{"paper":{"title":"Quaternionic octahedral fields: SU(2) parameterization of 3D frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Christophe Geuzaine, Jean-Francois Remacle, Jonathan Lambrechts, Pierre-Alexandre Beaufort","submitted_at":"2019-10-14T16:19:17Z","abstract_excerpt":"3D frame fields are auxiliary for hexahedral mesh generation.\n  There mainly exist three ways to represent 3D frames: combination of rotations, spherical harmonics and fourth order tensor.\n  We propose here a representation carried out by the special unitary group.\n  The article strongly relies on \\cite{du1964homographies}.\n  We first describe the rotations with quaternions, \\cite[\\S 13-15]{du1964homographies}.\n  We define and show the isomorphism between unit quaternions and the special unitary group, \\cite[\\S 16]{du1964homographies}.\n  The frame field space is identified as the quotient grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.06240","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.06240/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}