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Necessary conditions for the generic global rigidity of frameworks on surfaces

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Necessary conditions for the generic global rigidity of frameworks on surfaces. / Jackson, Bill; McCourt, Tom; Nixon, Anthony.
In: Discrete and Computational Geometry, Vol. 52, No. 2, 09.2014, p. 344-360.

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

Harvard

Jackson, B, McCourt, T & Nixon, A 2014, 'Necessary conditions for the generic global rigidity of frameworks on surfaces', Discrete and Computational Geometry, vol. 52, no. 2, pp. 344-360. https://doi.org/10.1007/s00454-014-9616-3

APA

Jackson, B., McCourt, T., & Nixon, A. (2014). Necessary conditions for the generic global rigidity of frameworks on surfaces. Discrete and Computational Geometry, 52(2), 344-360. https://doi.org/10.1007/s00454-014-9616-3

Vancouver

Jackson B, McCourt T, Nixon A. Necessary conditions for the generic global rigidity of frameworks on surfaces. Discrete and Computational Geometry. 2014 Sept;52(2):344-360. doi: 10.1007/s00454-014-9616-3

Author

Jackson, Bill ; McCourt, Tom ; Nixon, Anthony. / Necessary conditions for the generic global rigidity of frameworks on surfaces. In: Discrete and Computational Geometry. 2014 ; Vol. 52, No. 2. pp. 344-360.

Bibtex

@article{50abe681a7a94a61b5e4e1195f9f5490,
title = "Necessary conditions for the generic global rigidity of frameworks on surfaces",
abstract = "A result due in its various parts to Hendrickson, Connelly, and Jackson and Jord{\'a}n, provides a purely combinatorial characterisation of global rigidity for generic bar-joint frameworks in TeX. The analogous conditions are known to be insufficient to characterise generic global rigidity in higher dimensions. Recently Laman-type characterisations of rigidity have been obtained for generic frameworks in TeX when the vertices are constrained to lie on various surfaces, such as the cylinder and the cone. In this paper we obtain analogues of Hendrickson{\textquoteright}s necessary conditions for the global rigidity of generic frameworks on the cylinder, cone and ellipsoid.",
keywords = "Rigidity, Global rigidity, Framework on a surface",
author = "Bill Jackson and Tom McCourt and Anthony Nixon",
note = "The original publication is available at www.link.springer.com",
year = "2014",
month = sep,
doi = "10.1007/s00454-014-9616-3",
language = "English",
volume = "52",
pages = "344--360",
journal = "Discrete and Computational Geometry",
issn = "0179-5376",
publisher = "Springer New York",
number = "2",

}

RIS

TY - JOUR

T1 - Necessary conditions for the generic global rigidity of frameworks on surfaces

AU - Jackson, Bill

AU - McCourt, Tom

AU - Nixon, Anthony

N1 - The original publication is available at www.link.springer.com

PY - 2014/9

Y1 - 2014/9

N2 - A result due in its various parts to Hendrickson, Connelly, and Jackson and Jordán, provides a purely combinatorial characterisation of global rigidity for generic bar-joint frameworks in TeX. The analogous conditions are known to be insufficient to characterise generic global rigidity in higher dimensions. Recently Laman-type characterisations of rigidity have been obtained for generic frameworks in TeX when the vertices are constrained to lie on various surfaces, such as the cylinder and the cone. In this paper we obtain analogues of Hendrickson’s necessary conditions for the global rigidity of generic frameworks on the cylinder, cone and ellipsoid.

AB - A result due in its various parts to Hendrickson, Connelly, and Jackson and Jordán, provides a purely combinatorial characterisation of global rigidity for generic bar-joint frameworks in TeX. The analogous conditions are known to be insufficient to characterise generic global rigidity in higher dimensions. Recently Laman-type characterisations of rigidity have been obtained for generic frameworks in TeX when the vertices are constrained to lie on various surfaces, such as the cylinder and the cone. In this paper we obtain analogues of Hendrickson’s necessary conditions for the global rigidity of generic frameworks on the cylinder, cone and ellipsoid.

KW - Rigidity

KW - Global rigidity

KW - Framework on a surface

U2 - 10.1007/s00454-014-9616-3

DO - 10.1007/s00454-014-9616-3

M3 - Journal article

VL - 52

SP - 344

EP - 360

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -