Application Domains
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography
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## Section: Partnerships and Cooperations

### International Initiatives

#### Inria Associate Teams Not Involved in an Inria International Labs

##### TRIP
• Title: Triangulation and Random Incremental Paths

• International Partner (Institution - Laboratory - Researcher):

• Carleton University (Canada) - CGLab - Prosenjit Bose

• Start year: 2018

• The two teams are specialists of Delaunay triangulation with a focus on computation algorithms on the French side and routing on the Canadian side. We plan to attack several problems where the two teams are complementary:

• Stretch factor of the Delaunay triangulation in 3D.

• Probabilistic analysis of Theta-graphs and Yao-graphs.

• Smoothed analysis of a walk in Delaunay triangulation.

• Walking in/on surfaces.

• Routing un non-Euclidean spaces.

##### Astonishing
• Title: ASsociate Team On Non-ISH euclIdeaN Geometry

• International Partner (Institution - Laboratory - Researcher):

• University of Groningen (Netherlands) - Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence - Gert Vegter

• Start year: 2017

• 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.