{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:19:56Z","timestamp":1778717996121,"version":"3.51.4"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2015,7,27]],"date-time":"2015-07-27T00:00:00Z","timestamp":1437955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2015,7,27]]},"abstract":"<jats:p>\n            This paper presents a new technique for frame field generation. As generic frame fields (with arbitrary anisotropy, orientation, and sizing) can be regarded as cross fields in a specific Riemannian metric, we tackle frame field design by first computing a discrete metric on the input surface that is compatible with a sparse or dense set of input constraints. The final frame field is then found by computing an optimal cross field in this customized metric. We propose frame field design constraints on alignment, size, and skewness at arbitrary locations on the mesh as well as along feature curves, offering much improved flexibility over previous approaches. We demonstrate the advantages of our frame field generation through the automatic quadrangulation of man-made and organic shapes with controllable anisotropy, robust handling of narrow surface strips, and precise feature alignment. We also extend our technique to the design of\n            <jats:italic>n<\/jats:italic>\n            -vector fields.\n          <\/jats:p>","DOI":"10.1145\/2766927","type":"journal-article","created":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T12:26:38Z","timestamp":1438086398000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":35,"title":["Frame field generation through metric customization"],"prefix":"10.1145","volume":"34","author":[{"given":"Tengfei","family":"Jiang","sequence":"first","affiliation":[{"name":"Zhejiang University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianzhong","family":"Fang","sequence":"additional","affiliation":[{"name":"Zhejiang University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Huang","sequence":"additional","affiliation":[{"name":"Zhejiang University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hujun","family":"Bao","sequence":"additional","affiliation":[{"name":"Zhejiang University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiying","family":"Tong","sequence":"additional","affiliation":[{"name":"Michigan State University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mathieu","family":"Desbrun","sequence":"additional","affiliation":[{"name":"Caltech"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882296"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01142.x"},{"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\/j.1467-8659.2010.01761.x"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12427"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12426"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508372"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.345074"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/VISUAL.2004.75"},{"key":"e_1_2_2_10_1","volume-title":"Proceedings of the 12th IMA International Conference on Mathematics of Surfaces XII, Springer-Verlag, 209--232","author":"Jin M.","unstructured":"Jin , M. , Kim , J. , and Gu , X. D . 2007. Discrete surface ricci flow: Theory and applications . In Proceedings of the 12th IMA International Conference on Mathematics of Surfaces XII, Springer-Verlag, 209--232 . Jin, M., Kim, J., and Gu, X. D. 2007. Discrete surface ricci flow: Theory and applications. In Proceedings of the 12th IMA International Conference on Mathematics of Surfaces XII, Springer-Verlag, 209--232."},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2462005"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2009.59"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2653476"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024174"},{"key":"e_1_2_2_15_1","article-title":"Discrete connection and covariant derivative for vector field analysis and design. ACM","author":"Liu B.","year":"2015","unstructured":"Liu , B. , Tong , Y. , de Goes , F. , and Desbrun , M. 2015 . Discrete connection and covariant derivative for vector field analysis and design. ACM Trans. Graph. (to appear). Liu, B., Tong, Y., de Goes, F., and Desbrun, M. 2015. Discrete connection and covariant derivative for vector field analysis and design. ACM Trans. Graph. (to appear).","journal-title":"Trans. Graph. (to appear)."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/S00361445024180"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185605"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461970"},{"key":"e_1_2_2_19_1","volume-title":"Differential Geometry and Its Applications","author":"Oprea J.","unstructured":"Oprea , J. 2007. Differential Geometry and Its Applications . Mathematical Association of America . Oprea, J. 2007. Differential Geometry and Its Applications. Mathematical Association of America."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276446"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601179"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1356682.1356683"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1640443.1640444"},{"key":"e_1_2_2_24_1","unstructured":"Schelter W. 2015. Maxima -- a computer algebra system (version 5.35). http:\/\/maxima.sourceforge.net.  Schelter W. 2015. Maxima -- a computer algebra system (version 5.35). http:\/\/maxima.sourceforge.net."},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360676"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2766927","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2766927","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T18:56:02Z","timestamp":1750272962000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2766927"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,27]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,7,27]]}},"alternative-id":["10.1145\/2766927"],"URL":"https:\/\/doi.org\/10.1145\/2766927","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,27]]},"assertion":[{"value":"2015-07-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}