Small question: What happens if you just want y to be x? What value would f, z, r be? I try to solve for it, but 1. The result is dependent on T. So if you have a variable framerate, you must update the value every frame 2. In your writeup post, it impossible to derive the value from the fully implicit Euler

if you want y to be x, it corresponds to f=infinity. You can show that in the limit this results in y=x. k1 k2 and k3 all become 0, so if you really need to support it in code, the 0/0 would need a special case to handle.

@@t3ssel8r That's one way to do it, but k1, k2, and k3 can be non-zero. Because y = x and dy = dx, you just need to make sure k2*ddy = (k3 - k1)*dx. But the problem is after solving this, f, z, and r must be recalculated every frame because they are dependent on T.

@@t3ssel8r@ t3ssel8r Actually, k1/2/3 cannot be zero. Because y is updated by dy, and dy is updated by ddy, to make y equal to x, dy must be equal to dx. This means ddy can't be equal to zero, because if ddy is equal to zero, dy never changes. This means k1/2/3 must equal some non-zero/non-infinite value. Does it make sense, or am I missing something? Sorry if this sounds confusing, but math isn't my strong suit, and I just really want to solve this.

I’ve been trying to write this up in Desmos for a while now but I can’t figure it out, I wrote a function which takes a collection of points and translates it into a usable format but when I try to implement the formulas it either gives me lines ghat stretch way too far or lines that are just the input, and how does second derivative work for y? it always goes to 0 and the derivative of x is 1 so what’s the point of it? edit: NVM, I rewatched and noticed that you said that x is the dynamic change which would mean that my calc is wrong, I used the change as the y

I started to think this is the reason why Elden Ring has this "Long Zipping" glitch used by speedrunners.

It'sa me! aaaaaaaaaaaaaaaaand he's gone.

& .5 button presses

@@samic no, they cannot remove/fix it without completely overhauling a small part of the physics rendering, sadly.

This comment really raised my scuttlebugs

Especially it being explained to the masses so well by a youtuber. It'd be one thing to see your own eq at a lecture hall but this just gives me tingles

"Don't worry, you don't need math and physics to take animation class." Animation class:

Euler is the greatest mathematician ever.

Included in the Bucket List ✅

He would be so ashamed

This was my thought too! May have paid more attention in theory lectures if I was animating a robot rather than a MATLAB figure 😂

I dont know why he's sticking with the time domain when complex Laplace transform and Pole Zero analysis make these problems much easier to analyse

It took me a whole semester of learning this (while performing well on tests) to actually understand what the hell I was doing. It would certainly be good to have a more visual simulation instead of a dry graph.

@@brightquark he used pole zero matching

@@brightquarkwell Laplace does not do so well in mimo-systems... but here (as you said) Laplace would suffice... I guess it is more difficult to explain the whole laplace-transfo to someone who had no course for that in university...

Ikr

i just used calc in a gamejam, so this suprised sentiment is very valid

😂

:O finally

I can't believe this too xd

_"But first, we need to talk about parallel universes"_

@@ultimaxkom8728 i see what you did there

CODEPARADE REFERENCE?!?!?!

I just came back to watch this video after a long time. When he got to that part I immediately remembered your comment. Even the second time around, very accurate description of my thoughts at that moment!

guess what, baby, technical is a SPECTRUM

Ooh, one of my favorite gamedev youtubers commenting on another one of my favorite gamedev youtuber's video!

"I'm absolutely stealing this." practically a motto of game dev lol

KZfaq inception

its not stealing, this is math. mathematical breakthroughs in fundamental understanding represents a milestone for all humanity, not just the discoverers. to try and stay away from them is to stand in the way of progress. in other words, you have a DUTY to use the techniques laid down by scientists before you to your own ends.

I'm happy to hear that the animations of the game are going to be even better than what they already were xD

what did you study in your physics degree?

I failed physics so hard but love the subject

Not really when you consider the fact that people without physics degrees...or any degrees at all, can easily understand this video and replicate his implementation. Scientists, especially mathematicians, tend to ivory tower their knowledge presentation to seem more grandeur than it is to feed their ego. I believe thats considered having delusions of grandeur.

​@@eyegenesys You are totally right, the educational system is a failure. I have to talk every day with people with math, physics and engineering degrees, sometime even multiple, from Oxford to who-knows-who-rich-university, and when it comes to specific domain knowledge, they are like robots, can spit it out all by memory, but when it comes to use some common sense or to approach something in a different way, well... they are like robots indeed. Anyway, I believe that a degree is very helpful, for who has the correct mindset already, for the others is just a piece of paper and a bunch of words memorized to look good the day you need to say them.

Kinda disagree with you, not to feed their ego but rather just to merely explain how it works in scientific way ( Their brain are like programmed into this particular way of thinking in math, probably to explain more and more knowledge for others to know )@@eyegenesys

Why you were watching this then? And why you came here to comment this exact message? Looks like propaganda pro-university. I notice many people like you feel the urge to defend themselves somehow. It's very odd.

thanks! I had a feeling I went a bit hard on the math, but at least it's an honest presentation of the real process that usually happens behind the scenes.

I feel the same way. I've been wanting to learn more of the types of math to do these things but didn't even know where to start with what types of math. This gave me a better general understanding of how it's applied but also more info on what to learn.

Adam!

Love you Adam

Imagine an enemy coded by t3ssel8r and drawn by Adam. :O

I’m glad someone else sees the engineering connection, it threw me for a loop. I’m taking a system dynamics class right now!

@@Mrjcraft00 I learnt about this in a classical mechanics course

Exactly what I was thinking

I'm doing a differential equations and linear algebra class, it all clicks in place.

I took a computational physics class earlier this year and I walked into this video expecting another thing completely, but was shocked when they resumed the core of the class beautifully in 15 minutes, what a great video.

Beat me to it

I'm an Engineering Physics student and I was studying co/contra-variant vectors for hw in a physics math class. Found this video and it's awesome to see all the crap we had to learn in such an elegant animation and idea

Mechatronics engineering student here, adding my thanks to the pile!

I wish I could talk to all of you if you found going to university helped understand concepts in this video. I find programming alone is limiting me.

@@georgeforester3366 I think it does. Having a degree in Computer Engineering, I can tell you every concept mentioned in the video is something you come back to time and again in different courses. Even the thing mentioned at the end, ”pole-zero matching”. Videos like this are a good reminder that the things taught in academia have real applications, even as a programmer.

A lot of videos (this included) go beyond that and are more valuable than a lot of equivalent college lectures, even. In one of my machine learning classes as an undergrad, the professor showed us 3B1B's video on neural networks as an introduction. I'm now a PhD student and when I teach my students eigenvectors, I recommend 3B1B's video as a refresher, but also as a conceptual starting point for the inexperienced. I've seen hundreds of academic talks now in my early career and it's hard to think of more than a handful that are comparable or better in terms of clarity than videos like this, and I think people are sleeping on that. Personally I take a lot of inspiration from videos like this since visualizations are incredibly potent and really force you as the presenter to break things down into parsimonious chunks. The only obvious drawback is that making something like this takes more time than probably four weeks of upper-div lecture material haha

I think it shows the exciting ways that math can be applied in this world - ESPECIALLY ways that will grab young students' attention. I wish I stumbled upon videos like this when I was in middle school or high school, because I would have learned to actually give a shit about math.

@@adrianlowery7175 That is exactly the reason why we were not taught in that way. We would be too smart to control... All by design

Yeah, in real life it's physics that makes things lag and oscillate, and if you could design a PID loop to get a fast and crisp response (without bending the machine) it would be considered a perfect success. In the game world, there are no constraints coming from physics, but if we want to *add* constraints to make things look realistic, they end up taking almost the same form as the controller we use to fight against those constraints in the real world.

I was first introduced to it in a circuits course analyzing 2nd order transitions

I took this kind of math in engineering school too. At the time, I had no idea what the application was. I blame my professor for being unrelatable. Now I understand exactly what it's used for and how to apply it. Awesome.

Instrumentation tech?

yeah, but it's nothing new really. The action of get a mathematical equations to mimic a real process(or system) behavior is very important to same people that use to control industrial process. It's commonly called modeling or system identification

So true

Yep, took a semester of control systems and this video made more sense that that class

I have this belief that all engineers must learn to program. Most of the older professors are getting outdated quickly by not incorporating interactive tools (specially if they built themselves). If I ever go back to university to teach my classes I DEFINITELY will create gorgeous animations every time I can. Already did for my own assignments, and blew teachers out of the water

This, 100%, impact being a critically important element of both animation and gameplay, this would probably have even greater impact than would seem immediately apparent. Very good idea, I really hope that he takes your suggestion.

Well if I understood this video correctly, he has essentially already implemented this. The robot dynamically moves to a position. So if a force, such as an attack struck the robot, the desired position of the robot would move and robot would move accordingly to the implented physics, if he wanted the robot to move in a certain way to convey being pushed back, he could adjust the f zeta and r values.

@@tuc_mage Wait, he's letting the physics solver take precedence over the procedural animation? I think I missed that part, is there a timestamp or something? Thank you!

@@NilesBlackX his procedural animation system is based on physics, he has implented a physics system where the object reacts to the acceleration velocity and position of the desired location. It's not a complete physics simulation, but it does just what he has set it up to do.

​@@tuc_mage ohhhhh I wouldn't call just velocity + position anything close to a physics solver. As an example, for what you're describing, he needs to have not just collision but the location and vector of the hit, which this system doesn't have the mechanisms for currently. And that's not a small amount of additional work, we're talking a jump from 1st grade math (floating point multiplication) to calculus (bounding box of a convex hull). That's a non-trivial amount of work.

the only youtube notification i actually click on

I would suggest iterating multiple times in case of delays. We can choose a fixed duration that the delta time should not exceed, let's say 0.016 (60 fps). Than, in case we got a frame with a delta time of 0.25 we should run our calculation logic 15 times with a delta of 0.016 and 1 time with a delta of 0.01. var processedTime = 0 var fixedDeltaTime = 1 / 60 while processedTime < deltaTime { processedTime += fixedDeltaTime if processedTime < deltaTime { RunOurCalculations(fixedDeltaTime) } else { RunOurCalculations(deltaTime - (processedTime - fixedDeltaTime)) } }

Nice video, although i would have really liked something MORE "approachable"... you went too hard on maths, more specifically equation algebra math, not the linear algebra math which is at least more understandable... 🥲 Out of the 15 min video, 6 mins are shifting around gibberish, and 5 min shifting around gibberish with nice graphs... and almost all the remaining are visual examples of the results(which are nice, i like examples and results) and just like 20 seconds of code example. The concept and the idea are well explained, but no clue on how you actually implemented this in your game. Top tier video for a math channel, but if you are planning into do game dev content(as i guess by watching your channel uploads) i suggest you to take simpler approaches in your videos. I think it's the second or third time i stumbled on your channel as i do a lot of game dev, new techniques and game mechanics research and your videos just pop into my recommendations, but I feel like they just present cool ideas/concepts but leaves too much of "do your own research afterwards" and/or "you already should know what i'm talking about" feelings... so i usually end up leaving more confused than smarter(and probably the reason i'm not subscribed yet)... lol If you would accept my humble recommendation, if you are gonna present math, try presenting it in a simple way instead of pure equations, i get it, you like maths, you are proud of it, but many of us don't share that enthusiasm, most of us came here to your videos seeking knowledge about how to improve our games, not be defeated by one of our school enemies(math cough)... The equations are nice to have, but please explain it by simple means afterwards and give code examples, as me, most people interested in game development don't know how to read complex equations with strange to us constants as we don't use them ever, and added to that in 15 seconds you shift the equations like 5 times, i don't even know what most of the constants means or how are you using them, i want to make cool games, not comprehend the essence of what moves the universe, but i'm not stupid, if you put it in code(literally, any high level programming language) i will understand it, because code is made in a way to make everything simple. I did not knew what the heck was going on until i paused the video at 13:05 and started going through the little code you put on screen, then i started to get a grasp of what was going on and things started clicking here and there, but still some things were guesses as how you implemented it in game as you showed zero examples of usage... i guessed that you are using the position and/or rotation vectors of chosen joints or moving objects to apply the formula on, using the previous stored result and the current values, but you don't explain anything of that on detail... Seriously, more practical examples and in game implementation examples(code) side by side with in game visuals of the results are much more helpful than heavy theory, equations and theory. IMHO this approach is mostly ASMR to the regular youtube user, closer to "two minute papers" than to "How to rig a hand on blender tutorial", hope that changes as you grow your channel, peace

@@SGGhostRider I somewhat agree to this myself. The reason I say somewhat is because this video, and the aim assist, really makes me want to learn these mathematical concepts. That said, I would have loved a small breakdown of the equations into code a ton though. These effects are absolutely gorgeous and having a simpler “onboarding” to the concepts while given information on the deeper math behind it would be truly next level stuff.

this 3d to pixel art effect. is it a shader? how did you make it, it looks so cool. is there a tutorial for it?

@@SGGhostRider I disagree completely. There are more than enough videos for game dev out there which remain shallow in the concepts they present. Here we have a creator who instead of watering it down expects the audience to actually **have** the minium knowledge each and every developer _should_ have. Development _is_ Maths and while it is true that many, many things nowadays can be made without understanding the concepts behind it, and most often one does not need to know and understand it all, I personally like this channel especially _because_ it is presenting concepts in a nice, digestible way _for people who have an actual Computer Science background_. There are a lot of content out there which is less 'advanced', it is nice to also have 'advanced' high-quality stuff. Please do not change that, t3ssel8r.

Ikr

A bit unrelated but are you interested in ML? If so you might be surprised to hear that State Space Representations are making a comeback, via the Structured State Space Model, aka S4 (The extra S comes from the title of the paper that introduced it)

As an electrical engineer the moment i saw the equation and graphs i thought "oh, a basic PID parameters of pretty much every motor controlling frequency inverter". It`s such a cool universal concept of describing dynamics of real life elements.

@@zumszum as a computer engineer i was like "shit this has practical applications other than radio antennas and line following robots"

@@TheBigW300 Can you expand on how this is used in radio antennas? Can you point to some reading material where you got that from?

admittedly, I don't use that inspector in my actual project and only made it for the video, but it might be a pretty good idea to make it into a little self-contained asset.

@@t3ssel8r Out of curisity how did you draw the curve in the inspector ?

a bunch of calls to Handles.DrawLine lol

@@t3ssel8r Ahaha, my kind of code xD

@@t3ssel8r Could you please share the code for your inspector visualization?

I had the same thought watching this, super cool stuff

Yeah, my first thought was at 1:53 that this calls for a PID controller where I have a lot of freedom with the terms to tune smoothness, speed or overshot (if desired).

No it wasn't. It was a quick overview and that's it. The meat of the material was taught in your courses.

@@jong7100 such classroom joke he is.. i wish i wasn't like him during my college years.

You are right, I don't understand why all these people are hating, there is like an ongoing propaganda pro-university? Or is a matter of fragile egos offended? You can see the trend not only in this comments section, almost everywhere online, I think it coincides with low level payment for high level jobs, that is increasing the frustration of people getting out with a good degree to then have a miserable work experience, I have some coworkers that confessed that to me at least, I don't know if it applies to others as well, but I would say that is related somehow.

fuck yes

stop saying stupid things online

so f, zeta and r just turn into PID. A cheme with PTSD from control course.

thanks, means a lot

This math is a bit above high school math. You'll need at least uni level single variable calculus, linear algebra, and then ordinary differential equations. Personally I feel like maths is much better to study than something like computer science if you wanna do game dev... Although there are a few critical courses in Computer science, but can be boiled down to just needing to do some low-level programming/assembly (with cache knowledge).

this is undergraduate math lol

Do it! Good old trigonometry an vector formulas can get you too a lot of sweet spots for basic video game needs (distance, angle, direction)

@@muuubiee You cover everything you have mentioned in a regular CS program unless the math you need is way above partial differential equations. Do you need things such as topology or something in higher level maths?.

It would be really interesting to learn how you approached the shading on these. The outlines are very clean

In general, accurate physics simulations, for example fluid simulations or planetary motion, is guided by math (often differential equations). Surely that kind of simulation could be considered a type of procedural animation? They are often convincing and visually appealing.