Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming

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.

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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
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:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3095740