Necessary conditions for the generic global rigidity of frameworks on surfaces

Jackson, Bill and McCourt, Tom and Nixon, Anthony (2014) Necessary conditions for the generic global rigidity of frameworks on surfaces. Discrete and Computational Geometry, 52 (2). pp. 344-360. ISSN 0179-5376

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Abstract

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.

Item Type:
Journal Article
Journal or Publication Title:
Discrete and Computational Geometry
Additional Information:
The original publication is available at www.link.springer.com
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2614
Subjects:
ID Code:
71117
Deposited By:
Deposited On:
06 Oct 2014 11:00
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 09:00