{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T16:50:10Z","timestamp":1777567810155,"version":"3.51.4"},"reference-count":46,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2014,7,27]],"date-time":"2014-07-27T00:00:00Z","timestamp":1406419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["StG-2012-306877"],"award-info":[{"award-number":["StG-2012-306877"]}],"id":[{"id":"10.13039\/501100000781","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":[[2014,7,27]]},"abstract":"<jats:p>We introduce frame fields, which are a non-orthogonal and non-unit-length generalization of cross fields. Frame fields represent smoothly varying linear transformations on tangent spaces of a surface. We propose an algorithm to create discrete, dense frame fields that satisfy a sparse set of constraints. By computing a surface deformation that warps a frame field into a cross field, we generalize existing quadrangulation algorithms to generate anisotropic and non-uniform quad meshes whose elements shapes match the frame field. With this, our framework enables users to control not only the alignment but also the density and anisotropy of the elements' distribution, resulting in high-quality adaptive quad meshing.<\/jats:p>","DOI":"10.1145\/2601097.2601179","type":"journal-article","created":{"date-parts":[[2014,7,22]],"date-time":"2014-07-22T15:08:20Z","timestamp":1406041700000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":86,"title":["Frame fields"],"prefix":"10.1145","volume":"33","author":[{"given":"Daniele","family":"Panozzo","sequence":"first","affiliation":[{"name":"ETH Zurich"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enrico","family":"Puppo","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Genova"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Tarini","sequence":"additional","affiliation":[{"name":"Universit\u00e0 dell'Insubria, Varese and ISTI-CNR Pisa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Olga","family":"Sorkine-Hornung","sequence":"additional","affiliation":[{"name":"ETH Zurich"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2014,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344859"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882296"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531383"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12014"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2462014"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01253.x"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01761.x"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280826"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508372"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276447"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.345074"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1409060.1409100"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964973"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01060.x"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2462005"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1839778.1839797"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2009.59"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141921"},{"key":"e_1_2_2_19_1","volume-title":"Proc. 21st Int. Meshing Roundtable, 349--366","author":"L\u00e9vy B.","unstructured":"L\u00e9vy , B. , and Bonneel , N . 2012. Variational anisotropic surface meshing with Voronoi parallel linear enumeration . In Proc. 21st Int. Meshing Roundtable, 349--366 . L\u00e9vy, B., and Bonneel, N. 2012. Variational anisotropic surface meshing with Voronoi parallel linear enumeration. In Proc. 21st Int. Meshing Roundtable, 349--366."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.36"},{"key":"e_1_2_2_21_1","unstructured":"Ling R. Huang J. Sun F. Juttler B. Bao H. and Wang W. 2011. Spectral quadrangulation with boundary conformation. Tech. rep. TR-2011-13 The University of Hong Kong. Ling R. Huang J. Sun F. Juttler B. Bao H. and Wang W. 2011. Spectral quadrangulation with boundary conformation. Tech. rep. TR-2011-13 The University of Hong Kong."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.5555\/1731309.1731336"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024174"},{"key":"e_1_2_2_24_1","volume-title":"Proc. 12th Pacific Graphics, 207--216","author":"Marinov M.","unstructured":"Marinov , M. , and Kobbelt , L . 2004. Direct anisotropic quad-dominant remeshing . In Proc. 12th Pacific Graphics, 207--216 . Marinov, M., and Kobbelt, L. 2004. Direct anisotropic quad-dominant remeshing. In Proc. 12th Pacific Graphics, 207--216."},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.2307\/1969989"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12299"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276446"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.121"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461958"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024183"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1993.10504266"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/1356682.1356683"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1640443.1640444"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/2019627.2019635"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141920"},{"key":"e_1_2_2_37_1","volume-title":"Proc. Symp. Geometry Processing, 109--116","author":"Sorkine O.","unstructured":"Sorkine , O. , and Alexa , M . 2007. As-rigid-as-possible surface modeling . In Proc. Symp. Geometry Processing, 109--116 . Sorkine, O., and Alexa, M. 2007. As-rigid-as-possible surface modeling. In Proc. Symp. Geometry Processing, 109--116."},{"key":"e_1_2_2_38_1","doi-asserted-by":"crossref","unstructured":"Sorkine O. Cohen-Or D. Goldenthal R. and Lischinski D. 2002. Bounded-distortion piecewise mesh parameterization. In IEEE Visualization 355--362. Sorkine O. Cohen-Or D. Goldenthal R. and Lischinski D. 2002. Bounded-distortion piecewise mesh parameterization. In IEEE Visualization 355--362.","DOI":"10.1109\/VISUAL.2002.1183795"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461955"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024176"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185583"},{"key":"e_1_2_2_42_1","volume-title":"Proc. Symp. Geometry Processing, 33--37","author":"Wardetzky M.","unstructured":"Wardetzky , M. , Mathur , S. , K\u00e4lberer , F. , and Grinspun , E . 2007. Discrete Laplace operators: No free lunch . In Proc. Symp. Geometry Processing, 33--37 . Wardetzky, M., Mathur, S., K\u00e4lberer, F., and Grinspun, E. 2007. Discrete Laplace operators: No free lunch. In Proc. Symp. Geometry Processing, 33--37."},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366195"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183290"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778855"},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461946"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2601097.2601179","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2601097.2601179","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T07:19:11Z","timestamp":1750231151000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2601097.2601179"}},"subtitle":["anisotropic and non-orthogonal cross fields"],"short-title":[],"issued":{"date-parts":[[2014,7,27]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,7,27]]}},"alternative-id":["10.1145\/2601097.2601179"],"URL":"https:\/\/doi.org\/10.1145\/2601097.2601179","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7,27]]},"assertion":[{"value":"2014-07-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}