In this course, we plan to study the fundamental algorithms, data structures, and mathematics behind the current approaches for manipulating and processing geometric data in a variety of real world applications, like computer aided design, interactive computer graphics, reliable physical simulations, and robust 3D representations for machine learning.
The course will present the data structures for simplicial complexes and the current discrete representations used to manage 3D shapes in common applications. The course will also introduce the basic notions of differential geometry and Topology that can be useful for a better comprehension of algorithms in Computer Graphics.
The most common mesh processing algorithms will be explained with their practical applications and available implementations.
The purpose of the course is to illustrate the most critical mathematical, geometric and algorithmic foundations for representing and processing 3D shapes in computer graphics.

Syllabus :
1. Basics of Differential Geometry and Topology for Computer Graphics
2. Discrete Representations and Data Structures for Simplicial Complexes and spatial Indexing
3. Mesh Processing Algorithms
a. Remeshing, Refinement & Simplification
b. Parametrization and Texturing
c. Fairing and Smoothing
d. Surface reconstruction and Sampling
4. Shape Analysis and Representations for Machine Learning

Prerequisites: Knowledge of linear algebra and calculus.
Advisement recommendations: C++, Python