Rigid frameworks with dilation constraints
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917595223949312 |
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| author | Dewar, Sean Nixon, Anthony Sainsbury, Andrew |
| author_facet | Dewar, Sean Nixon, Anthony Sainsbury, Andrew |
| contents | We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14093 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigid frameworks with dilation constraints Dewar, Sean Nixon, Anthony Sainsbury, Andrew Combinatorics Metric Geometry We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints. |
| title | Rigid frameworks with dilation constraints |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2402.14093 |