Freya Holmér | Math for Game Devs [2022, part 10] • Abstract Algebra, Procedural Animation & Splines @acegikmo | Uploaded November 2022 | Updated October 2024, 4 hours ago.
Primarily for my students at FutureGames - I will only read chat/superchats during breaks!

Assignments & Lecture links ❱ https://acegikmo.notion.site/Lectures-Assignments-a4419295f33f46c3af113eb74b407607

Find out more about the school at https://futuregames.se/
❓ FAQ ❱ https://acegikmo.notion.site/FAQ-8b62a1634746473db702565d890dd3dd

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0:00:00 Intro
0:11:06 Lecture Start
0:18:24 Smoothing & Easing functions
0:54:00 Deriving Hermite Interpolation
1:20:00 Splines
1:29:12 i (imaginary unit)
1:39:12 Complex Plane
1:42:05 Complex Numbers
1:50:38 Euler’s Formula & Identity
1:56:00 e (the constant)
2:07:03 Dual Numbers
2:10:43 Why use quaternions in games?
2:17:27 Vector Algebra (an alternate perspective)
2:24:30 Multiplying vectors?
2:30:00 2D Bivectors & the wedge product
2:34:40 Geometric Product
2:43:00 Multivector & Bases
2:48:03 3D Geometric Algebra
2:52:49 Full 3D Multivector
2:57:56 The generality of GA
3:00:26 Quaternions (from a GA perspective)
3:05:05 4D Games
3:07:28 Why quaternions rotate well
3:09:21 Q&A Outro & how I animate in Unity