Supervisor and Location
Monique Teillaud
Gamble group, INRIA Nancy - Grand Est,
LORIA
Topic
Geometric problems are central in many areas of science and
engineering. Computational geometry, the study of combinatorial and
algorithmic problems in a geometric setting, has tremendous practical
applications in areas such as computer graphics, computer vision and
imaging, scientific visualization, geographic information systems,...
Traditionally, the scope of computational geometry research was
limited to manipulations of geometric elements in the Euclidean spaces
R^{d}.
More recently, motivated by needs in other application domains,
algorithms were proposed to compute triangulations in d-dimensional
closed Euclidean manifolds [1,2].
In practice, a software package
computing Delaunay triangulations in the special case of the flat
torus with cubic domain was distributed in the CGAL library [3]. Such
triangulations can equivalently be seen as periodic triangulations,
where the periodicity domain is a cube (see the video). The software package was
successfully used in several fields, including astronomy [4].
Handling other types of periodicity in practice is necessary to extend
the applicability of previous work to a wider range of fields.
The objectives of the PhD consist in extending previous work in both
theoretical and practical directions:
References
[1] Manuel Caroli and Monique Teillaud. Delaunay triangulations of
closed Euclidean d-orbifolds. Discrete & Computational Geometry,
55(4):827-853, 2016.
[WWW]
[2] Manuel Caroli. Triangulating Point Sets in Orbit
Spaces. PhD thesis, Université de Nice Sophia Antipolis, 2010.
[WWW]
[3] Manuel Caroli and Monique Teillaud. 3D Periodic
Triangulations. In CGAL Editorial Board, editor, CGAL User and
Reference Manual.
[WWW]
[4] Johan Hidding, Rien van de Weygaert, Gert Vegter,
Bernard J.T. Jones, and Monique Teillaud. Video: The sticky Geometry of the
Cosmic Web. In Proceedings 28th Annual Symposium on Computational
Geometry, pages 421-422, 2012.
[WWW]
Skills and profile
Required qualification: Master in mathematics or computer science
Required skills and knowledge: