Algorithmic Geometry of Triangulations
Jean-Daniel Boissonnat, Dorian Mazauric, Pierre Alliez
January 26-30, 2015 – INRIA Sophia Antipolis
Triangulations are fundamental geometric structures used to represent and analyze complex shapes. Applications can be found in many areas such as geometric modeling, computer graphics, numerical simulations or topological data analysis. The course surveys some basic results in Computational and Topological Geometry and offers an introduction to recent research topics. Lectures in the morning are intended to provide the foundations of the subject while the talks in the afternoons will present recent results. The talks will be followed by discussions and exercises.
26/01
09:00-12:00: Simplicial complexes in metric spaces (J-D. Boissonnat) 1a 1b
14:00-17:00: Representation of simplicial complexes (D. Mazauric)1c
27/01
09:00-12:00: Delaunay complexes, Voronoi diagrams and convex hulls (J-D. Boissonnat) 2
14:00-17:00: Exercises (A.C. De Vitis)
28/01
09:00-12:00: Union of balls and a-complexes (J-D. Boissonnat) 3
14:00-17:00 Exercises (M. Rouxel-Labbé)
29/01
09:00-12:00: Mesh Generation (J-D. Boissonnat) 4a 4b
14:00-17:00: Surface reconstruction (P. Alliez) 4c
30/01
09:00-12:00: Reconstruction of submanifolds (J-D. Boissonnat) 5
14:00-17:00: Exam
Further reading:
Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars. Computational Geometry: Algorithms and Applications. Springer-Verlag 2008.
Jean-Daniel Boissonnat, Mariette Yvinec. Algorithmic Geometry. Cambridge University Press 1998.
Herbert Edelsbrunner. Geometry and Topology for Mesh Generation. Cambridge University Press 2001.
Herbert Edelsbrunner, John Harer. Computational Topology : an Introduction. AMS 2010.
