{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T22:38:05Z","timestamp":1767825485557,"version":"3.49.0"},"reference-count":31,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2015,3,2]],"date-time":"2015-03-02T00:00:00Z","timestamp":1425254400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Agence Nationale de la Recherche (ANR) under project GIGA (Geometric Inference and Geometric Approximation)"},{"name":"Chinese 973 Program (2010CB328001), Chinese 863 Program (2012AA040902), and the NSFC (61035002, 61272235)"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2015,3,2]]},"abstract":"<jats:p>\n            Anisotropic simplicial meshes are triangulations with elements elongated along prescribed directions. Anisotropic meshes have been shown well suited for interpolation of functions or solving PDEs. They can also significantly enhance the accuracy of a surface representation. Given a surface\n            <jats:italic>S<\/jats:italic>\n            endowed with a metric tensor field, we propose a new approach to generate an anisotropic mesh that approximates\n            <jats:italic>S<\/jats:italic>\n            with elements shaped according to the metric field. The algorithm relies on the well-established concepts of restricted Delaunay triangulation and Delaunay refinement and comes with theoretical guarantees. The star of each vertex in the output mesh is Delaunay for the metric attached to this vertex. Each facet has a good aspect ratio with respect to the metric specified at any of its vertices. The algorithm is easy to implement. It can mesh various types of surfaces like implicit surfaces, polyhedra, or isosurfaces in 3D images. It can handle complicated geometries and topologies, and very anisotropic metric fields.\n          <\/jats:p>","DOI":"10.1145\/2721895","type":"journal-article","created":{"date-parts":[[2015,3,3]],"date-time":"2015-03-03T14:08:19Z","timestamp":1425391699000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":18,"title":["Anisotropic Delaunay Meshes of Surfaces"],"prefix":"10.1145","volume":"34","author":[{"given":"Jean-Daniel","family":"Boissonnat","sequence":"first","affiliation":[{"name":"INRIA Sophia-Antipolis, Valbonne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kan-Le","family":"Shi","sequence":"additional","affiliation":[{"name":"Tsinghua University, Haidian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jane","family":"Tournois","sequence":"additional","affiliation":[{"name":"GeometryFactory, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariette","family":"Yvinec","sequence":"additional","affiliation":[{"name":"INRIA Sophia-Antipolis, Valbonne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,3,2]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073238"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009475"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195902000773"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of the 16th International Meshing Roundtable (IMR'08)","author":"Antani L.","unstructured":"L. Antani , C., Delage and P. Alliez . 2008. Mesh sizing with additively weighted Voronoi diagrams . In Proceedings of the 16th International Meshing Roundtable (IMR'08) . Springer, 335--346. L. Antani, C., Delage and P. Alliez. 2008. Mesh sizing with additively weighted Voronoi diagrams. In Proceedings of the 16th International Meshing Roundtable (IMR'08). Springer, 335--346."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/SMI.2005.5"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1810959.1811013"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2005.01.004"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1377676.1377724"},{"key":"e_1_2_1_9_1","unstructured":"J.-D. Boissonnat C. Wormser and M. Yvinec. 2011. Anisotropic Delaunay mesh generation. Tech. rep. RR-7712 INRIA. https:\/\/hal.inria.fr\/file\/index\/docid\/615486\/filename\/RR-7712.pdf.  J.-D. Boissonnat C. Wormser and M. Yvinec. 2011. Anisotropic Delaunay mesh generation. Tech. rep. RR-7712 INRIA. https:\/\/hal.inria.fr\/file\/index\/docid\/615486\/filename\/RR-7712.pdf."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-874X(96)00057-1"},{"key":"e_1_2_1_11_1","volume-title":"Proceedings of the 5th International Meshing Roundtable (IMR'96)","author":"Bossen F.","unstructured":"F. Bossen and P. Heckbert . 1996. A pliant method for anisotropic mesh generation . In Proceedings of the 5th International Meshing Roundtable (IMR'96) . F. Bossen and P. Heckbert. 1996. A pliant method for anisotropic mesh generation. In Proceedings of the 5th International Meshing Roundtable (IMR'96)."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-011-9372-6"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2004.09.004"},{"key":"e_1_2_1_14_1","unstructured":"CGAL. 2014. Computational geometry algorithms library. http:\/\/www.cgal.org.  CGAL. 2014. Computational geometry algorithms library. http:\/\/www.cgal.org."},{"key":"e_1_2_1_15_1","volume-title":"Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'06)","author":"Cheng S.-W.","unstructured":"S.-W. Cheng , T. K. Dey , E. A. Ramos , and R. Wenger . 2006. Anisotropic surface meshing . In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'06) . ACM Press, New York, 202--211. S.-W. Cheng, T. K. Dey, E. A. Ramos, and R. Wenger. 2006. Anisotropic surface meshing. In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'06). ACM Press, New York, 202--211."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/160985.161150"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/0910064"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.3390\/a2041327"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827503428527"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(99)00030-9"},{"key":"e_1_2_1_21_1","volume-title":"CS-03-05. Department of Computer Science","author":"Hughes J.","unstructured":"J. Hughes . 2003. Differential geometry of implicit surfaces in 3-space -A primer. Tech. rep ., CS-03-05. Department of Computer Science , Brown University , Providence, R.I. J. Hughes. 2003. Differential geometry of implicit surfaces in 3-space -A primer. Tech. rep., CS-03-05. Department of Computer Science, Brown University, Providence, R.I."},{"key":"e_1_2_1_22_1","volume-title":"Proceedings of the 15th International Meshing Roundtable (IMR'06)","author":"Jiao X.","unstructured":"X. Jiao , A. Colombi , X. Ni , and J. C. Hart . 2006. Anisotropic mesh adaptation for evolving triangulated surfaces . In Proceedings of the 15th International Meshing Roundtable (IMR'06) . 173--190. X. Jiao, A. Colombi, X. Ni, and J. C. Hart. 2006. Anisotropic mesh adaptation for evolving triangulated surfaces. In Proceedings of the 15th International Meshing Roundtable (IMR'06). 173--190."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/777792.777822"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/336154.336221"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778856"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(02)00437-1"},{"key":"e_1_2_1_27_1","volume-title":"Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'01)","author":"Li X.-Y.","year":"2001","unstructured":"X.-Y. Li and S.-H. Teng . 2001 . Generating well-shaped Delaunay meshed in 3D . In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'01) . SIAM, 28--37. X.-Y. Li and S.-H. Teng. 2001. Generating well-shaped Delaunay meshed in 3D. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'01). SIAM, 28--37."},{"key":"e_1_2_1_28_1","volume-title":"Proceedings of the 8th International Meshing Roundtable (IMR'99)","author":"Li X.-Y.","unstructured":"X.-Y. Li , S.-H. Teng , and A. Ungor . 1999. Biting ellipses to generate anisotropic mesh . In Proceedings of the 8th International Meshing Roundtable (IMR'99) . X.-Y. Li, S.-H. Teng, and A. Ungor. 1999. Biting ellipses to generate anisotropic mesh. In Proceedings of the 8th International Meshing Roundtable (IMR'99)."},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-010-9090-y"},{"key":"e_1_2_1_31_1","volume-title":"What is a good linear finite element-&quest","author":"Shewchuk J. R.","unstructured":"J. R. Shewchuk . 2002. What is a good linear finite element-&quest ; Interpolation , conditioning, anisotropy, and quality measures. http:\/\/www.cs.cmu.edu\/~jrs\/jrspapers.html. J. R. Shewchuk. 2002. What is a good linear finite element-&quest; Interpolation, conditioning, anisotropy, and quality measures. http:\/\/www.cs.cmu.edu\/~jrs\/jrspapers.html."},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/1064092.1064129"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2721895","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2721895","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:13:27Z","timestamp":1750227207000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2721895"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,2]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,3,2]]}},"alternative-id":["10.1145\/2721895"],"URL":"https:\/\/doi.org\/10.1145\/2721895","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,2]]},"assertion":[{"value":"2011-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-03-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-03-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}