{"paper":{"title":"Maintaining Contour Trees of Dynamic Terrains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jungwoo Yang, Lars Arge, Morten Revsb{\\ae}k, Pankaj K. Agarwal, Thomas M{\\o}lhave","submitted_at":"2014-06-16T13:19:22Z","abstract_excerpt":"We consider maintaining the contour tree $\\mathbb{T}$ of a piecewise-linear triangulation $\\mathbb{M}$ that is the graph of a time varying height function $h: \\mathbb{R}^2 \\rightarrow \\mathbb{R}$. We carefully describe the combinatorial change in $\\mathbb{T}$ that happen as $h$ varies over time and how these changes relate to topological changes in $\\mathbb{M}$. We present a kinetic data structure that maintains the contour tree of $h$ over time. Our data structure maintains certificates that fail only when $h(v)=h(u)$ for two adjacent vertices $v$ and $u$ in $\\mathbb{M}$, or when two saddle v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4005","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"}