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.

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

[tsselr]

For FAQ and a deeper discussion on this video, check out the writeup:

[zaraimpala]

or you could leave the glitch in
and in 10 years speedrunners are going to use their unlimited in game frame rate to backwards long jump into a parallel universe

[ojonasar]

Imagine being able to bring Euler into the present and show him the sort of things his maths has led to.

[vex]

I'm a controls engineer and this video was very fascinating. They really should be teaching this stuff in Universities with practical applications that students can understand rather than just raw math. Thanks for sharing!

[PPSzB]

Now my physics degree pays off finally, I can understand what's happening in this random youtube video that youtube algorithm showed me. Btw. good content, the animations and the game looks gorgeous

[jeffstienstra]

t3ssel8r: "...but to understand it properly, we'll have to get a bit more technical with our analysis." 9:42
me: "hey whoa whoa, wait a sec...I thought we were being technical this whole time."

[aarthificial]

Up until this point, I've been using the spring equation for all my procedural animation.
How come I've never seen it written as a second-order system is beyond me.
This is a perfect generalization.
I'm absolutely stealing this.
Thank you so much for making this video <3

[viln]

Having just taken my ODE course i didn't realize what i was learning. This made me appreciate all the pain and suffering i just went through

[TheMultipower]

That direct swap between code and math was so helpful. One of the best explanation channels I have seen

[AdamCYounis]

Great stuff! I'm really not literate enough to understand the math, but your way of explaining these things made it really easy to see the effect and value of what you're doing. The results are seriously impressive, and your game is looking fantastic. Can't wait to see more :)

[canadian_spaceman]

You just walked me through my 3rd and 4th year engineering stability & controls class like it was nothing. Great content, and much appreciated on the refresher!

[LucasLima-ehto]

I’m having control classes at my graduation on computer engineering and this video showed absolutely everything was taught me… I’ve got so excited with the didatics that I even sent it to my teachers. Basically a resume of everything I saw like, frequency, zeta, stability, peak time, overload, poles…
Wow! You should create a course of this, I definitely would take it!

[xXKIKOXx]

seeing that last bit made me so happy. at first it went from "oh this is some really clean fluid movement" to "wow... i now understand the attention and effort behind such a beautifuly 'simple' movement"

[rohanselvan]

I am an engineering student, and I gotta just say I really appreciated the time you spent illustrating second-order damped responses with the little animations! It was awesome!

[fakestiv]

The internet (and specifically YouTube) has become such an important early source of information for those willing to learn more than what they are taught in high school that I find it extremely important for videos like this to exist... To show what actually goes into making this kind of things: from coming up with an analytical solution, to parametrizing it in an artist-friendly way, to finally coming up with a numerical solution that satisfies all prerequisites. This is extremely important for those who have access to all the information in the world but desperately need a direction... Having been there I really can't stress this enough...

[JorisBohnson]

As a second year electronics student at uni, it’s insane to me how these exact concepts can be applied to game development. Super interesting and motivating to hear

[layneraczy]

Stumbled across this channel from Summer of Math, just finished binging all of your videos. This has instantly become one of my favorite YouTube channels. Keep up the amazing work!

[stylextv]

Damn, that robot looks so clean and feels so smooth. I especially like the shooting sfx.

[tkinllunts]

Your explanation of the parameterized functions was better than that of my college professor, in an engineering class specifically on dynamics and controls, in less than 1/10th the time. Great job with the intuitive visuals!

[ulaasKb]

In Turkish, there is a saying as "Alaylı ve okullu kişi."
It separates people according to the way of education or self-education in a subject.
Alaylı(Self-taught): A person who has trained himself without the school education required for a profession.
Okullu(Schooled): A person who has received the school education required for a profession.

Both "Alaylı" and "Okullu" people are seen as the most competent and knowledgeable in a subject.
These are the people who can convey and explain the best information on the subject.
For you, I can say "You are both "Alaylı" and "Okullu".

It was a great explanation. I wish my teachers were so devoted to teaching something when I was studying at university.
Congratulations and thank you.