Giving Personality to Procedural Animations using Math -

Giving Personality to Procedural Animations using Math

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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:
Twitter thread about rope animation:
Semi-implicit Newton’s Method:
Verlet Integration:
Pole-Zero Matching:

Math animations made using the community-maintained version of manim:

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

lofi geek – give me
lofi geek – souls
lofi geek – real
lofi geek – two lifes
lofi geek – lights



  1. Lol you got it wrong literally on the first moving circle animation you show.

  2. im still waiting for new video.

  3. nice spider animation I really liked it 😁😁😁

  4. Your shader looks great, I would really like to see a video about it too.

  5. Ah yes math and animation. "Second Order derivatives" Oh yeah, I dropped out of math for a reason.

  6. Suprisingly good overview of fundamental controls concepts in a place I was not expecting. Good job.

  7. Did you just trick me into learning calculus?

  8. Which is the argument in physic to find it on the net?

  9. What tools are you using?
    I'm a backend developer, working with php..
    I'm really interested in the topic you discussed. How can I get started if I wanted to learn more about your world?

  10. I'm definitely gonna need to play that game when it comes out. The robot is 🔥

  11. Is this not way too computationally expensive to apply to a large amount of entities in a scene? (I'm really hoping it's not, this is so insanely cool!)

  12. As someone without a university education on letter maths, but fluency in math programming I desperately need to see this stuff in code more often to comprehend it. Letter and associative values get lost on me extremely quickly.

    None the less I got something out of this at least, so thank you.

  13. Just a quick question if anybody is interested in explaining this to a non programmer
    How is (5:09 e.g) this different to a regulation on a motor like P I D ? what are the benifits to using this equation ?

  14. I'm trying to make my own implementation of this in 2d space and I'm having trouble:

    From what I'm seeing from the video, the X input into Update is a desired position for the object in motion, and XD is the current speed at which it is moving. However, looking at the arguments for the Update function, X AND XD are vectors which doesn't make any sense to me since position is not a vector.

    What am I misunderstanding about the Update function's arguments?

  15. Jesus dude, these videos are so great, and your game looks amazing! :O

  16. It's so sad to see people frustrated by the time and money they are wasting at the university, to come here assaulting self-taught people just to protect their own ego.
    Just to double up on the dose of a failed educational system. Why can't we just be objective and see that everything is far from optimal on both sides?
    Self-taught people need formal education, as much as formally educated alumni need better teachers, and both need different mindsets.

  17. music too loud, makes it hard to listen.
    Other then that – great lecture, gives great introduction, and leads further, to be useful for more advanced users.

  18. This is probably the most satisfying video I've ever seen.

  19. Your game looks amazing ! 😯
    Liked the explanations although I am a bit lost lol
    Can you recommend any good book (or online course) to level up in maths and be more comfy with all ot this ? Thanks 👍

  20. They don't lie when they say game development takes a lot of maths

  21. Has anybody actually implemented this into their Unity game? I've watched through this 7 times now and I just cannot get a grasp of how to implement this whatsoever 'nor do I understand what any of the variables stand for

  22. I feel like a ton of this is what Rain World did for it's animations. Seeing the math break explains a ton of weird things I've seen break in that game in unique ways.

  23. Given the title of video, it's incredible the video itself seems to be lacking personality. I have no real idea what I just watched but I m almost certain this is not the right way to show this content to people. It's highly theorical and in the end provides almost no example of application

  24. Cartesian camels geometry node live streams brought me here. Very excited to be learning to wield these systems and solutuons. Thanks for the video mate🤝🏾

  25. How does your code work at 8:53 there are only vector3 and vector2 and what's the Vector x0 thing about?

  26. I'm a profesional Mountainbiker and Europian Astronaout and this video was very fascinating.
    Thanks for shaing

  27. This was cool but I hope you would make a video with an actual tutorial with code of the process of making these animations. It will be much deeper and will create better understanding.

  28. At 14:15 it looks like you compute k1_stable but never use it. Was it meant to replace k1 in the last line of code before returning y?

  29. I am an automation engineer and I’ll be dang (honoured) if I use this video to control my PID tunings.

  30. Wow, just wow.
    Incredible video man. I don't know anything about game design (and I don't intend to make one anytime soon) but it was such an interesting video !
    Your explanations were super clear and the animations very helpful.
    It helped me understand what all of my courses in signal processing, system control etc can actually do !

  31. i dont know what most of this means but i like it

  32. Hey bro, what software do you use to make the animations in this explainer? A short tutorial of your process would be helpful too.

  33. what is x' in this video? it doesn't make sense to me to use the derivative of a step function. x' looks more like a condition on y'(0) to me

  34. Damn it , These are stuff I learned in a control class. I never thought it could be used in games.

  35. Honestly, I knew all the math stuff presented here but the way you conveyed it was so clean and result is beautiful. Very well done, congrats !

  36. This is the best video I've seen in a long time. Just amazing. Thank you very much, please keep them coming!!!

  37. I am absolutely hating Calculus 2 in University right now, but you make the math so beautiful.

  38. I'm not great with maths, but this seems very similar to what I know of PID loop control. Dynamic systems are difficult to understand and model from a layman's perspective, but also really cool.

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