{"paper":{"title":"Bijective Deformations in $\\mathbb{R}^n$ via Integral Curve Coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Lisa Huynh, Yotam Gingold","submitted_at":"2015-05-01T02:47:12Z","abstract_excerpt":"We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function $f$ on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Curve Coordinates provide a natural bijective mapping from one domain to another given a bijection of the boundary. Our approach can be applied to shapes in any dimension, provided that the boundary of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00073","kind":"arxiv","version":1},"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"}