This project deals with different surfaces. A surface is represented by a triangle mesh, meaning that it has many triangles that compose the surface.

We start with a random surface in 3D which can have zero, one, two, or more genus (hole in the surface). Then, we want to flatten it in a 2D fundamental domain. Hamilton introduced in 1981 a method called Ricci Flow, in order to produce datas that will be used for the flattening. The hope is that this will accelerate the process.

We want to flatten the surface because many applications can be deduced from it. For instance, a surface parametrization can be useful in digital geometry for texturing and re-meshing, a flat metric is helpful for constructing manifold spline.

The fundamental domain is a projective structure.

The objective of this project is to use the Ricci Flow method to generate projective structures and the hope is that would help getting better projective structures in a more quick and efficient way.