Geometry Processing applied to Computer Graphics

The popularization of 3D digitization techniques has led to the development of complex digital object models. It is indeed essential to benefit from efficient and fast treatments to obtain, transmit, edit and deform quality models that are produced from raw data that may be very noisy and redundant. The purpose of this course is to introduce the notion of Geometry Processing useful for shape modeling. In particular, we will examine the problem of generating a surface mesh as a discretization of the geometry of a 2D or 3D shape, and we will present the approaches of Computational Geometry to generate, simplify, refine and manipulate them, by relying on geometric structures. with particular properties.

Meshes:

• Definitions
• Generation of meshes, 3D reconstruction and virtual sculpture
• Simplification and refinement of meshes
• Meshes improvement, coding

Geometry Processing and Computational Geometry (CG):

• Elementary notions of CG in 2D (planar maps, graphs, triangulation, convex hull)
• Construction of convex hull in 2D: optimal algorithm (divide and conquer)
• Incremental algorithms
• Triangulation of Delaunay in 2D (and its dual: Voronoi diagram): general definitions, properties
• Power diagrams
• Algorithm for optimal construction of Delaunay triangulation (divide and conquer), and incremental algorithms