Encoding and topological computation on textile structures

Bright, Matt and Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 (2020) Encoding and topological computation on textile structures. Computers & Graphics, 90. pp. 51-61.

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Abstract

A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The first important problem is to encode all textile structures in a simple combinatorial way. This paper extends the notion of the Gauss code in classical knot theory, providing a tool for topological computation on these structures. As a first application, we present a linear time algorithm for determining whether a code represents a textile in the physical sense. This algorithm, along with invariants of textile structures, allowed us for the first time to classify all oriented textile structures woven from a single component up to complexity five.

Item Type:	Article
Additional Information:	Special Proceedings of Shape Modelling International Conference 2020
Uncontrolled Keywords:	computational topology, topological classification, knot, link, periodic structure, ambient isotopy
Depositing User:	Symplectic Admin
Date Deposited:	20 May 2020 09:27
Last Modified:	18 Jan 2023 23:51
DOI:	10.1016/j.cag.2020.05.014
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3088049