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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.15121 |
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| _version_ | 1866910787493167104 |
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| author | Denkowski, Maciej Panina, Gaiane Siersma, Dirk |
| author_facet | Denkowski, Maciej Panina, Gaiane Siersma, Dirk |
| contents | Spider mechanisms are the simplest examples of arachnoid mechanisms, they are one step more complicated than polygonal linkages. Their configuration spaces have been studied intensively, but are yet not completely understood. In the paper we study them using the Morse theory of the squared distance function from the "body" of the spider to some fixed point in the plane. Generically, it is a Morse-Bott function. We list its critical manifolds, describe them as products of polygon spaces, and derive a formula for their Morse-Bott indices. We apply the obtained results to Hooke energy and Voronoi distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Squared Distance Function on the Configuration Space of a planar Spider with Applications to Hooke Energy and Voronoi Distance Denkowski, Maciej Panina, Gaiane Siersma, Dirk Geometric Topology 58K05, 70B15 Spider mechanisms are the simplest examples of arachnoid mechanisms, they are one step more complicated than polygonal linkages. Their configuration spaces have been studied intensively, but are yet not completely understood. In the paper we study them using the Morse theory of the squared distance function from the "body" of the spider to some fixed point in the plane. Generically, it is a Morse-Bott function. We list its critical manifolds, describe them as products of polygon spaces, and derive a formula for their Morse-Bott indices. We apply the obtained results to Hooke energy and Voronoi distance. |
| title | Squared Distance Function on the Configuration Space of a planar Spider with Applications to Hooke Energy and Voronoi Distance |
| topic | Geometric Topology 58K05, 70B15 |
| url | https://arxiv.org/abs/2407.15121 |