The vectors, matrices, and transforms every game runs on. Vector algebra and what the dot and cross products actually tell you, using vectors for movement and reflection, matrices and the transforms that move objects, rotations and quaternions and why they beat Euler angles, the coordinate spaces a vertex passes through, and smooth curves for paths and animation.
Before you start
No advanced math required — just comfort reading code. Examples are in Python (the Python course is enough), and the concepts transfer to any engine or language.
Vectors
Vectors are the atoms of game math — position, velocity, direction, and force are all vectors. Learn the operations (add, scale, length, normalize) and the dot and cross products that power everything else.
Vectors in Practice
Turn vector operations into gameplay: move toward a target, compute distances cheaply, reflect a ball off a wall, and steer smoothly. The everyday vector recipes you reach for constantly.
Matrices & Transforms
Matrices pack translation, rotation, and scale into one object that transforms points. Learn how the transforms work, why matrix multiplication order matters, and how one matrix moves a whole model.
Rotations & Quaternions
Rotating in 3D is subtle. Euler angles are intuitive but suffer gimbal lock; quaternions rotate smoothly without it and interpolate cleanly. Learn when to use each and how to think about quaternions.
Coordinate Spaces
A vertex travels through several coordinate spaces on its way to the screen — local, world, view, and clip. Understanding these spaces and the matrices between them is the key to 3D rendering and gameplay.
Curves & Interpolation
Straight lines are rarely enough — paths, camera moves, and animation need smooth curves. Learn lerp and easing, Bézier curves for authored paths, and Catmull-Rom splines that pass through points.