{"paper":{"title":"Reconstructing a convex polygon from its $\\omega$-cloud","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Elena Arseneva, Jean-Lou De Carufel, Prosenjit Bose, Sander Verdonschot","submitted_at":"2018-01-07T09:14:08Z","abstract_excerpt":"An $\\omega$-wedge is the closed set of points contained between two rays that are emanating from a single point (the apex), and are separated by an angle $\\omega < \\pi$. Given a convex polygon $P$, we place the $\\omega$-wedge such that $P$ is inside the wedge and both rays are tangent to $P$. The set of apex positions of all such placements of the $\\omega$-wedge is called the $\\omega$-cloud of $P$.\n  We investigate reconstructing a polygon $P$ from its $\\omega$-cloud. Previous work on reconstructing $P$ from probes with the $\\omega$-wedge required knowledge of the points of tangency between $P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02162","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}