12 citations · 26 across the 5 of their papers we have counts for
7 papers
Computing a Dirichlet domain for a hyperbolic surface
Vincent Despré, Benedikt Kolbe, Hugo Parlier +1
The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a funda…
Delaunay triangulations of generalized Bolza surfaces
Matthijs Ebbens, Iordan Iordanov, Monique Teillaud +1
The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincaré disk model, under the action of the group generated by the hyperbolic isometries…
Flipping Geometric Triangulations on Hyperbolic Surfaces
Vincent Despré, Jean-Marc Schlenker, Monique Teillaud
We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally geodesic segments. We prove that the flip graph of geometric…
Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
Rien van de Weygaert, Gert Vegter, Herbert Edelsbrunner +13
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 distributio…
The Sticky Geometry of the Cosmic Web
Johan Hidding, Rien van de Weygaert, Gert Vegter +2
In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and perva…
Probing Dark Energy with Alpha Shapes and Betti Numbers
Rien van de Weygaert, Pratyush Pranav, Bernard J. T. Jones +8
We introduce a new descriptor of the weblike pattern in the distribution of galaxies and matter: the scale dependent Betti numbers which formalize the topological information conte…
Triangulating the Real Projective Plane
Mridul Aanjaneya, Monique Teillaud
We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 alwa…