Related papers: An additive algorithm for origami design
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
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…
Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are…
The packing problem, also known as cutting or nesting, has diverse applications in logistics, manufacturing, layout design, and atlas generation. It involves arranging irregularly shaped pieces to minimize waste while avoiding overlap.…
Origami, the ancient art of folding thin sheets, has attracted increasing attention for its practical value in diverse fields: architectural design, therapeutics, deployable space structures, medical stent design, antenna design and…
We introduce the study of forcing sets in mathematical origami. The origami material folds flat along straight line segments called creases, each of which is assigned a folding direction of mountain or valley. A subset $F$ of creases is…
We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet…
We find a closed-form expression for the Poisson's coefficient of curved-crease variants of the ``Miura ori'' origami tessellation. This is done by explicitly constructing a continuous one-parameter family of isometric piecewise-smooth…
The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape…
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…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
Origami design principles are scale invariant and enable direct miniaturization of origami structures provided the sheets used for folding have equal thickness to length ratios. Recently, seminal steps have been taken to fabricate…
Let $S_{g}$ denote the closed orientable surface of genus $g$. In joint work with Huang, the first author constructed exponentially-many (in $g$) mapping class group orbits of pairs of simple closed curves whose complement is a single…
Design - especially of physical objects - can be understood as creative acts solving practical problems. In this paper we describe a biologically-inspired developmental model as the basis of a generative form-finding system. Using local…
Fold-and-cut theorem claims the possibility to cut out from a sheet a set of straight-line drawing using only one cut of scissors, without producing any other cut in the sheet and separating all the figures at the same time, just by folding…
We consider several quadrilateral origami tilings, including the Miura-ori crease pattern, allowing for crease-reversal defects above the ground state which maintain local flat-foldability. Using exactly solvable models, we show that these…
This paper gives one set of axioms for origami constructions, and describes the set of constructible points under these axioms. The determination of the set of cunstructible points for this particular set of axioms is related to Hilbert's…
We perform a comprehensive study of the formation of three dimensional (pyramidal) structures in a large range of conditions, including the possible evaporation of adatoms from the surface and the presence of surface defects. We compare our…
We explore the intersection of human and machine creativity by generating sculptural objects through machine learning. This research raises questions about both the technical details of automatic art generation and the interaction between…
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…