• Publications
  • Influence
Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web
TLDR
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
  • 57
  • 2
  • PDF
Computing 3D Periodic Triangulations
TLDR
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
  • 31
  • 2
Robust and Efficient Delaunay Triangulations of Points on Or Close to a Sphere
TLDR
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
  • 20
  • 2
Delaunay triangulations of point sets in closed euclidean d-manifolds
TLDR
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
  • 14
On the computation of 3d periodic triangulations
TLDR
In this video, we first review the incremental algorithm to compute Delaunay triangulations in R<sup>3</sup>. Expand
  • 8
  • PDF
Delaunay Triangulations of Closed Euclidean d-Orbifolds
TLDR
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
  • 9
Triangulating Point Sets in Orbit Spaces
TLDR
Au contraire des travaux anterieurs sur les triangulations periodiques, nous evitons de maintenir plusieurs copies periodiques des points, lorsque cela est possible. Expand
  • 9
  • PDF
Decoupling the CGAL 3D Triangulations from the Underlying Space
TLDR
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
  • 4
Computing Periodic Triangulations
TLDR
The talk presents work on periodic triangulations and meshes, in the Euclidean case as well as the hyperbolic case. Expand
  • 1