Computational geometry is a rather novel field whose aim is to study the properties of geometric objects such as point clouds, arrangements, geometric graphs or triangulations, both from a combinatorial and from an algorithmic point of view.
This course proposes a walkthrough of the discipline, to illustrate its variety in terms of topics as well as its potential in terms of applications. In this context, we will introduce a panel of theoretical questions, from very classical (e.g. computing convex hulls or Delaunay triangulations) to very recent (e.g. reconstruction from unorganized point clouds, approximation of geometric NP-complete problems, or effective proximity queries in high dimensions). Our goal will be twofold: on the one hand, to emphasize the elegance and theoretical soundness of the proposed approaches; on the other hand, to illustrate their practicality through a range of applications in computer graphics, robotics, machine learning, and image processing.
Lectures are in PC41 (8h30 à 10h30), TD sessions are from 14h00 to 16h00
| Lecture 1: Convex hulls + 3D meshes | TD1
(2D convex hulls+point location) |
january 7 | ||
| Lecture 2: Voronoi Diagrams and Delaunay Triangulations |
january 14 |
|||
| Lecture 3: Proximity search |
|
|
||
| Lecture 4: Graphs I: Tutte barycentric method |
|
|||
| Lecture 5: |
|
|||
| Lecture 6: |
|
|||
| |
Lecture 7: |
|||
| Lecture 8: | ||||
| Lecture 9: |
Nous avons plusieurs sujets de stages à proposer, à la frontière entre la géométrie algorithmique, la modélisation géométrique et l'analyse de données. N'hésitez pas à venir en discuter avec nous !
La communauté représente environ une centaine de chercheurs permanents à travers le monde, dont un peu plus d'une vingtaine en France.
Équipes en France :