Math for Game Devs [2022, part 10] • Abstract Algebra, Procedural Animation & Splines

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 💖 Support me on Patreon ❱ https://www.patreon.com/acegikmo 📺 I usually stream on twitch ❱ https://www.twitch.tv/acegikmo 💬 Join my discord ❱ https://discord.gg/acegikmo 🐦 Follow me on twitter ❱ https://twitter.com/FreyaHolmer 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