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We focus specifically on the challenge caused by the intersections resulting from the conversion of the vertices coordinates from their exact mathematical values to a fixed\u2010precision floating\u2010point format. Our method takes as input a soup of triangles and outputs intersection\u2010free models whose vertices coordinates are all represented with double\u2010precision floating\u2010point format. We evaluated our approach thoroughly, considering a large collection of meshes. In particular, we can process all the 4524 models in Thingi10K [ZJ16] that contain self\u2010intersections. This outperforms previous state\u2010of\u2010the\u2010art approaches: On the 527 models of Thingi10K for which naive rounding fails, Zhou et al.'s approach [ZGZJ16] is capable of handling 91% of them, and Valque's 94% [Val24]. In terms of time efficiency, our approach handles about 50k vertices per second on average, which is faster to that of Zhou et al. by a factor 1.4 on these non\u2010trivial models and is faster than that of Valque by several order of magnitude.<\/jats:p>","DOI":"10.1111\/cgf.70197","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T15:25:12Z","timestamp":1756394712000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Resolving self\u2010intersections in 3D meshes while preserving floating\u2010point coordinates"],"prefix":"10.1111","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9829-8978","authenticated-orcid":false,"given":"L\u00e9o","family":"Valque","sequence":"first","affiliation":[{"name":"GeometryFactory  France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6032-0802","authenticated-orcid":false,"given":"Sylvain","family":"Lazard","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA  Nancy F\u201054000 France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,8,28]]},"reference":[{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2014.09.002"},{"key":"e_1_2_7_3_2","doi-asserted-by":"crossref","DOI":"10.1016\/j.cad.2020.102856","article-title":"Indirect predicates for geometric constructions","volume":"126","author":"Attene M.","year":"2020","journal-title":"Computer-Aided Design"},{"key":"e_1_2_7_4_2","volume-title":"CGAL User and Reference Manual","author":"CGAL Project"},{"key":"e_1_2_7_5_2","volume-title":"CGAL User and Reference Manual","author":"Coeurjolly D.","year":"2024"},{"issue":"6","key":"e_1_2_7_6_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3414685.3417818","article-title":"Fast and robust mesh arrangements using floating-point arithmetic","volume":"39","author":"Cherchi G.","year":"2020","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555460"},{"key":"e_1_2_7_7_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3550454.3555460. 2","DOI":"10.1145\/3550454.3555460"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356507"},{"key":"e_1_2_7_8_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3355089.3356507. 2","DOI":"10.1145\/3355089.3356507"},{"issue":"6","key":"e_1_2_7_9_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3478513.3480564","article-title":"Convex polyhedral meshing for robust solid modeling","volume":"40","author":"Diazzi L.","year":"2021","journal-title":"ACM Transactions on Graphics (TOG)"},{"issue":"1","key":"e_1_2_7_10_2","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/s00454-020-00202-2","article-title":"Rounding meshes in 3D","volume":"64","author":"Devillers O.","year":"2020","journal-title":"Discrete and Computational Geometry"},{"key":"e_1_2_7_10_3","doi-asserted-by":"crossref","unstructured":"doi:10.1007\/s00454-020-00202-2. 3","DOI":"10.1007\/s00454-020-00202-2"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009480"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/3687925"},{"key":"e_1_2_7_12_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3687925. 2","DOI":"10.1145\/3687925"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/262839.262985"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392385"},{"key":"e_1_2_7_14_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3386569.3392385. 2","DOI":"10.1145\/3386569.3392385"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201353"},{"key":"e_1_2_7_15_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3197517.3201353. 2","DOI":"10.1145\/3197517.3201353"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015815"},{"key":"e_1_2_7_16_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/1015706.1015815. 2","DOI":"10.1145\/1015706.1015815"},{"key":"e_1_2_7_17_2","unstructured":"L\u00e9vyB.:Exact predicates exact constructions and combinatorics for mesh csg 2024. 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