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We construct a convex function over each mesh simplex whose Hessian locally matches the Riemannian metric, and iteratively adapt vertex positions and mesh connectivity to minimize the difference between the target convex functions and their piecewise-linear interpolation over the mesh. Our method generalizes optimal Delaunay triangulation and leads to a simple and efficient algorithm. We demonstrate its quality and speed compared to state-of-the-art methods on a variety of domains and metrics.<\/jats:p>","DOI":"10.1145\/2661229.2661235","type":"journal-article","created":{"date-parts":[[2014,11,18]],"date-time":"2014-11-18T14:21:03Z","timestamp":1416320463000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":27,"title":["Anisotropic simplicial meshing using local convex functions"],"prefix":"10.1145","volume":"33","author":[{"given":"Xiao-Ming","family":"Fu","sequence":"first","affiliation":[{"name":"University of Science and Technology of China and Microsoft Research"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"Microsoft Research"}]},{"given":"John","family":"Snyder","sequence":"additional","affiliation":[{"name":"Microsoft Research"}]},{"given":"Baining","family":"Guo","sequence":"additional","affiliation":[{"name":"Microsoft Research and University of Science and Technology of China"}]}],"member":"320","published-online":{"date-parts":[[2014,11,19]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073238"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.difgeo.2014.01.001"},{"key":"e_1_2_2_3_1","doi-asserted-by":"crossref","unstructured":"Boissonnat J.-D. Cohen-Steiner D. and Yvinec M. 2008. Comparison of algorithms for anisotropic meshing and adaptive refinement. Tech. rep. INRIA. ACS-TR-362603.  Boissonnat J.-D. Cohen-Steiner D. and Yvinec M. 2008. Comparison of algorithms for anisotropic meshing and adaptive refinement. Tech. rep. INRIA. ACS-TR-362603.","DOI":"10.1145\/1377676.1377724"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1377676.1377724"},{"key":"e_1_2_2_5_1","unstructured":"Boissonnat J.-D. Wormser C. and Yvinec M. 2011. Anisotropic Delaunay mesh generation. Tech. rep. INRIA. INRIA-00615486.  Boissonnat J.-D. Wormser C. and Yvinec M. 2011. Anisotropic Delaunay mesh generation. Tech. rep. INRIA. INRIA-00615486."},{"key":"e_1_2_2_6_1","article-title":"Anisotropic Delaunay meshes of surfaces. ACM","author":"Boissonnat J.-D.","year":"2014","unstructured":"Boissonnat , J.-D. , Shi , K.-L. , Tournois , J. , and Yvinec , M. 2014 . Anisotropic Delaunay meshes of surfaces. ACM Trans. Graph., to appear. 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