This 3D Computer Animation course teaches the computational methods for real-time animation and deformation of 3D shapes used in video games, special effects, and animated films, or more generally in animated and interactive virtual worlds. The course details geometric-based animation approaches such as procedural animation, manual 3D deformers, and character animation, as well as physically-based simulation for particle systems, cloth and fluid simulation.
Learning outcome
The lectures bring knowledge of the industry-standard methods for real-time and interactive animation methods used in VFX, animation cinema, and video games, as well as toward research oriented approaches.
In addition, students following the class should acquire fundamentals of physically-based simulation, and in particular advanced knowledge on particle-based methods.
The class has a strong focus toward programming application. Enrolled students will therefore not only be able to understand these approach, but also to fully implement them in C++/OpenGL in an interactive context.
Application area
The applications illustrated throughout the class will be mostly related to the field of entertainment (animated films, video games, virtual and/or augmented reality), or real-time simulation for modeling physical phenomena. The underlying mechanisms can further be applied in other scientific disciplines (medical sciences, biology, etc.).
Examples of cases treated in the lectures and practical exercises: Implementing animation and interactive deformation of an articulated character, Modeling the deformation of a garment and managing collisions in real time, Simulating the surface of a moving fluid, Managing crowds of characters moving coherently, etc.
Organization
The course is largely practice-oriented with half lectures and half practical sessions. The practice is done in the form of programming exercises in the computer machine room in C++ language, with OpenGL.
A short project involving an animated virtual scene is carried out in the last sessions.
Prerequisits
C++ programming, and basics of Computer Graphics. Knowledge of OpenGL is a plus, but not required.
Affine transformations and parameterization in matrix form. Interpolation of affine transform and Polar Decomposition. Camera and view matrix construction. Interactive camera representation and ArcBall method.
Presentation of different methods for volume based deformation. Free Form Deformation (FFD) using a lattice. Cage based deformation using mean value coordinates and extensions. Vector field deformation with a focus on divergence free constraint.
Notions of differential coordinates on discrete surface with a focuss on Laplacian coordinates, and their use for smooth surface deformation in solving a sparse least square problem. Extension to As-Rigid-As-Possible (ARAP) deformation.
A general introductive presentation on methods and steps used in the 3D Animation Production PipeLine such as Animation Cinema and Visual Effects. A final focus on expressive animation principles.
Encoding and animating a skeletal structure using Forward Kinematics and Inverse Kinematics. Motion synthesis and design: Motion Graphs, Controlers, Learning-based approaches, User control.
Presentation of the fundamental models of physically-based simulation. Particle based models; Rigid bodies: angular velocity, inertia, dynamics of forces and torques; Continuum material: Notion of stress and strain; Lagrange representation and fundamental equation of dynamics, Euler representation and derivation of Navier-Stokes equation.
Numerical solution of ODEs: Explicit methods, Implicit methods, Runge Kutta, Symplectic integrators. Cloth simulation using mass springs, collision handling and extensions.
Presentation of various fluids models: Procedural method for ocean models; Level set approaches; PIC/FLIP approaches mixing grid and particles; and final focus on Smoothed Particle Hydrodynamics (SPH) for purely particle based model.
The pracical session are done in C++ and OpenGL using a dedicated library to facilitate the scene display.
The first step is to make sure that you can compile and execute some code using the first tutorial. Then all the exercises will follow the same principle.
Compilation tutorial
Steps to follow to compile the code used in the various exercises. These steps will need to be reproduced for each exercise.
Implementing a stable fluids simulation on a grid: Compute diffusion and divergence free constraint in solving a Poisson equation using Gauss Seidel method.