---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Gert
foaf_name: Vegter, Gert
foaf_surname: Vegter
- foaf_Person:
foaf_givenName: Mathijs
foaf_name: Wintraecken, Mathijs
foaf_surname: Wintraecken
foaf_workInfoHomepage: http://www.librecat.org/personId=307CFBC8-F248-11E8-B48F-1D18A9856A87
dct_date: 2019^xs_gYear
dct_language: eng
dct_title: The extrinsic nature of the Hausdorff distance of optimal triangulations
of manifolds@
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