Manim Tutorial: A "very mathematical" Updater Animation example

Manim is a free and open-source, community-maintained Python library for creating (mathematical) animations originally started by Grant "3blue1brown" Sanderson. This tutorial series is a guided tour of Manim's features. This episode discusses the mathematical background relevant for a sample scene (the winding number, and normal vector equations), as well as how exactly vectorized mobjects are built from Bézier curves. We also revisit the topic of episode 4 (   • Manim Tutorial Series E04: Updater Functio...  ): updater functions! #manim #tutorial #animation #python #programming #math #3blue1brown Links to resources Jupyter worksheet: https://mybinder.org/v2/gh/behackl/ma... - ‪@acegikmo‬'s video essay "The Beauty of Bézier Curves":    • The Beauty of Bézier Curves   Pomax' Primer on Bézier Curves: https://pomax.github.io/bezierinfo/ A Deep Dive into Manim's internals: https://docs.manim.community/en/stabl... GitHub repo with series materials: https://github.com/behackl/manim-with... Manim: https://www.manim.community Discord: https://manim.community/discord More about me Homepage: https://benjamin-hackl.at Twitch:   / behackl   Twitter:   / behackl   Discord: https://benjamin-hackl.at/discord Music Album: A Moment Away, by cxlt. x Nuver | Provided by Lofi Records | https://lofigirl.com/blogs/releases/a... Album: Stories of Synergy, by Tonion x xander. | Provided by Lofi Records | https://lofigirl.com/blogs/releases/s... --- Video contents: 0:00 Introduction 1:52 Implementation Overview 4:11 When is a point in a circle? 7:41 The Winding Number 14:31 Vectorized Mobjects, Bézier Curves 22:54 Normal Vector Line Equation 32:30 color_updater and play calls 35:45 Outro