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

Dive into an extensive 3-hour 47-minute lecture on advanced mathematical concepts for game development. Explore a wide range of topics including smoothing and easing functions, Hermite interpolation, splines, complex numbers, Euler's formula, dual numbers, quaternions, vector algebra, geometric algebra, and their applications in game development. Learn about the imaginary unit, complex plane, and Euler's identity. Discover the reasons behind using quaternions in games, alternative perspectives on vector algebra, and the intricacies of geometric product and multivectors. Gain insights into 3D geometric algebra, full 3D multivectors, and the generality of geometric algebra. Conclude with discussions on quaternions from a geometric algebra perspective, 4D games, and practical animation techniques in Unity.

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