A weak characterisation of the Delaunay triangulation |
| |
Authors: | Vin de Silva |
| |
Institution: | (1) Department of Mathematics, Pomona College, 610 N. College Avenue, Claremont, CA 91711, USA |
| |
Abstract: | We consider a new construction, the weak Delaunay triangulation of a finite point set in a metric space, which contains as a subcomplex the traditional (strong) Delaunay triangulation. The two simplicial complexes turn out to be equal for point sets in Euclidean space, as well as
in the (hemi)sphere, hyperbolic space, and certain other geometries. There are weighted and approximate versions of the weak
and strong complexes in all these geometries, and we prove equality theorems in those cases also. On the other hand, for discrete
metric spaces the weak and strong complexes are decidedly different. We give a short empirical demonstration that weak Delaunay
complexes can lead to dramatically clean results in the problem of estimating the homology groups of a manifold represented
by a finite point sample.
|
| |
Keywords: | Delaunay triangulation Voronoi diagram Laguerre diagram Witness complex Manifold reconstruction Topological approximation |
本文献已被 SpringerLink 等数据库收录! |
|