{"paper":{"title":"Space of $C^2$-smooth geometrically continuous isogeometric functions on planar multi-patch geometries: Dimension and numerical experiments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Mario Kapl, Vito Vitrih","submitted_at":"2017-01-24T07:22:22Z","abstract_excerpt":"We study the space of $C^{2}$-smooth isogeometric functions on bilinearly parameterized multi-patch domains $\\Omega \\subset \\mathbb{R}^{2}$, where the graph of each isogeometric function is a multi-patch spline surface of bidegree $(d,d)$, $d \\in \\{5,6 \\}$. The space is fully characterized by the equivalence of the $C^2$-smoothness of an isogeometric function and the $G^2$-smoothness of its graph surface, cf. (Groisser and Peters,2015; Kapl et al.,2015). This is the reason to call its functions $C^{2}$-smooth geometrically continuous isogeometric functions. In particular, the dimension of this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06753","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"}