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. While the Bettiâ€¦ (More)

We propose two ways to compute the Delaunay triangulation of points on a sphere, or of rounded points close to a sphere, both based on the classic incremental algorithm initially designed for theâ€¦ (More)

We give a definition of the Delaunay triangulation of a point set in a closed Euclidean d-manifold, i.e. a compact quotient space of the Euclidean space for a discrete group of isometries (aâ€¦ (More)

Transformations of geometric objects, like translation and rotation, are fundamental operations in CADsystems. Rotations trigger the need to deal with trigonometric functions, which is hard toâ€¦ (More)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching andâ€¦ (More)

In this video, we first review the incremental algorithm to compute Delaunay triangulations in R<sup>3</sup>. Then we examine the case of the periodic space T<sup>3</sup>, focusing on the differencesâ€¦ (More)

The Computational Geometry Algorithms Library Cgal currently provides packages to compute triangulations in R and R. In this paper we describe a new design for the 3D triangulation package thatâ€¦ (More)

This work is motivated by the need for software computing 3D periodic triangulations in numerous domains including astronomy, material engineering, biomedical computing, fluid dynamics etc. We designâ€¦ (More)

We give a definition of the Delaunay triangulation of a point set in a closed Euclidean d-manifold, i.e. a compact quotient space of the Euclidean space for a discrete group of isometries (aâ€¦ (More)