Giving Personality to Procedural Animations using Math

Hola, estoy desarrollando un videojuego estilo RPG en Unity y me he encontrado con el problema de los pisos superiores e inferiores, al buscar diferentes formas de fade, transparect, etc. no encuentro la solución deseada, alguien ofrece el servicio para que me ayude a solucionar mi problema?

damn rip unity lmao

Amazing

Hello, i have a question, can i show someone this video in education purpose? I had seen, that some of my groupmates in university had problems with understanding, how some of the principles in math models working, because of dry explanation on lessons, and with good examples it's a lot easier for them to understand. If you let it, i can show this video as an example for future classes, how math models can be used in real life with good visualisation, so that it'll be easier for them to understand difficult themes.

I can't belive how excited I i got by this bone dry title.

I want to play the game you're making!!!

second order system looks just like electronic switch debounce. amazing this maths pops up all over

Artist: Make the character squishy
Designer: Say no more

This just explained control systems to me better than my real college lecture

I just got out of my control theory test, I wish I would've seen this video earlier!

That's one way to handle discretization! Why fuss with z-transforms when you can just ignore sample rates you don't like 😂

watch out 3blue1brown! other people are learning how to create cool animations of their math!

God is that interesting and clever !

math cannot be used in real lif-

when the interpolation at the start of the video is not linear

This video is *incredible*. The way you explained everything and the order was perfect. The visualizations. Everything. Thank you so much for making this.

cool! I would like to try your game 1 day

I'm at the same time incredibly amazed by this and also extremely confused. Just yesterday I searched about procedural animation thinking it could be an interesting topic to learn.

That's just way beyond my knowledge, but at the same time made me really curious to learn more.

Great video! Very helpful
There's a saying in math that everything in math is named after the second person that invented it, because the first person is always Euler
Anyway, nice to know where this Verlet formula comes from. I have been using it but now it will make much more sense

i should listened to math teacher

nice

Such a mind! :)

wow, this is a great new ppiece of knowledge to know and it is also so greatly explained with animations

Hello , could you please tell us how to make these animations ?
animated graphs ... and other stuff

I got an A in geometry and barely passed anything else. This video is monumental for me. Thank you so much. It makes me sad that math is not visual learner friendly in most cases these days. This video gives me hope

Thanks!

amazing content

This looks like differential equations, is there a video on linear algebra and vectors used to move the camera for example?

For a different approach to the stability issue you mentioned, you can consider using a Bilinear Transformation (Tustin's method) instead of Euler's method. It has stronger stability guarantees and it actually ensures stability if the sampling period is constant.

By the way, awesome video and exciting to see concepts control theory surfacing in game development!

This sounds exactly like the functions used for determining the strength of response from a heating system to the change in temperature in large automation air conditioning systems in large buildings, to make sure that we get to the target temperature quickly, but without causing a vibration-like fluctuation in the temperature that lasts a long time. One term is derivative (strength of response is the derivative of what we are trying to control) and the other is integrative (strength of response is the integration of the difference between the desired value and current value over time) and by using multipliers for each we get pretty much exactly the kind of behavior that you are getting here (there might've been a third, constant term too). That algorithm results in the amount of heating that has to be applied, so in case of movement, it would produce forces.

The reason I'm saying this, is because the algorithms for producing the forces are much less complicated than what you are having to calculate and since it produces forces, it can be used directly with the physics engine in unity. Since that application is pretty old too, the field has come up with formulas that can be used to calculate the multipliers based on how the system behaves, so all the end user wouldn't even have to figure those out, just pick out a type of behavior from a list and the system could calculate the multipliers for them (unless they wanted to control them).

Unfortunately I only know those things in my own language and can't find a direct reference to what I'm talking about. Anyway, if you wish to make a version of this that is usable by the physics engine and a bit simpler, that is where the solution can be found :)

The time domain and Space State are one of the many tools you could use for the same purpose. Another way, could be to desing a digital filter (maybe low pass filter) than may match the expected output.
The critical T is the maximum sampling time required for the algorith to function properly. The best you can do when the sampling frequency (1/T) is reduced is not to change second order system but to create a feedback controller that may always stabilize the output. This is a separate system and it could be easier than changing the system from its coeficient. What I meant is do not change the system, but use a automatic feedback control system to fix the problem for you. A typical, well known is the PID controller that is fairly easy to desing. Maybe it could help you to get the solution you want with less memory or computation impact.

My control systems module was finally worth it! Now I can understand the maths in a random yt video!

Why no 2nd order equation for the X term?

giving curve interpolation between A and B

aah man, I should have paid attention in college, this stuff is kinda cool

Who are you people? how do you learn these skills to the level that you even explain it that easy to others? I probably need to study another 4 years just to be that good !

Thank you so much. This worked like a charm <3

Giving a semblance of personality that is good enough for the people who would confuse the two.

this is just so cool

I learned this as an electrical engineer, can't believe I still have to be tormented by it as a game dev

My brain is not good rn

I don't have an engineering or a CompSci degree so Dumb dumb question but I'm getting errors on cosh and Vector what am I missing??

this melted my brain, my math game is too weak for this video

@t3ssel8r Would you be willing to share your final code as well as the Unity editor you show in the video?

Oh my I saw my basic control theory professor's face here

Just implemented this in Unreal, increible tutorial, the motion of the robot character its just something else. Thank you for sharing. I was missing this node from VVVV.

I've thought about this kind of thing, what if I didn't have to animate every frame far down the line if i make a game. This is basically it in words and fully explained.