{"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"file":[{"file_id":"6629","file_name":"IntrinsicExtrinsicCCCG2019.pdf","creator":"mwintrae","date_updated":"2020-07-14T12:47:34Z","content_type":"application/pdf","date_created":"2019-07-12T08:32:46Z","checksum":"ceabd152cfa55170d57763f9c6c60a53","access_level":"open_access","file_size":321176,"relation":"main_file"}],"date_published":"2019-08-01T00:00:00Z","citation":{"mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” <i>The 31st Canadian Conference in Computational Geometry</i>, 2019, pp. 275–79.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in <i>The 31st Canadian Conference in Computational Geometry</i>, Edmonton, Canada, 2019, pp. 275–279.","ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: <i>The 31st Canadian Conference in Computational Geometry</i>. ; 2019:275-279.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In <i>The 31st Canadian Conference in Computational Geometry</i>, 275–79, 2019.","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.","apa":"Vegter, G., &#38; Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In <i>The 31st Canadian Conference in Computational Geometry</i> (pp. 275–279). Edmonton, Canada."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"month":"08","year":"2019","day":"01","department":[{"_id":"HeEd"}],"status":"public","date_created":"2019-07-12T08:34:57Z","conference":{"location":"Edmonton, Canada","start_date":"2019-08-08","end_date":"2019-08-10","name":"CCCG: Canadian Conference in Computational Geometry"},"author":[{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Submitted Version","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."}],"date_updated":"2021-01-12T08:08:16Z","file_date_updated":"2020-07-14T12:47:34Z","_id":"6628","scopus_import":1,"oa":1,"has_accepted_license":"1","page":"275-279","type":"conference","publication_status":"published","language":[{"iso":"eng"}],"publication":"The 31st Canadian Conference in Computational Geometry","ddc":["004"]}