We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution.Expand

We propose an incremental algorithm that computes the Delaunay triangulation of a set of points in the 3D flat torus without duplicating any point, whenever possible; our algorithmic test detects when such a duplication can be avoided, which is usually possible in practical situations.Expand

We propose two ways to compute the Delaunay triangulation of points on a sphere, or of rounded points close to the sphere, both based on the classic incremental algorithm initially designed for the plane.Expand

We give a definition of the Delaunay triangulation of a point set in a closed Euclidean d-manifold, i.e. a compact quotient space for a discrete group of isometries (a so-called Bieberbach group or crystallographic group).Expand

We give a definition of the Delaunay triangulation of a point set in a closed Euclidean d-manifold, i.e. a compact quotient space for a discrete group of isometries (a so-called Bieberbach group or crystallographic group).Expand

Au contraire des travaux anterieurs sur les triangulations periodiques, nous evitons de maintenir plusieurs copies periodiques des points, lorsque cela est possible.Expand

In this paper we describe a new design for the 3D triangulation package that permits to easily add functionality to compute triangulations in other spaces.Expand