Geometry and Topology for Mesh Generation and Manifold Learning

Autor: Jean-Daniel Boissonnat A
The triangulation of manifolds has been a central question in Differential Topology all along the 20th century. In addition to be a question in pure mathematics, triangulating manifolds is a central problem in mesh generation for numerical simulations, visualization and computer graphics, and in machine learning where one needs to infer a geometric shape from a finite set of points sampling the shape. The lectures will present the algorithms aspects of the triangulation of manifolds, including recent results and applications. Both complexity issues and the quality of the computed approximations will be discussed in detail. 1. Polytopes and triangulations. 2. Nets, thickness and protection. 3. Mesh generation. 4. Manifold learning.