Giving Personality to Procedural Animations using Math

It's been a while since the last video hasn't it? I've made quite a bit of progress since the last update, and since one of the things I worked on was some procedurally animated characters, I decided to make a video about the subject. In particular, this video highlights the entire process from initial motivation, to the technical design, technical analysis, and game design considerations.

Codeer's video on procedural animation: https://www.youtube.com/watch?v=e6Gjhr1IP6w
Twitter thread about rope animation: https://twitter.com/t3ssel8r/s....tatus/14700399815029
Semi-implicit Newton's Method: https://en.wikipedia.org/wiki/....Semi-implicit_Euler_
Verlet Integration: https://en.wikipedia.org/wiki/Verlet_integration
Pole-Zero Matching: https://en.wikipedia.org/wiki/....Matched_Z-transform_

Math animations made using the community-maintained version of manim: https://www.manim.community/

Timestamps:
0:00 intro
1:43 second order systems
7:03 implementation
8:55 testing
9:50 stability
13:30 conclusion

Music:
lofi geek - give me
lofi geek - souls
lofi geek - real
lofi geek - two lifes
lofi geek - lights

#SoME2