Geometry processing is a fast-growing area of research that designs efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation and transmission of 3D models. This course covers different aspects of Geometry Processing, related with the reconstruction of high-level information from raw data. The first part of the course explains how starting with a point set (e.g. acquired with a 3D scanner), one can reconstruct a valid mesh, and then recover higher-level information (symmetry, structuration into parts). The second part is related with mesh-based computations (e.g. UV mapping and deformations) that need to define a function space over the mesh. We will introduce finite elements, spectral function bases and some of their applications. The course is based on the following courses/book, together with new elements : • Geometry Processing based on Polygonal Meshes (SIGGRAPH and EUROGRAPHICS Courses, Botsch et.al) • Polygon Mesh Processing (AK Peters / CRC Press, Botsch et.al) • Spectral Mesh Processing (SIGGRAPH and SIGGRAPH ASIA Course, Levy and Zhang)

Level
Advanced

Prerequisites
Attendees need to be familiar with at least one programming language, notions of geometry, linear algebra, data structures and algorithms.

Course Schedule
Session 1
5 min. Lecture 0: Introduction (Lévy)
45 min. Lecture 1: Low Level: Reconstruction, Meshing and Sampling (Lévy)
45 min. Lecture 2: High Level: Recovering Structure and Symmetry (Zhang)

-------------- 15 min. Break ---------------

Session 2
45 min. Lecture 3: Function Spaces I: Finite Element Modeling for Geometry Processing (Lévy)
45 min. Lecture 4: Function Spaces II: Spectral Mesh Processing (Zhang)
5 min. Wrapup, Q&A

Presenter(s)
Bruno Lévy directs the ALICE project team in INRIA Nancy Grand-Est and in the LORIA lab. His research topic is numerical geometry, with applications in numerical simulation, real-time rendering and scientific visualization. Some of his results (e.g. LSCM) are used in several commercial and open-source softwares.

He defended his Ph.D. thesis in 1999 and received the Gilles Kahn / Académie des Sciences SPECIF award in 2000. Then he did a post-doc in Stanford. He was program co-chair of ACM SPM in 2007 and 2008, and program co-chair of ACM/EG SGP in 2010. He is associate editor of TVCG (IEEE) and Graphical Models (Elsevier). He was awarded a grant from the European Research Council in 2008, received the Lorraine regional young researcher award in 2010 and the INRIA young researcher award in 2011.


Hao Richard Zhang co-directs the Graphics, Usability, and Visualization Lab at Simon Fraser University, Canada, where he is an associate professor in the School of Computing Science. He received his Ph.D. from the Dynamic Graphics Project (DGP), Department of Computer Science, University of Toronto in 2003 and M. Math and B. Math degrees from the University of Waterloo. His research interests include geometry processing, shape analysis, and computer graphics. He was a winner of the Best Paper Award from SGP 2008 and the Most Cited Paper Award for the journal Computer-Aided Design in 2010.