimensions a "flat" Klein bottle -- one whose local intrinsic geometry is the same as that of a flat plane -- which preserves most its topological and geometric structure.…
We prove several hardness results on folding origami crease patterns. Flat-folding finite crease patterns is fixed-parameter tractable in the ply of the folded pattern (how many layers overlap at any point) and the treewidth of an…
An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface where it is like the pullback of a symplectic form by a folding map and its kernel fibrates with oriented circle fibers over a…
Origami metamaterial design enables drastic qualitative changes in the response properties of a thin sheet via the addition of a repeating pattern of folds based around a rigid folding motion. Known also as a mechanism, this folding motion…
A polyomino is called a development if it can make a box by folding edges of unit squares forming the polyomino. It is known that there are developments that can fold into a box (or boxes) in multiple ways. In this work, we conducted a…
Rigid foldability allows an origami pattern to fold about crease lines without twisting or stretching component panels. It enables folding of rigid materials, facilitating the design of foldable structures. Recent study shows that rigid…
Lattices and their underlying symmetries play a central role in determining the physical properties and applications of many natural and engineered materials. By bridging the lattice geometry and rigid-folding kinematics, this study…