On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions
| dc.creator | Oudot, Steve Y. | |
| dc.date | 2008-03-09 | |
| dc.date.accessioned | 2026-07-07T12:17:31Z | |
| dc.date.available | 2026-07-07T12:17:31Z | |
| dc.description | It is a well-known fact that, under mild sampling conditions, the restricted Delaunay triangulation provides good topological approximations of 1- and 2-manifolds. We show that this is not the case for higher-dimensional manifolds, even under stronger sampling conditions. Specifically, it is not true that, for any compact closed submanifold M of R^n, and any sufficiently dense uniform sampling L of M, the Delaunay triangulation of L restricted to M is homeomorphic to M, or even homotopy equivalent to it. Besides, it is not true either that, for any sufficiently dense set W of witnesses, the witness complex of L relative to M contains or is contained in the restricted Delaunay triangulation of L. | |
| dc.identifier | https://arxiv.org/abs/0803.1296 | |
| dc.identifier | http://arxiv.org/abs/0803.1296 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212100 | |
| dc.subject | Computational Geometry | |
| dc.title | On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions | |
| dc.type | text |