Chen, Yao, Fan, Linzi, Bai, Yongtao, Feng, Jian and Sareh, Pooya ORCID: 0000-0003-1836-2598
(2020)
Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming.
Computers & Structures, 239.
p. 106328.
Text
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Abstract
Traditional origami design is generally based on designers’ artistic intuition and skills, mathematical calculations, and experimentations, which can involve challenges for crease patterns with a large number of vertices. To develop novel origami structures for engineering applications, systematic and easy-to-implement approaches capable of generating diverse origami patterns are desired, without requiring extensive artistic skills and experience in origami mathematics. Here, we present a computational method for automatically assigning mountain-valley fold lines to given geometric configurations of origami structures. This method is based upon a geometric-graph-theoretic representation approach combined with a graph-theoretic cycle detection algorithm, taking the subgraphs of a given structure as inputs. Then, a mixed-integer linear programming (MILP) model is established to find flat-foldable origami patterns under given constraints on the local flat-foldability and degree of vertices, leading to the identification of crease lines associated with local minimum angles. Numerical examples are presented to demonstrate the performance of the proposed approach for a range of origami structures with degree-4 or -6 vertices represented by their corresponding subgraphs.
Item Type: | Article |
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Uncontrolled Keywords: | Origami, Crease pattern, Particle swarm optimization, Graph theory, Folding |
Depositing User: | Symplectic Admin |
Date Deposited: | 30 Jul 2020 15:47 |
Last Modified: | 18 Jan 2023 23:38 |
DOI: | 10.1016/j.compstruc.2020.106328 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3095740 |