Hedgehog Reconstruction of Polygons: Non-Central Sections and Slabs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912931422142464 |
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| author | Matthews, Brendan |
| author_facet | Matthews, Brendan |
| contents | We show that a polygon can be uniquely determined by the lengths of non-central sections supporting a piecewise-analytic hedgehog in the interior of the polygon. We also prove the analogous result for slab areas - centrally-symmetric polygon can be reconstructed based on the areas of slabs supporting an analytic centrally-symmetric hedgehog in the interior of the polygon |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hedgehog Reconstruction of Polygons: Non-Central Sections and Slabs Matthews, Brendan Metric Geometry 52A10, 52B15, 52A38 We show that a polygon can be uniquely determined by the lengths of non-central sections supporting a piecewise-analytic hedgehog in the interior of the polygon. We also prove the analogous result for slab areas - centrally-symmetric polygon can be reconstructed based on the areas of slabs supporting an analytic centrally-symmetric hedgehog in the interior of the polygon |
| title | Hedgehog Reconstruction of Polygons: Non-Central Sections and Slabs |
| topic | Metric Geometry 52A10, 52B15, 52A38 |
| url | https://arxiv.org/abs/2603.00002 |