{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T01:31:37Z","timestamp":1773538297598,"version":"3.50.1"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2009,12,15]],"date-time":"2009-12-15T00:00:00Z","timestamp":1260835200000},"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":[[2009,12,15]]},"abstract":"<jats:p>\n            Many algorithms in texture synthesis, nonphotorealistic rendering (hatching), or remeshing require to define the orientation of some features (texture, hatches, or edges) at each point of a surface. In early works, tangent vector (or tensor) fields were used to define the orientation of these features. Extrapolating and smoothing such fields is usually performed by minimizing an energy composed of a smoothness term and of a data fitting term. More recently, dedicated structures (\n            <jats:italic>N<\/jats:italic>\n            -RoSy and\n            <jats:italic>N<\/jats:italic>\n            -symmetry direction fields ) were introduced in order to unify the manipulation of these fields, and provide control over the field's topology (singularities). On the one hand, controlling the topology makes it possible to have few singularities, even in the presence of high frequencies (fine details) in the surface geometry. On the other hand, the user has to explicitly specify all singularities, which can be a tedious task. It would be better to let them emerge naturally from the direction extrapolation and smoothing.\n          <\/jats:p>\n          <jats:p>This article introduces an intermediate representation that still allows the intuitive design operations such as smoothing and directional constraints, but restates the objective function in a way that avoids the singularities yielded by smaller geometric details. The resulting design tool is intuitive, simple, and allows to create fields with simple topology, even in the presence of high geometric frequencies. The generated field can be used to steer global parameterization methods (e.g., QuadCover).<\/jats:p>","DOI":"10.1145\/1640443.1640444","type":"journal-article","created":{"date-parts":[[2009,12,15]],"date-time":"2009-12-15T12:55:54Z","timestamp":1260881754000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":91,"title":["Geometry-aware direction field processing"],"prefix":"10.1145","volume":"29","author":[{"given":"Nicolas","family":"Ray","sequence":"first","affiliation":[{"name":"INRIA, Villers les Nancy Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno","family":"Vallet","sequence":"additional","affiliation":[{"name":"INRIA, Villers les Nancy Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Alonso","sequence":"additional","affiliation":[{"name":"INRIA, Villers les Nancy Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno","family":"Levy","sequence":"additional","affiliation":[{"name":"INRIA, Villers les Nancy Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2009,12,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1201775.882296"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the IEEE Eurographics. Eurographics.","author":"Ben-Chen M.","unstructured":"Ben-Chen , M. , Gotsman , C. , and Bunin , G . 2008. Conformal flattening by curvature prescription and metric scaling . In Proceedings of the IEEE Eurographics. Eurographics. Ben-Chen, M., Gotsman, C., and Bunin, G. 2008. Conformal flattening by curvature prescription and metric scaling. In Proceedings of the IEEE Eurographics. Eurographics."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/S089547980343641X"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1198555.1198666"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2004.09.035"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1275808.1276447"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/566570.566589"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.345074"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01060.x"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1138450.1138461"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1179352.1141921"},{"key":"e_1_2_1_12_1","volume-title":"Proceedings of Israel Korea Bi-National Conference.","author":"Levy B.","year":"2005","unstructured":"Levy , B. 2005 . Numerical methods for digital geometry processing . In Proceedings of Israel Korea Bi-National Conference. Levy, B. 2005. Numerical methods for digital geometry processing. In Proceedings of Israel Korea Bi-National Conference."},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of EG\/ACM Symposium on Geometry Processing.","author":"Li W.-C.","unstructured":"Li , W.-C. , Ray , N. , and Levy , B . 2006a. Automatic and interactive mesh to T-spline conversion . In Proceedings of EG\/ACM Symposium on Geometry Processing. Li, W.-C., Ray, N., and Levy, B. 2006a. Automatic and interactive mesh to T-spline conversion. In Proceedings of EG\/ACM Symposium on Geometry Processing."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2006.173"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1275808.1276446"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1993.10504266"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344987"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383328"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1356682.1356683"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360676"},{"key":"e_1_2_1_22_1","volume-title":"Proceedings of the Symposium on Geometry Processing. Eurographics, 201--210","author":"Tong Y.","unstructured":"Tong , Y. , Alliez , P. , Cohen-Steiner , D. , and Desbrun , M . 2006. Designing quadrangulations with discrete harmonic forms . In Proceedings of the Symposium on Geometry Processing. Eurographics, 201--210 . Tong, Y., Alliez, P., Cohen-Steiner, D., and Desbrun, M. 2006. Designing quadrangulations with discrete harmonic forms. In Proceedings of the Symposium on Geometry Processing. Eurographics, 201--210."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383297"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183290"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1640443.1640444","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1640443.1640444","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:23:26Z","timestamp":1750249406000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1640443.1640444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,15]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,12,15]]}},"alternative-id":["10.1145\/1640443.1640444"],"URL":"https:\/\/doi.org\/10.1145\/1640443.1640444","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12,15]]},"assertion":[{"value":"2008-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-12-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}