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Double-distance frameworks and mixed sparsity graphs

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Double-distance frameworks and mixed sparsity graphs. / Nixon, Anthony; Power, Stephen.
In: Discrete and Computational Geometry, Vol. 63, No. 2, 31.03.2020, p. 294-318.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Nixon, A & Power, S 2020, 'Double-distance frameworks and mixed sparsity graphs', Discrete and Computational Geometry, vol. 63, no. 2, pp. 294-318. https://doi.org/10.1007/s00454-019-00164-0

APA

Nixon, A., & Power, S. (2020). Double-distance frameworks and mixed sparsity graphs. Discrete and Computational Geometry, 63(2), 294-318. https://doi.org/10.1007/s00454-019-00164-0

Vancouver

Nixon A, Power S. Double-distance frameworks and mixed sparsity graphs. Discrete and Computational Geometry. 2020 Mar 31;63(2):294-318. Epub 2019 Dec 18. doi: 10.1007/s00454-019-00164-0

Author

Nixon, Anthony ; Power, Stephen. / Double-distance frameworks and mixed sparsity graphs. In: Discrete and Computational Geometry. 2020 ; Vol. 63, No. 2. pp. 294-318.

Bibtex

@article{e3239c84e0ea4dcf9e36395b36894397,
title = "Double-distance frameworks and mixed sparsity graphs",
abstract = "A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint frameworks in a variety of such contexts. The main results are combinatorial characterisations for (i) frameworks restricted to surfaces with both Euclidean and geodesic distance constraints, (ii) frameworks in the plane with Euclidean and non-Euclidean distance constraints, and (iii) direction-length frameworks in the non-Euclidean plane.",
keywords = "Bar-joint framework, Infinitesimal rigidity, Double-distance, Coloured graphs, Mixed sparsity",
author = "Anthony Nixon and Stephen Power",
year = "2020",
month = mar,
day = "31",
doi = "10.1007/s00454-019-00164-0",
language = "English",
volume = "63",
pages = "294--318",
journal = "Discrete and Computational Geometry",
issn = "0179-5376",
publisher = "Springer New York",
number = "2",

}

RIS

TY - JOUR

T1 - Double-distance frameworks and mixed sparsity graphs

AU - Nixon, Anthony

AU - Power, Stephen

PY - 2020/3/31

Y1 - 2020/3/31

N2 - A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint frameworks in a variety of such contexts. The main results are combinatorial characterisations for (i) frameworks restricted to surfaces with both Euclidean and geodesic distance constraints, (ii) frameworks in the plane with Euclidean and non-Euclidean distance constraints, and (iii) direction-length frameworks in the non-Euclidean plane.

AB - A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint frameworks in a variety of such contexts. The main results are combinatorial characterisations for (i) frameworks restricted to surfaces with both Euclidean and geodesic distance constraints, (ii) frameworks in the plane with Euclidean and non-Euclidean distance constraints, and (iii) direction-length frameworks in the non-Euclidean plane.

KW - Bar-joint framework

KW - Infinitesimal rigidity

KW - Double-distance

KW - Coloured graphs

KW - Mixed sparsity

U2 - 10.1007/s00454-019-00164-0

DO - 10.1007/s00454-019-00164-0

M3 - Journal article

VL - 63

SP - 294

EP - 318

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -