Related papers: An Efficient Enumeration of Flat-Foldings : Study …
When can a plane graph with prescribed edge lengths and prescribed angles (from among $\{0,180^\circ, 360^\circ$\}) be folded flat to lie in an infinitesimally thin line, without crossings? This problem generalizes the classic theory of…
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…
Rigid origami, with applications ranging from nano-robots to unfolding solar sails in space, describes when a material is folded along straight crease line segments while keeping the regions between the creases planar. Prior work has found…
Origami has shown the potential to approximate three-dimensional curved surfaces by folding through designed crease patterns on flat materials. The Miura-ori tessellation is a widely used pattern in engineering and tiles the plane when…
Designing a robot or structure that can fold itself into a target shape is a process that involves challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
One-dimensional slender bodies can be deformed or shaped into spatially complex curves relatively easily due to their inherent compliance. However, traditional methods of fabricating complex spatial shapes are cumbersome, prone to error…
Origami as a deployable structure offers the unique advantage of achieving compact stowage via flat-folding while forming a well-defined surface composed of rigid panels upon deployment. However, since origami consists of flat facets, it is…
Origami is the art of folding paper into various patterns without cutting or tearing the paper. By viewing the paper as the complex plane, we iteratively compute and record all intersection points to construct mathematical origami sets.…
The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials.…
Random tilings are interesting as idealizations of atomistic models of quasicrystals and for their connection to problems in combinatorics and algorithms. Of particular interest is the tiling entropy density, which measures the relation of…
Origami structures enabled by folding and unfolding can create complex 3D shapes. However, even a small 3D shape can have large 2D unfoldings. The huge initial dimension of the 2D flattened structure makes fabrication difficult, and defeats…
We study the spontaneous folding of a 2D template of microscopic panels into a 3D pyramid, driven by thermal fluctuations. Combining numerical simulations and analytical calculations, we find that the total folding time is a non-monotonic…
Origami structures have been widely explored in robotics due to their many potential advantages. Origami robots can be very compact, as well as cheap and efficient to produce. In particular, they can be constructed in a flat format using…
We analyze the problem of folding one polyhedron, viewed as a metric graph of its edges, into the shape of another, similar to 1D origami. We find such foldings between all pairs of Platonic solids and prove corresponding lower bounds,…
The forcing number of a graph with a perfect matching $M$ is the minimum number of edges in $M$ whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in…
Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major…
This note describes an algorithm for enumerating all the elements in a finite set based on uniformly random sampling from the set. This algorithm can be used for enumeration by fair sampling with quantum annealing. Our algorithm is based on…
We consider a problem in computational origami. Given a piece of paper as a convex polygon $P$ and a point $f$ located within, fold every point on a boundary of $P$ to $f$ and compute a region that is safe from folding, i.e., the region…
Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…