On affine rigidity
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...
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| Language: | English |
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Carleton University
2013-12-01
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| Series: | Journal of Computational Geometry |
| Online Access: | http://jocg.org/index.php/jocg/article/view/49 |
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doaj-332e5e5be8bb4b7080d71b1cf4ff010a2020-11-24T22:09:16ZengCarleton UniversityJournal of Computational Geometry1920-180X2013-12-014110.20382/jocg.v4i1a740On affine rigiditySteven J. Gortler0Craig Gotsman1Ligang Liu2Dylan P. Thurston3Harvard UniversityTechnionZhejiang UniversityBarnard College, Columbia UniversityWe 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 <em>d</em>-dimensional space if it is (<em>d</em>+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.http://jocg.org/index.php/jocg/article/view/49 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Steven J. Gortler Craig Gotsman Ligang Liu Dylan P. Thurston |
| spellingShingle |
Steven J. Gortler Craig Gotsman Ligang Liu Dylan P. Thurston On affine rigidity Journal of Computational Geometry |
| author_facet |
Steven J. Gortler Craig Gotsman Ligang Liu Dylan P. Thurston |
| author_sort |
Steven J. Gortler |
| title |
On affine rigidity |
| title_short |
On affine rigidity |
| title_full |
On affine rigidity |
| title_fullStr |
On affine rigidity |
| title_full_unstemmed |
On affine rigidity |
| title_sort |
on affine rigidity |
| publisher |
Carleton University |
| series |
Journal of Computational Geometry |
| issn |
1920-180X |
| publishDate |
2013-12-01 |
| description |
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 <em>d</em>-dimensional space if it is (<em>d</em>+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. |
| url |
http://jocg.org/index.php/jocg/article/view/49 |
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AT stevenjgortler onaffinerigidity AT craiggotsman onaffinerigidity AT ligangliu onaffinerigidity AT dylanpthurston onaffinerigidity |
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