A general introduction to the organization of the class and to Computer Animation
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.
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.
Use of kinematics-based particle systems to model complex looking animation, and their representation using sprites.
The use of procedural noise - Perlin Noise - to add details to shapes and animations.
Keyframe-based interpolation position using Spline curve - focuss on Catmull Rom spline.
Facial animation using Blenshape.
Reminder on relation between affine transformation and their parameterization as 4x4 matrices. Focuss on affine transform inversion.
Reminder on rotation parameterizaion using matrices, euler angle, axis angle, and quaternion.
Interpolation between rotation and affine transform using polar decomposition.
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.
Skin deformation using Skinning. Presentation of Rigid skinning, Linear Blend Skinning, and improvement using Dual Quaternion Skinning.
Encoding and animating a skeletal structure using Forward Kinematics and Inverse Kinematics.
Motion synthesis and design: Motion Graphs, Controlers, Learning-based approaches, User control.
Crowd animation using Boids models.
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.
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.
Application case of colliding spheres in a box. Collision between sphere and plane, collision between spheres.
Modeling elastic shape using mass spring structure.
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.
Steps to follow to compile the code used in the various exercises. These steps will need to be reproduced for each exercise.
Introduction to the use of the code to handle basic shape primitives and transformations.
Exercise on simple procedural motion applied to particles displayed as spheres and billboards.
Facial deformation using blend shape interpolation.
Facial deformation using blend shape interpolation.
Implementation of a Free Form Deformation for interactive volume deformation.
Implementing Laplacian deformation with hard and soft positional constraints on a surface using Eigen. Extention to As-Rigid-As-Possible deformation.
Implementing a Linear Blend Skinning, followed by Dual Quaternion Skinning.
Implementing a box filled with colliding spheres using numerical integration. Handle collision betwenn spheres and the box as well as between spheres.
Cloth simulation using mass springs: generate spring topology and compute spring forces, handle collisions with surrounding elements.
Implementing a stable fluids simulation on a grid: Compute diffusion and divergence free constraint in solving a Poisson equation using Gauss Seidel method.
Implementing a SPH fluid simulation: Compute the density, pressure force and viscosity.