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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

Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…

Graphics · Computer Science 2023-06-16 Chao Yuan , Nan Cao , Yang Shi

Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design and self-folding structures, it is essential to understand the interplay between the set of folds in…

Soft Condensed Matter · Physics 2018-03-01 Bryan Gin-ge Chen , Christian D. Santangelo

Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer…

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…

Computational Geometry · Computer Science 2018-03-12 Zhonghua Xi , Yu-Ki Lee , Young-Joo Lee , Yun-hyeong Kim , Huangxin Wang , Yue Hao , Young-Chang Joo , In-Suk Choi , Jyh-Ming Lien

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…

Robotics · Computer Science 2026-03-17 Bohan Zhang , Bo Wang , Huajiang Ouyang , Zhigang Wu , Haohao Bi , Jiawei Xu , Mingchao Liu , Weicheng Huang

A flat plate can bend into a curved surface if it experiences an inhomogeneous growth field. In this article a method is described that numerically determines the optimal growth field giving rise to an arbitrary target shape, optimizing for…

Soft Condensed Matter · Physics 2015-08-05 Gareth Wyn Jones , L. Mahadevan

When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is…

Soft Condensed Matter · Physics 2018-07-25 Leonid V. Mirantsev , André M. Sonnet , Epifanio G. Virga

We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to…

Soft Condensed Matter · Physics 2016-02-17 Daniel M. Sussman , Yigil Cho , Toen Castle , Xingting Gong , Euiyeon Jung , Shu Yang , Randall D. Kamien

Traditional origami structures can be continuously deformed back to a flat sheet of paper, while traditional kirigami requires glue or seams in order to maintain its rigidity. In the former, non-trivial geometry can be created through…

Materials Science · Physics 2020-01-29 Xinyu Wang , Simon D. Guest , Randall D. Kamien

Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. There are similarly a variety of methods for wrapping, from pressing a film onto a hard substrate, to using…

Soft Condensed Matter · Physics 2019-04-30 Joseph D. Paulsen

Two-dimensional (2D) origami tessellations such as the Miura-ori are often generalized to build three-dimensional (3D) architected materials with sandwich or cellular structures. However, such 3D blocks are densely packed with continuity of…

Soft Condensed Matter · Physics 2025-07-02 Guowei Wayne Tu , Evgueni T. Filipov

We propose a novel computational framework for modeling and simulating origami structures. In this framework, bilinear solid-shell elements are employed to model the origami panels while crease folding is considered through the angle…

Graphics · Computer Science 2026-01-05 Qixin Liang

We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…

Graphics · Computer Science 2017-07-27 Michael Rabinovich , Tim Hoffmann , Olga Sorkine-Hornung

We investigate the mechanical response of thin sheets perforated with a square array of mutually orthogonal cuts, which leaves a network of squares connected by small ligaments. Our combined analytical, experimental and numerical results…

Soft Condensed Matter · Physics 2017-03-06 Ahmad Rafsanjani , Katia Bertoldi

Fully soft bistable mechanisms have shown extensive applications ranging from soft robotics, wearable devices, and medical tools, to energy harvesting. However, the lack of design and fabrication methods that are easy and potentially…

Robotics · Computer Science 2023-02-15 Mrunmayi Mungekar , Leixin Ma , Wenzhong Yan , Vishal Kackar , Shyan Shokrzadeh , M. Khalid Jawed

A characterization of real numbers constructible by paper folding.

History and Overview · Mathematics 2007-09-21 Antonio M. Oller

Object manipulation is a fundamental challenge in robotics, where systems must balance trade-offs among manipulation capabilities, system complexity, and throughput. Distributed manipulator systems (DMS) use the coordinated motion of…

Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…

Soft Condensed Matter · Physics 2025-10-20 João C. Neves , Bernardo R. Marques , Cristóvão S. Dias , Nuno A. M. Araújo

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