Related papers: Pillow Box Design
An "origami" (or flat structure) on a closed oriented surface, $S_g$, of genus $g \geq 2$ is obtained from a finite collection of unit Euclidean squares by gluing each right edge to a left one and each top edge to a bottom one. The main…
The field of rigid origami concerns the folding of stiff, inelastic plates of material along crease lines that act like hinges and form a straight-line planar graph, called the crease pattern of the origami. Crease pattern vertices in the…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
In this paper we present a new algorithm for a layout optimization problem: this concerns the placement of weighted polygons inside a circular container, the two objectives being to minimize imbalance of mass and to minimize the radius of…
The desirable properties when constructing collections of subspaces often include the algebraic constraint that the projections onto the subspaces yield a resolution of the identity like the projections onto lines spanned by vectors of an…
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…
Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…
This review presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing non-trivial textures, focusing in particular on the common motifs of twisted and…
Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there has been heuristic developments in constructing patterns with desirable…
Kirigami, an ancient paper cutting art, offers a promising strategy for 2D-to-3D shape morphing through cut-guided deformation. Existing kirigami designs for target 3D curved shapes rely on intricate cut patterns in thin sheets, making the…
In this paper we describe a method for packing tubes and boxes in containers. Each container is divided into parts (holders) which are allocated to subsets of objects. The method consists of a recursive procedure which, based on a…
Rigidly and flat-foldable quadrilateral mesh origami is the class of quadrilateral mesh crease patterns with one fundamental property: the patterns can be folded from flat to fully-folded flat by a continuous one-parameter family of…
This article is concerned with an example of complex planar geometry arising from flat origami challenges. The complexity of solution algorithms is illustrated, depending on the depth of the initial analysis of the problem, starting from…
Origami structures have been receiving a lot of attention from engineering and scientific researchers owing to their unique properties such as deployability, multi-stability, negative stiffness, etc. However, dynamic properties of origami…
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.…
Rigid origami has shown potential in large diversity of practical applications. However, current rigid origami crease pattern design mostly relies on known tessellations. This strongly limits the diversity and novelty of patterns that can…
An origami extrusion is a folding of a 3D object in the middle of a flat piece of paper, using 3D gadgets which create faces with solid angles. In this paper we focus on 3D gadgets which create a top face parallel to the ambient paper and…
Orthogonally assembled double-layered corrugated (OADLC) mechanisms are a class of foldable structures that harness origami-inspired methods to enhance the structural stiffness of resulting devices; these mechanisms have extensive…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…