---
_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'
...