Bézier curves - how do they do?

They're used for animation, text rendering, and all sorts of curved shapes! But how do they actually work? well, like, that's what the video is about, so, watch it to find out etc!!

• Lots of love to 💛 Jazz "queenjazz" Mickle for making the music ❱ https://queenjazz.bandcamp.com/ 💙 Grant "3Blue1Brown" Sanderson for pushing me to finally do this ❱ https://youtube.com/3blue1brown 🐦 Pomax for their wonderful writeup on Bézier curves ❱ https://pomax.github.io/bezierinfo 🐈 Thor the cat for.. hanging out.. when I was trying to record audio with no interruptions

• How was this video made? 🔨 Created in the Unity game engine ⭕ Using Shapes, my vector graphics plugin ❱ https://u3d.as/1W37 📈 Using Mathfs, my math library ❱ https://github.com/FreyaHolmer/Mathfs ...along with a bunch of hacky, partially broken, procedural animation tools I made specifically for this video

• Links 💖 Patreon ❱ https://www.patreon.com/acegikmo 🐦 Twitter ❱ https://twitter.com/FreyaHolmer 📺 Twitch ❱ https://www.twitch.tv/acegikmo 💬 Discord ❱ https://discord.gg/v5VWuga 🌸 Instagram ❱ https://instagram.com/freya_holmer

00:00 Intro 01:06 Use Cases of Bézier Curves 01:56 Lerp 02:34 Quadratic Béziers 03:07 Cubic Béziers 03:57 De Casteljau's Algorithm 04:25 Bernstein Polynomial Form 06:18 1st Derivative (Velocity) 07:31 Tangents & Normals 08:03 2nd Derivative (Acceleration) 08:31 3rd Derivative (Jerk/Jolt) 09:07 Curvature 11:05 Bounding Box 14:14 Arc Length 15:07 Arc Length Parameterization & Uniform Animation 19:13 Outro 19:54 Credits 23:57 Thor helping me record this at 2am