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In this article, we investigate the topology of frame fields and derive conditions on their meshability, which are the basis for a novel algorithm to automatically turn a given non-meshable frame field into a similar but locally meshable one. Despite local meshability is only a necessary but not sufficient condition for the stronger requirement of meshability, our algorithm increases the 2% success rate of generating valid integer-grid maps with state-of-the-art methods to 58%, when compared on the challenging HexMe dataset [Beaufort et al. 2022]. The source code of our implementation and the data of our experiments are available at https:\/\/lib.algohex.eu.<\/jats:p>","DOI":"10.1145\/3592457","type":"journal-article","created":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T14:29:21Z","timestamp":1690381761000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":17,"title":["Locally Meshable Frame Fields"],"prefix":"10.1145","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5973-6491","authenticated-orcid":false,"given":"Heng","family":"Liu","sequence":"first","affiliation":[{"name":"University of Bern, Bern, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3190-1341","authenticated-orcid":false,"given":"David","family":"Bommes","sequence":"additional","affiliation":[{"name":"University of Bern, Bern, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2023,7,26]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.proeng.2015.10.123"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14608"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2462014"},{"key":"e_1_2_2_5_1","volume-title":"Computer graphics forum","author":"Bommes David","unstructured":"David Bommes, Bruno L\u00e9vy, Nico Pietroni, Enrico Puppo, Claudio Silva, Marco Tarini, and Denis Zorin. 2013b. 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