Finite and infinitesimal rigidity with polyhedral norms

Kitson, Derek (2015) Finite and infinitesimal rigidity with polyhedral norms. Discrete and Computational Geometry, 54 (2). pp. 390-411. ISSN 0179-5376

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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’s theorem is obtained for all polyhedral norms on R2.

Item Type:

Journal Article

Journal or Publication Title:

Discrete and Computational Geometry

Additional Information:

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.

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2607

Subjects:

?? bar-joint frameworkinfinitesimally rigidlaman’s theorem polyhedral normdiscrete mathematics and combinatoricscomputational theory and mathematicsgeometry and topologytheoretical computer science ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

73627

Deposited By:

ep_importer_pure

Deposited On:

18 Jun 2015 05:26

Refereed?:

Yes

Published?:

Published