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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.
Final published version, 543 KB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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 -