Géométrie numérique
Master InformatiqueParcours Image et 3D (I3D)
Description
This unit introduces the fundamentals of digital geometry processing.
Compétences requises
Mathematics: vector calculus, matrix algebra. C++ programming.
Compétences visées
At the end of this teaching unit, a student will know :
- The context of digitizing 3D geometric shapes and the basics of surface representations in the form of 3D point clouds;
- How to put into perspective and compare different shape representations such as 3D point clouds, polygonal meshes, parametric surfaces, implicit surfaces, and voxel sets;
- How to compute differential features (curvatures, Laplacian) on a triangular mesh;
- How to modify a 3D shape represented as a polygonal mesh: smoothing/denoising, simplification, remeshing.
Disciplines
- Informatique
Syllabus
Lectures begin by presenting the acquisition processes (digitization) and the main discrete representations of 3D shapes. It then focuses on polygonal meshes and presents the mathematical and algorithmic tools allowing their analysis and modification. The practical sessions complete and put into practice the concepts seen in class, in particular through the realization of a real software project on this theme.
Bibliographie
- Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, Bruno Lévy, “Polygon Mesh Processing”. AK Peters/CRC Press, 2010. https://www.pmp-book.org/
- Jean-Luc Mari, Franck Hétroy-Wheeler, Gérard Subsol, “Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis”. ISTE/Wiley, 2019. https://www.iste.co.uk/book.php?id=1555
- Jakob Andreas Baerentzen, Jens Gravesen, François Anton, Henrik Aanaes, “Guide to Computational Geometry Processing”. Springer, 2012. https://books.google.fr/books?id=0lb4_pLIyP8C