**Goal:**
given a set of points in the plane (resp. in Euclidean 3-dimensional
space, or in higher dimensions) one can define a "Delaunay triangulation" of
their convex hull, as defined for instance in
this
wikipedia page. It is a basic tool in computational geometry. The
definition involves the positions of the points with respects of circles
(resp. spheres).
More recently, more exotic types of Delaunay-like decompositions have been
proved to exist, where the circles (resp. spheres) are replaced by special
kinds of hyperboloids or paraboloids. The main goal of the project is to
compute those "exotic" Delaunay triangulations.
To achieve this goal, the students involved will be lead to understand
relatively simple notions of projective geometry as well as
the basic geometry of spaces of constant curvature, and in particular
their projective and conformal models.

**Schedule:** to be determined.

**Persons involved:**
Advised by Jean-Marc Schlenker, NN.

**Difficulty level:**
medium.

**Tools:**
programs in python/sage, use of computational tools to compute
and visualize the various types of Delaunay decompositions considered.

**Expected results:**
first, produce a running program to compute the Delaunay decomposition
of a set of points in the Euclidean plane or Euclidean space of dimension
3 (or possibly higher). Then, extend this algorithm to the more exotic
versions where circles/spheres are replaced by hyperboloids or paraboloids.