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Graph."],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p>\n            Decomposing a volume into high-quality hexahedral cells is a challenging task in geometric modeling and computational geometry. Inspired by the use of cross field in quad meshing and the CubeCover approach in hex meshing, we present a complete all-hex meshing framework based on\n            <jats:italic>singularity-restricted field<\/jats:italic>\n            that is essential to induce a valid all-hex structure. Given a volume represented by a tetrahedral mesh, we first compute a boundary-aligned 3D frame field inside it, then convert the frame field to be singularity-restricted by our effective topological operations. In our all-hex meshing framework, we apply the CubeCover method to achieve the volume parametrization. For reducing degenerate elements appearing in the volume parametrization, we also propose novel tetrahedral split operations to preprocess singularity-restricted frame fields. Experimental results show that our algorithm generates high-quality all-hex meshes from a variety of 3D volumes robustly and efficiently.\n          <\/jats:p>","DOI":"10.1145\/2366145.2366196","type":"journal-article","created":{"date-parts":[[2012,11,14]],"date-time":"2012-11-14T20:36:17Z","timestamp":1352925377000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":112,"title":["All-hex meshing using singularity-restricted field"],"prefix":"10.1145","volume":"31","author":[{"given":"Yufei","family":"Li","sequence":"first","affiliation":[{"name":"The University of Hong Kong"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"Microsoft Research Asia"}]},{"given":"Weiwei","family":"Xu","sequence":"additional","affiliation":[{"name":"Microsoft Research Asia"}]},{"given":"Wenping","family":"Wang","sequence":"additional","affiliation":[{"name":"The University of Hong Kong"}]},{"given":"Baining","family":"Guo","sequence":"additional","affiliation":[{"name":"Microsoft Research Asia"}]}],"member":"320","published-online":{"date-parts":[[2012,11]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531383"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01868.x"},{"key":"e_1_2_2_3_1","volume-title":"Proc. 12th Inter. Mesh. Roundtable.","author":"Brewer M.","unstructured":"Brewer , M. , Diachin , L. F. , Knupp , P. , Leurent , T. , and Melander , D . 2003. The mesquite mesh quality improvement toolkit . In Proc. 12th Inter. Mesh. Roundtable. Brewer, M., Diachin, L. F., Knupp, P., Leurent, T., and Melander, D. 2003. The mesquite mesh quality improvement toolkit. In Proc. 12th Inter. Mesh. Roundtable."},{"key":"e_1_2_2_4_1","volume-title":"Proc. 15th Inter. Mesh. Roundtable, 435--452","author":"Carbonera C. D.","unstructured":"Carbonera , C. D. , and Shepherd , J. F . 2006. A constructive approach to constrained hexahedral mesh generation . In Proc. 15th Inter. Mesh. Roundtable, 435--452 . Carbonera, C. D., and Shepherd, J. F. 2006. A constructive approach to constrained hexahedral mesh generation. In Proc. 15th Inter. Mesh. Roundtable, 435--452."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01761.x"},{"key":"e_1_2_2_6_1","unstructured":"Dey T. K. Edelsbrunner H. Guha S. and Nekhayev D. V. 1999. Topology preserving edge contraction. PUBLICATIONS DE L'INSTITUT MATH\u00c9MATIQUE (Beograd) 66 80 23--45.  Dey T. K. Edelsbrunner H. Guha S. and Nekhayev D. V. 1999. Topology preserving edge contraction. PUBLICATIONS DE L'INSTITUT MATH\u00c9MATIQUE (Beograd) 66 80 23--45."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141993"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.02015.x"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1839778.1839796"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1409060.1409100"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024177"},{"key":"e_1_2_2_12_1","unstructured":"Joe B. 2008. Shape measures for quadrilaterals pyramids wedges and hexahedra. Tech. rep.  Joe B. 2008. Shape measures for quadrilaterals pyramids wedges and hexahedra. 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Mesh. Roundtable, 399--416","author":"Staten M. L.","unstructured":"Staten , M. L. , Owen , S. J. , and Blacker , T. D . 2005. Unconstrained paving and plastering: a new idea for all hexahedral mesh generation . In Proc. 14th Inter. Mesh. Roundtable, 399--416 . Staten, M. L., Owen, S. J., and Blacker, T. D. 2005. Unconstrained paving and plastering: a new idea for all hexahedral mesh generation. In Proc. 14th Inter. Mesh. Roundtable, 399--416."},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015810"},{"key":"e_1_2_2_28_1","volume-title":"Proc., 201--210","author":"Tong Y.","unstructured":"Tong , Y. , Alliez , P. , Cohen-Steiner , D. , and Desbrun , M . 2006. Designing quadrangulations with discrete harmonic forms. In Symp. Geom . Proc., 201--210 . Tong, Y., Alliez, P., Cohen-Steiner, D., and Desbrun, M. 2006. Designing quadrangulations with discrete harmonic forms. In Symp. Geom. Proc., 201--210."},{"key":"e_1_2_2_29_1","volume-title":"Visualization '98. 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Roundtable, 449--468."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2366145.2366196","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2366145.2366196","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T09:34:44Z","timestamp":1750239284000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2366145.2366196"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11]]},"references-count":30,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2012,11]]}},"alternative-id":["10.1145\/2366145.2366196"],"URL":"https:\/\/doi.org\/10.1145\/2366145.2366196","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11]]},"assertion":[{"value":"2012-11-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}