A Topological Study of Textile Structures. Part I: An Introduction to Topological Methods

Grishanov, S. A.; Meshkov, Vadim R.; Omelchenko, Alexander

doi:10.1177/0040517508095600

Cited by 37 publications

(37 citation statements)

References 25 publications

(34 reference statements)

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“…Additionally, due to the huge diversity of textile structures, it is impractical to come up with a complete natural language classification of every possible structure. Consequently, there have been • • • ⊂ several attempts to define textile structures in a formal and mathematical way [12,13].…”

Section: Related Workmentioning

confidence: 99%

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A Similarity Measure for Weaving Patterns in Textiles

Helmer

Ngo

2015

Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval

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We propose a novel approach for measuring the similarity between weaving patterns that can provide similarity-based search functionality for textile archives. We represent textile structures using hypergraphs and extract multisets of k-neighborhoods from these graphs. The resulting multisets are then compared using Jaccard coefficients, Hamming distances, and cosine measures. We evaluate the different variants of our similarity measure experimentally, showing that it can be implemented efficiently and illustrating its quality using it to cluster and query a data set containing more than a thousand textile samples.

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Section: Related Workmentioning

confidence: 99%

“…Nevertheless, we show some typical examples of textile structures in Figure 1 In the following we give a brief informal summary of topological concepts that have been used to model textile structures, in particular knots, links, tangles, and their two-dimensional projections. Detailed, formal definitions can be found in [7,12].…”

Section: Textile Modelingmentioning

confidence: 99%

A Similarity Measure for Weaving Patterns in Textiles

Helmer

Ngo

2015

Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval

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“…The topological rules correct errors without ambiguity. Topological algebras appeared in textile science a quarter of a century ago and recently became a key part of generating textile models (94,(102)(103)(104)(105). Correcting ordering errors during virtual-specimen generation by invoking formally tabulated topological ordering rules leads to very robust methods that can deal with arbitrary errors.…”

Section: Solid Tow Representationsmentioning

confidence: 99%

Stochastic Virtual Tests for High-Temperature Ceramic Matrix Composites

Cox

Bale

Begley

et al. 2014

Annu. Rev. Mater. Res.

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We review the development of virtual tests for high-temperature ceramic matrix composites with textile reinforcement. Success hinges on understanding the relationship between the microstructure of continuous-fiber composites, including its stochastic variability, and the evolution of damage events leading to failure. The virtual tests combine advanced experiments and theories to address physical, mathematical, and engineering aspects of material definition and failure prediction. Key new experiments include surface image correlation methods and synchrotron-based, micrometer-resolution 3D imaging, both executed at temperatures exceeding 1,500• C. Computational methods include new probabilistic algorithms for generating stochastic virtual specimens, as well as a new augmented finite element method that deals efficiently with arbitrary systems of crack initiation, bifurcation, and coalescence in heterogeneous materials. Conceptual advances include the use of topology to characterize stochastic microstructures. We discuss the challenge of predicting the probability of an extreme failure event in a computationally tractable manner while retaining the necessary physical detail. 17.1

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“…A survey of various areas, including knitting and weaving, is presented by Belcastro and Yackel [3]. Grishanov look into knot theory and its relevance to the topology of textiles [6]. The second author and Ruskey [7] were the first to develop a mathematical model for bobbin lace and express its patterns using graph drawings.…”

Section: Introductionmentioning

confidence: 99%

Drawing Bobbin Lace Graphs, or, Fundamental Cycles for a Subclass of Periodic Graphs

Biedl

Irvine

2018

Lecture Notes in Computer Science

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In this paper, we study a class of graph drawings that arise from bobbin lace patterns. The drawings are periodic and require a combinatorial embedding with specific properties which we outline and demonstrate can be verified in linear time. In addition, a lace graph drawing has a topological requirement: it contains a set of non-contractible directed cycles which must be homotopic to (1, 0), that is, when drawn on a torus, each cycle wraps once around the minor meridian axis and zero times around the major longitude axis. We provide an algorithm for finding the two fundamental cycles of a canonical rectangular schema in a supergraph that enforces this topological constraint. The polygonal schema is then used to produce a straight-line drawing of the lace graph inside a rectangular frame. We argue that such a polygonal schema always exists for combinatorial embeddings satisfying the conditions of bobbin lace patterns, and that we can therefore create a pattern, given a graph with a fixed combinatorial embedding of genus one.Research supported by NSERC. Thank you to Anna Lubiw for helpful input.

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A Topological Study of Textile Structures. Part I: An Introduction to Topological Methods

Cited by 37 publications

References 25 publications

A Similarity Measure for Weaving Patterns in Textiles

A Similarity Measure for Weaving Patterns in Textiles

Stochastic Virtual Tests for High-Temperature Ceramic Matrix Composites

Drawing Bobbin Lace Graphs, or, Fundamental Cycles for a Subclass of Periodic Graphs

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