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Necessary conditions for the generic global rigidity of frameworks on surfaces

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<mark>Journal publication date</mark>09/2014
<mark>Journal</mark>Discrete and Computational Geometry
Issue number2
Volume52
Number of pages17
Pages (from-to)344-360
Publication StatusPublished
<mark>Original language</mark>English

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.

Bibliographic note

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