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 ❱    / 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
🇫🇷 French subtitles by @damqui on Twitter

• 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

• Did you know that "osculating" isn't pronounced that way?
✅ yes I do now in fact please stop commenting on it ;-; ❱   / 1429472399389507591  

• Links
💖 Patreon ❱   / acegikmo  
🐦 Twitter ❱   / freyaholmer  
📺 Twitch ❱   / acegikmo  
💬 Discord ❱   / discord  
🌸 Instagram ❱   / 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