{"paper":{"title":"Surface Parametrization of Nonsimply Connected Planar B\\'ezier Regions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"John C. Bowman, Orest Shardt","submitted_at":"2010-05-17T07:25:49Z","abstract_excerpt":"A technique is described for constructing three-dimensional vector graphics representations of planar regions bounded by cubic B\\'ezier curves, such as smooth glyphs. It relies on a novel algorithm for compactly partitioning planar B\\'ezier regions into nondegenerate Coons patches. New optimizations are also described for B\\'ezier inside-outside tests and the computation of global bounds of directionally monotonic functions over a B\\'ezier surface (such as its bounding box or optimal field-of-view angle). These algorithms underlie the three-dimensional illustration and typography features of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2822","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"}