Section: Partnerships and Cooperations

International Initiatives

Inria Associate Teams Not Involved in an Inria International Lab

Astonishing

• Title: ASsociate Team On Non-ISH euclIdeaN Geometry

• International Partners (Institution - Laboratory - Researcher):

  • University of Groningen (Netherlands) - Johann Bernouilli Institute of Mathematics and Computer Science - Gert Vegter

  • University of Luxembourg - Mathematics Research Unit - Jean-Marc Schlenker

  • Université Paris Est Marne-la-Vallée - Laboratoire d'Informatique Gaspard Monge - Éric Colin de Verdière

• Start year: 2017

• See also: https://members.loria.fr/Monique.Teillaud/collab/Astonishing/

• Some research directions in computational geometry have hardly been explored. The spaces in which most algorithms have been designed are the Euclidean spaces $R^d$. To extend further the scope of applicability of computational geometry, other spaces must be considered, as shown by the concrete needs expressed by our contacts in various fields as well as in the literature. Delaunay triangulations in non-Euclidean spaces are required, e.g., in geometric modeling, neuromathematics, or physics. Topological problems for curves and graphs on surfaces arise in various applications in computer graphics and road map design. Providing robust implementations of these results is a key towards their reusability in more applied fields. We aim at studying various structures and algorithms in other spaces than $R^d$, from a computational geometry viewpoint. Proposing algorithms operating in such spaces requires a prior deep study of the mathematical properties of the objects considered, which raises new fundamental and difficult questions that we want to tackle.