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