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We show that minimally 3-rigid block-and-hole graphs, with one block or one hole, are characterised as those which are constructible from $K_3$ by vertex splitting, and also, as those having associated looped face graphs which are…
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…
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…
In this paper we construct Ricci-positive metrics on the connected sum of products of arbitrarily many spheres provided the dimensions of all but one sphere in each summand are at least 3. There are two new technical theorems required to…
We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way,…
We study the canonical structure of the topological 3D gravity with torsion, assuming the anti-de Sitter asymptotic conditions. It is shown that the Poisson bracket algebra of the canonical generators has the form of two independent…
A characterization of real numbers constructible by paper folding.
Origami inspired architectures offer a powerful route toward lightweight, reconfigurable, and programmable robotic systems. Yet, a unified mechanics framework capable of seamlessly bridging rigid folding, elastic deformation, and stability…
One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…
We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…
By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with…
We present a new method for multimodal conditional 3D face geometry generation that allows user-friendly control over the output identity and expression via a number of different conditioning signals. Within a single model, we demonstrate…
The advent of 3D printing has revolutionized many industries and has had similar improvements for soft robots. However, many challenges persist for these functional devices. Magnetic soft robots require the addition of magnetic particles…
We consider the construction of a polygon $P$ with $n$ vertices whose turning angles at the vertices are given by a sequence $A=(\alpha_0,\ldots, \alpha_{n-1})$, $\alpha_i\in (-\pi,\pi)$, for $i\in\{0,\ldots, n-1\}$. The problem of…
A foundational result in origami mathematics is Kawasaki and Justin's simple, efficient characterization of flat foldability for unassigned single-vertex crease patterns (where each crease can fold mountain or valley) on flat material. This…
We propose a novel method to generate fabrication blueprints from images of carpentered items. While 3D reconstruction from images is a well-studied problem, typical approaches produce representations that are ill-suited for computer-aided…
The creation of manufacturable and editable 3D shapes through Computer-Aided Design (CAD) remains a highly manual and time-consuming task, hampered by the complex topology of boundary representations of 3D solids and unintuitive design…
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…
In this work, we present a geometry-based grasping algorithm that is capable of efficiently generating both top and side grasps for unknown objects, using a single view RGB-D camera, and of selecting the most promising one. We demonstrate…
Generating realistic 3D faces is of high importance for computer graphics and computer vision applications. Generally, research on 3D face generation revolves around linear statistical models of the facial surface. Nevertheless, these…