on affine rigidity
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2013
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Abstract
We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding). Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1)-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph. Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.
| Reference Key |
gortler2013journalon
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| Authors | ;Steven J. Gortler;Craig Gotsman;Ligang Liu;Dylan P. Thurston |
| Journal | canadian journal of infectious diseases and medical microbiology |
| Year | 2013 |
| DOI |
10.20382/jocg.v4i1a7
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