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Math for Game Devs - Abstract Algebra, Procedural Animation & Splines

Freya Holmér via YouTube

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Overview

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This course presents mathematical tools for game development, including smoothing and easing, Hermite interpolation, splines, complex numbers, dual numbers, vectors, geometric algebra, and quaternions. It connects these concepts to animation and rotation in games.

Syllabus

Intro
Lecture Start
Smoothing & Easing functions
Deriving Hermite Interpolation
Splines
i imaginary unit
Complex Plane
Complex Numbers
Euler’s Formula & Identity
e the constant
Dual Numbers
Why use quaternions in games?
Vector Algebra an alternate perspective
Multiplying vectors?
2D Bivectors & the wedge product
Geometric Product
Multivector & Bases
3D Geometric Algebra
Full 3D Multivector
The generality of GA
Quaternions from a GA perspective
4D Games
Why quaternions rotate well
Q&A Outro & how I animate in Unity

Taught by

Freya Holmér

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