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  • Finite and infinitesimal rigidity with polyhedral norms

    Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00454-015-9706-x

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    Available under license: CC BY: Creative Commons Attribution 4.0 International License

  • Finite and infinitesimal rigidity with polyhedral norms

    Rights statement: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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    Available under license: CC BY: Creative Commons Attribution 4.0 International License

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Finite and infinitesimal rigidity with polyhedral norms

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Finite and infinitesimal rigidity with polyhedral norms. / Kitson, Derek.

In: Discrete and Computational Geometry, Vol. 54, No. 2, 09.2015, p. 390-411.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Kitson, D 2015, 'Finite and infinitesimal rigidity with polyhedral norms', Discrete and Computational Geometry, vol. 54, no. 2, pp. 390-411. https://doi.org/10.1007/s00454-015-9706-x

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Kitson, Derek. / Finite and infinitesimal rigidity with polyhedral norms. In: Discrete and Computational Geometry. 2015 ; Vol. 54, No. 2. pp. 390-411.

Bibtex

@article{b7cc61ced6064cf3b60d27fae26f41b5,
title = "Finite and infinitesimal rigidity with polyhedral norms",
abstract = "We characterise finite and infinitesimal rigidity for bar-joint frameworks in Rd with respect to polyhedral norms (i.e. norms with closed unit ball P, a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be equivalent for finite frameworks in Rd which are well-positioned with respect to P. An edge-labelling determined by the facets of the unit ball and placement of the framework is used to characterise infinitesimal rigidity in Rd in terms of monochrome spanning trees. An analogue of Laman{\textquoteright}s theorem is obtained for all polyhedral norms on R2.",
keywords = "Bar-joint framework, Infinitesimally rigid, Laman{\textquoteright}s theorem , Polyhedral norm",
author = "Derek Kitson",
note = "Acceptance information is shown on publishers pdf. The final publication is available at Springer via http://dx.doi.org/10.1007/s00454-015-9706-x The publishers version of this article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. ",
year = "2015",
month = sep,
doi = "10.1007/s00454-015-9706-x",
language = "English",
volume = "54",
pages = "390--411",
journal = "Discrete and Computational Geometry",
issn = "0179-5376",
publisher = "Springer New York",
number = "2",

}

RIS

TY - JOUR

T1 - Finite and infinitesimal rigidity with polyhedral norms

AU - Kitson, Derek

N1 - Acceptance information is shown on publishers pdf. The final publication is available at Springer via http://dx.doi.org/10.1007/s00454-015-9706-x The publishers version of this article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

PY - 2015/9

Y1 - 2015/9

N2 - We characterise finite and infinitesimal rigidity for bar-joint frameworks in Rd with respect to polyhedral norms (i.e. norms with closed unit ball P, a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be equivalent for finite frameworks in Rd which are well-positioned with respect to P. An edge-labelling determined by the facets of the unit ball and placement of the framework is used to characterise infinitesimal rigidity in Rd in terms of monochrome spanning trees. An analogue of Laman’s theorem is obtained for all polyhedral norms on R2.

AB - We characterise finite and infinitesimal rigidity for bar-joint frameworks in Rd with respect to polyhedral norms (i.e. norms with closed unit ball P, a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be equivalent for finite frameworks in Rd which are well-positioned with respect to P. An edge-labelling determined by the facets of the unit ball and placement of the framework is used to characterise infinitesimal rigidity in Rd in terms of monochrome spanning trees. An analogue of Laman’s theorem is obtained for all polyhedral norms on R2.

KW - Bar-joint framework

KW - Infinitesimally rigid

KW - Laman’s theorem

KW - Polyhedral norm

U2 - 10.1007/s00454-015-9706-x

DO - 10.1007/s00454-015-9706-x

M3 - Journal article

VL - 54

SP - 390

EP - 411

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -