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Non-Euclidean origami is a promising technique for designing multistable deployable structures folded from nonplanar developable surfaces. The impossibility of flat foldability inherent to non-Euclidean origami results in two disconnected…

Soft Condensed Matter · Physics 2023-07-20 Clark Addis , Salvador Rojas , Andres F. Arrieta

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…

Numerical Analysis · Mathematics 2022-05-11 Pablo Antolin , Xiaodong Wei , Annalisa Buffa

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…

Symplectic Geometry · Mathematics 2016-11-03 A. Cannas da Silva , V. Guillemin , A. R. Pires

We characterize the phase-space of all Helical Miura Origami. These structures are obtained by taking a partially folded Miura parallelogram as the unit cell, applying a generic helical or rod group to the cell, and characterizing all the…

Soft Condensed Matter · Physics 2020-03-18 Fan Feng , Paul Plucinsky , Richard D. James

A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In…

Computational Geometry · Computer Science 2026-01-28 Péter Salvi

3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…

Computational Geometry · Computer Science 2024-05-28 Christian Amend , Tom Goertzen

We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zero-thickness paper. In contrast, we show that the…

Computational Geometry · Computer Science 2009-06-26 Erik D. Demaine , Martin L. Demaine , Vi Hart , Gregory N. Price , Tomohiro Tachi

While the grasping capability of robotic grippers has shown significant development, the ability to manipulate objects within the hand is still limited. One explanation for this limitation is the lack of controlled contact variation between…

Robotics · Computer Science 2024-04-16 Qiujie Lu , Angus B. Clark , Matthew Shen , Nicolas Rojas

Non-Euclidean surfaces are ubiquitous in numerous engineering fields, such as automotive, aerospace, and biomedical engineering domains. Morphing origami has numerous potential engineering applications, including soft robots, mechanical…

Materials Science · Physics 2023-12-13 Zihe Liang , Sibo Chai , Qinyun Ding , Kai Xiao , Ke Liu , Jiayao Ma , Jaehyung Ju

Define the augmented square twist origami crease pattern to be the classic square twist crease pattern with one crease added along a diagonal of the twisted square. In this paper we fully describe the rigid foldability of this new crease…

Metric Geometry · Mathematics 2018-09-14 Thomas C. Hull , Michael T. Urbanski

Kirigami involves cutting a flat, thin sheet that allows it to morph from a closed, compact configuration into an open deployed structure via coordinated rotations of the internal tiles. By recognizing and generalizing the geometric…

Soft Condensed Matter · Physics 2021-10-15 Gary P. T. Choi , Levi H. Dudte , L. Mahadevan

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…

Computational Geometry · Computer Science 2026-01-21 David Eppstein

Soft elastic sheets resting on rigid surfaces develop wrinkles, rucks, and folds due to the combined influence of elasticity, gravity, and contact interactions. Despite their ubiquity, the principles governing their morphology and…

Soft Condensed Matter · Physics 2026-05-18 Keisuke Yoshida , Hirofumi Wada

It is well-known that the Kresling pattern of congruent triangles can be arranged either circularly on a cylinder of revolution or in a helical way. In both cases the resulting cylindrical structures are multi-stable. We generalize these…

Computational Geometry · Computer Science 2022-03-22 Georg Nawratil

Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…

Soft Condensed Matter · Physics 2023-03-21 Ian Tobasco , Yousra Timounay , Desislava Todorova , Graham C. Leggat , Joseph D. Paulsen , Eleni Katifori

We construct five types of polyhedra by generalizing the description of Bricard octahedra and applying the generalizations to polyhedral suspensions. The resulting polyhedra are flexible, are of genus 0, exhibit self-intersections, have…

Metric Geometry · Mathematics 2012-06-13 Gerald D. Nelson

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…

Soft Condensed Matter · Physics 2016-03-31 Bryan Gin-ge Chen , Bin Liu , Arthur A. Evans , Jayson Paulose , Itai Cohen , Vincenzo Vitelli , C. D. Santangelo

Rigid origami is a branch of origami with great potential in engineering applications to deal with rigid-panel folding. One of the challenges is to compactly fold the polyhedra made from rigid facets with a single degree of freedom. In this…

Applied Physics · Physics 2020-05-15 Yuanqing Gu , Yan Chen

The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics, and mechanical metamaterials. However, finding foldable paths can be a formidable task as the…

Soft Condensed Matter · Physics 2024-09-30 Matthew Grasinger , Andrew Gillman , Philip Buskohl

The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic…

Computational Geometry · Computer Science 2015-10-20 Joseph O'Rourke