{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:04:11Z","timestamp":1761807851236,"version":"3.41.0"},"reference-count":30,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004052","name":"King Abdullah University of Science and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004052","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>We present a framework for exploring topologically unique quadrangulations of an input shape. First, the input shape is segmented into surface patches. Second, different topologies are enumerated and explored in each patch. This is realized by an efficient subdivision-based quadrangulation algorithm that can exhaustively enumerate all mesh topologies within a patch. To help users navigate the potentially huge collection of variations, we propose tools to preview and arrange the results. Furthermore, the requirement that all patches need to be jointly quadrangulatable is formulated as a linear integer program. Finally, we apply the framework to shape-space exploration, remeshing, and design to underline the importance of topology exploration.<\/jats:p>","DOI":"10.1145\/2541533","type":"journal-article","created":{"date-parts":[[2014,2,4]],"date-time":"2014-02-04T14:16:21Z","timestamp":1391523381000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":27,"title":["Exploring quadrangulations"],"prefix":"10.1145","volume":"33","author":[{"given":"Chi-Han","family":"Peng","sequence":"first","affiliation":[{"name":"Arizona State University, Phoenix, AZ"}]},{"given":"Michael","family":"Barton","sequence":"additional","affiliation":[{"name":"King Abdullah University of Science and Technology, Thuwal, Saudi Arabia"}]},{"given":"Caigui","family":"Jiang","sequence":"additional","affiliation":[{"name":"King Abdullah University of Science and Technology, Thuwal, Saudi Arabia"}]},{"given":"Peter","family":"Wonka","sequence":"additional","affiliation":[{"name":"Arizona State University and King Abdullah University of Science and Technology, Phoenix, AZ"}]}],"member":"320","published-online":{"date-parts":[[2014,2,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882296"},{"key":"e_1_2_2_2_1","volume-title":"Ipsolve: Open source (mixed-integer) linear programming system","author":"Berkelaar M.","year":"2004","unstructured":"M. Berkelaar , K. Eikland , and P. Notebaert . 2004 . Ipsolve: Open source (mixed-integer) linear programming system . http:\/\/lpsolve.sourceforge.net\/5.5\/ M. Berkelaar, K. Eikland, and P. Notebaert. 2004. Ipsolve: Open source (mixed-integer) linear programming system. http:\/\/lpsolve.sourceforge.net\/5.5\/"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366197"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620320410"},{"key":"e_1_2_2_5_1","unstructured":"D. Bommes B. Levy N. Pietroni E. Puppo M. Tarini and D. Zorin. 2012. State of the art in quad meshing. In EuroGraphics STARS.  D. Bommes B. Levy N. Pietroni E. Puppo M. Tarini and D. Zorin. 2012. State of the art in quad meshing. In EuroGraphics STARS."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531383"},{"key":"e_1_2_2_7_1","doi-asserted-by":"crossref","unstructured":"M. Botsch L. Kobbelt M. Pauly P. Alliez and B. Levy. 2010. Polygon Mesh Processing. A. K. Peters Natick MA.  M. Botsch L. Kobbelt M. Pauly P. Alliez and B. Levy. 2010. Polygon Mesh Processing. A. K. Peters Natick MA.","DOI":"10.1201\/b10688"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1186562.1015817"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1409060.1409101"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141993"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2005.04.004"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01060.x"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566590"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141941"},{"volume-title":"Proceedings of the 12th Pacific Conference on Computer Graphics and Applications (PG'04)","author":"Marinov M.","key":"e_1_2_2_15_1","unstructured":"M. Marinov and L. Kobbelt . 2004. Direct anisotropic quad-dominant remeshing . In Proceedings of the 12th Pacific Conference on Computer Graphics and Applications (PG'04) . 207--216. M. Marinov and L. Kobbelt. 2004. Direct anisotropic quad-dominant remeshing. In Proceedings of the 12th Pacific Conference on Computer Graphics and Applications (PG'04). 207--216."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2006.00973.x"},{"key":"e_1_2_2_17_1","doi-asserted-by":"crossref","unstructured":"S. Maza F. Noel and J. Leon. 1999. Generation of quadrilateral meshes on free-form surfaces. Comput. Struct. 71.  S. Maza F. Noel and J. Leon. 1999. Generation of quadrilateral meshes on free-form surfaces. Comput. Struct. 71.","DOI":"10.1016\/S0045-7949(98)00300-9"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01417.x"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276446"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2006.12.002"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024175"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1640443.1640444"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1356682.1356683"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1057432.1057447"},{"volume-title":"Proceedings of the 4th EuroGraphics Symposium on Geometry Processing (SGP'06)","author":"Tong Y.","key":"e_1_2_2_26_1","unstructured":"Y. Tong , P. Alliez , D. Cohen-Steiner , and M. Desbrun . 2006. Designing quadrangulations with discrete harmonic forms . In Proceedings of the 4th EuroGraphics Symposium on Geometry Processing (SGP'06) . 201--210. Y. Tong, P. Alliez, D. Cohen-Steiner, and M. Desbrun. 2006. Designing quadrangulations with discrete harmonic forms. In Proceedings of the 4th EuroGraphics Symposium on Geometry Processing (SGP'06). 201--210."},{"volume-title":"Proceedings of the 6th International Meshing Round Table. 323--335","author":"White D.","key":"e_1_2_2_27_1","unstructured":"D. White and P. Kinney . 1997. Redesign of the paving algorithm: Robustness enhancements through element by element meshing . In Proceedings of the 6th International Meshing Round Table. 323--335 . D. White and P. Kinney. 1997. Redesign of the paving algorithm: Robustness enhancements through element by element meshing. In Proceedings of the 6th International Meshing Round Table. 323--335."},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024158"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183290"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778855"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2541533","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2541533","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T07:35:02Z","timestamp":1750232102000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2541533"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1145\/2541533"],"URL":"https:\/\/doi.org\/10.1145\/2541533","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2014,1]]},"assertion":[{"value":"2012-11-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-11-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-02-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}