such that C W (L) is not included in D M (L) The constants hidden in the ? and O notations are absolute and do not depend on µ nor ?. Moreover, W can be made indifferently finite or infinite ,

Recall that tetrahedron whereas its facets do We assume without loss of generality that c is not an endpoint of the Voronoi edge e, which means that the bounding sphere of the Delaunay ball B(c, c ? p) contains no point of L other than p, u, v, w. This condition can be ensured by an infinitesimal perturbation of the points of L \ {p, u, v, w}. Let d c = min p ? ?L\{p,u,v,w} c ? p ? . This quantity is greater than c ? p since B(c, c ? p) contains no point of L \ {p, u, v, w}. Consider any (finite or infinite) set of witnesses W ? M ? such that, for each facet ? of, W contains at least one point of M ? ? V(?) (every such point witnesses ? and its subsimplices ,

Surface Reconstruction by Voronoi Filtering, Discrete & Computational Geometry, vol.22, issue.4, pp.481-504, 1999. ,

DOI : 10.1007/PL00009475

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.71

The Crust and the ??-Skeleton: Combinatorial Curve Reconstruction, Graphical Models and Image Processing, vol.60, issue.2, pp.125-135, 1998. ,

DOI : 10.1006/gmip.1998.0465

Weak witnesses for Delaunay triangulations of submanifolds, Proceedings of the 2007 ACM symposium on Solid and physical modeling , SPM '07, pp.143-150, 2007. ,

DOI : 10.1145/1236246.1236267

Manifold reconstruction in arbitrary dimensions using witness complexes, Proc. 23rd ACM Sympos, pp.194-203, 2007. ,

URL : https://hal.archives-ouvertes.fr/hal-00488434

Sliver exudation, Proceedings of the fifteenth annual symposium on Computational geometry , SCG '99, pp.883-904, 2000. ,

DOI : 10.1145/304893.304894

Manifold reconstruction from point samples, Proc. 16th Sympos. Discrete Algorithms, pp.1018-1027, 2005. ,

A weak definition of Delaunay triangulation, 2003. ,

Topological estimation using witness complexes, Proc. Sympos. Point-Based Graphics, pp.157-166, 2004. ,

Reconstruction Using Witness Complexes, Proc. 18th Sympos. on Discrete Algorithms, pp.1076-1085, 2007. ,

DOI : 10.1007/s00454-008-9094-6

URL : https://hal.archives-ouvertes.fr/hal-00488434