Hedgehog Reconstruction of Polygons: Non-Central Sections and Slabs
Metric Geometry
2026-03-03 v1
Abstract
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
Keywords
Cite
@article{arxiv.2603.00002,
title = {Hedgehog Reconstruction of Polygons: Non-Central Sections and Slabs},
author = {Brendan Matthews},
journal= {arXiv preprint arXiv:2603.00002},
year = {2026}
}
Comments
11 pages, 6 figures, 2 proofs