conference paper
The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds
published
yes
Gert
Vegter
author
Mathijs
Wintraecken
author 307CFBC8-F248-11E8-B48F-1D18A9856A87
HeEd
department
CCCG: Canadian Conference in Computational Geometry
ISTplus - Postdoctoral Fellowships
project
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.
https://research-explorer.app.ist.ac.at/download/6628/6629/IntrinsicExtrinsicCCCG2019.pdf
application/pdfno
2019Edmonton, Canada
eng
The 31st Canadian Conference in Computational Geometry
275-279
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.
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.
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.
G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.
Vegter, G., & 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.
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.
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.
66282019-07-12T08:34:57Z2020-01-16T12:38:06Z