{"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","_id":"6628","language":[{"iso":"eng"}],"oa_version":"Submitted Version","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","location":"Edmonton, Canada","start_date":"2019-08-08","end_date":"2019-08-10"},"ddc":["004"],"oa":1,"day":"01","publication":"The 31st Canadian Conference in Computational Geometry","abstract":[{"lang":"eng","text":"Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space."}],"quality_controlled":"1","citation":{"ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.","ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational Geometry. ; 2019:275-279.","apa":"Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada.","ista":"Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279.","mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–79.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference in Computational Geometry, 275–79, 2019.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279."},"date_created":"2019-07-12T08:34:57Z","publication_status":"published","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"author":[{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs"}],"department":[{"_id":"HeEd"}],"file":[{"checksum":"ceabd152cfa55170d57763f9c6c60a53","file_size":321176,"date_created":"2019-07-12T08:32:46Z","date_updated":"2020-07-14T12:47:34Z","file_name":"IntrinsicExtrinsicCCCG2019.pdf","relation":"main_file","file_id":"6629","content_type":"application/pdf","access_level":"open_access","creator":"mwintrae"}],"ec_funded":1,"date_updated":"2021-01-12T08:08:16Z","has_accepted_license":"1","month":"08","year":"2019","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"status":"public","page":"275-279","file_date_updated":"2020-07-14T12:47:34Z","date_published":"2019-08-01T00:00:00Z","type":"conference"}