Computer animation is the art and science of making things move — a character walking, a cape rippling, water crashing, a face breaking into a smile. Behind every second of a Pixar film or a AAA game lies a deep stack of mathematics and algorithms: curves that shape motion, skeletons that pose bodies, physics engines that simulate cloth and collisions, and — lately — neural networks that synthesise motion from data.

This master's-level course builds that stack from the ground up. It leans on game-development math (vectors, matrices, quaternions), the computer-graphics pipeline, and the numerical methods behind physics simulation, and turns them into moving pictures.

The course runs in twelve modules, from the twelve principles of animation and keyframing, through rigging, skinning and inverse kinematics, motion capture, and the physically based simulation of particles, cloth, rigid bodies and fluids, to procedural and crowd animation, facial and neural-motion synthesis, and finally rendering the animated frame. Work through them in order for the full climb, or dip into any topic that catches your eye.

Module 0 — Foundations & the animation pipeline

1. The animation pipeline
2. Time, frames and sampling
3. Keyframing vs simulation
4. Poses and rigs: an overview
5. Interpolation refresher

Module 1 — Principles & keyframe animation

1. The twelve principles of animation
2. The timeline and F-curves
3. Timing, spacing and easing
4. TCB and Kochanek–Bartels splines
5. Interpolating orientation with quaternions
6. Path animation and arc-length
7. Squash, stretch and anticipation

Module 2 — Curves, surfaces & deformation

1. Bézier and Catmull–Rom curves
2. B-splines and NURBS
3. Continuity: C⁰, C¹, C²
4. Subdivision surfaces
5. Mesh data structures (half-edge)
6. Free-form deformation
7. Lattice and cage deformers

Module 3 — Rigging & skeletal animation

1. Skeletons and joint hierarchies
2. Forward kinematics
3. The bind pose and skinning
4. Linear blend skinning
5. Dual-quaternion skinning
6. Blend shapes and morph targets

Module 4 — Inverse kinematics

1. The IK problem
2. Analytic two-bone IK
3. The Jacobian
4. Jacobian methods: transpose, pseudo-inverse, DLS
5. CCD and FABRIK
6. IK with constraints and full-body IK

Module 5 — Motion capture & data-driven motion

1. Motion capture systems
2. The mocap pipeline and solving
3. Motion retargeting
4. Motion graphs
5. Blend trees and state machines
6. Motion matching

Module 6 — Physically based animation I: particles & deformables

1. The simulation loop
2. Particle systems
3. Numerical integration for animation
4. Forces, springs and Hooke's law
5. Mass-spring cloth
6. Hair and strands
7. Position-based dynamics

Module 7 — Physically based animation II: rigid bodies & collision

1. Rigid-body dynamics
2. The inertia tensor and angular velocity
3. Collision detection: broad and narrow phase
4. The GJK algorithm
5. Impulse-based collision response
6. Constraints, contacts and friction
7. Ragdolls and articulated bodies

Module 8 — Fluids, smoke & natural phenomena

1. Eulerian fluids: stable fluids
2. Smoke and fire
3. SPH particle fluids
4. Level sets for liquids
5. Procedural noise phenomena

Module 9 — Procedural & behavioural animation

1. Perlin noise for motion
2. L-systems and procedural growth
3. Flocking and boids
4. Crowd simulation
5. Steering behaviours
6. Physics-based character control

Module 10 — Facial animation & the learning frontier

1. Facial animation and FACS
2. Blendshape and muscle faces
3. Lip sync
4. Secondary and soft-body motion
5. Learned motion: from motion matching to neural
6. Motion VAEs and diffusion
7. The state of the art

Module 11 — Rendering & production for animation

1. The rendering equation
2. BRDFs and physically based shading
3. Global illumination and path tracing
4. Monte Carlo sampling and noise
5. Motion blur
6. Temporal coherence and denoising
7. Real-time vs offline
8. The production pipeline