{"paper":{"title":"On the Embeddability of Delaunay Triangulations in Anisotropic, Normed, and Bregman Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Guillermo D. Canas, Steven J. Gortler","submitted_at":"2015-12-11T10:46:23Z","abstract_excerpt":"Given a two-dimensional space endowed with a divergence function that is convex in the first argument, continuously differentiable in the second, and satisfies suitable regularity conditions at Voronoi vertices, we show that orphan-freedom (the absence of disconnected Voronoi regions) is sufficient to ensure that Voronoi edges and vertices are also connected, and that the dual is a simple planar graph. We then prove that the straight-edge dual of an orphan-free Voronoi diagram (with sites as the first argument of the divergence) is always an embedded triangulation.\n  Among the divergences cove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03589","kind":"arxiv","version":2},"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"}