• [ENG] Master thesis (PDF)

• [FR] Mémoire de Master 2 (PDF)

I undertook this work at the National Institute of Informatics (NII) in Tokyo, Japan, under the supervision of Imari Sato. It was part of my year-end internship, during my second year of Master’s degree.

Throughout the internship I developped a rendering engine that accounts for the fluorescence of materials. It is based on Monte Carlo methods and uses a spectral path tracing algorithm.

The source code of the project is available on GitHub and of course, any contribution is welcomed.

This project was proposed and supervised by David Vanderhaeghe, associate professor at the University of Toulouse III - Paul Sabatier and part of the STORM team at the Toulouse Institute of Computer Science Research (IRIT).

The purpose of this project was to implement parts of the scientific publication, AniPaint: interactive painterly animation from video by Peter O’Donovan and Aaron Hertzmann.

Our final system renders painterly images from pictures.

I implemented this algorithm using C++ and OpenMesh for the half-edge structure.

Loop subdivision is an algorithm that can be applied to triangle meshes only. Its counterpart for quad meshes is the Catmull-Clark subdivision. Both are primal methods, which means that we will split the faces of the mesh, unlike dual methods that split the vertices of the mesh. Also, it is an approximation method, as opposed to interpolation methods (such as the Butterfly subdivision). It is called that way because we need to compute the position of all the vertices of the mesh. To compute them, there are subdivision rules with special cases at the boundaries of the mesh.

There are two main steps to perform Loop subdivision on a mesh:

First, we have to compute the positions of the newly added vertices. We will call them odd vertices. They are located on the edges of the mesh. Then, we have to compute the new positions of the old vertices of the mesh. We will call them even vertices.

In yellow, the old vertices of the mesh. In green and red the new vertices after respectively one and two steps of subdivision

When all the new positions of the vertices have been computed we need to correctly link them to create the new mesh topology. So we split each edge in two, and therefore each face in four smaller faces.