Hedgehog reconstruction of polygons: Non-central sections and slabs

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: an origin-symmetric polygon can be reconstructed from the areas of slabs supporting an analytic origin-symmetric hedgehog in the interior of the polygon.