Quick Corrections: 5:43 I was referring to the commutative property (I misspoke and said cumulative.) You can google "associative, commutative, and distributive" for more details on "basic" algebraic properties. But, yeah, some laws can break in higher dimensions.
imagine having a mind where you think everything's a conspiracy and that people are out to keep you down instead of, maybe, just maybe, you didn't put enough effort in to understanding a little bit of math. wow. just wow.
Very well done explaining Quaternions, so wish I saw this video years ago. Would like to see a video with this type of explanation of Transform3D/Basis too. I know many solutions (and other engines) use Quaternions, however, Godot uses T3D/Basis "under the hood"; the inspector Euler angles are just for ease-of-viewing, and the Quaternion methods are wrappers that interact with the underlying T3D/Basis variant.
Good catch! I'm working on a general Variant video now. I'm not sure if anything else will need to break out like Quaternions did, but I'll definitely be looking into T3Ds in more detail this week.
a) really great tutorial. Saved for linking to others when needed. b) one of the great results of Quaternions is that you can lerp from one random rotation to another and it won't do something weird as it would with eulers.
thank you so much! I loved every minute of it. Was trying at this for hours trying to find out how quaternions work in godot so your source code really helps
Thanks for the video! I had been stuck on 3d rotations in Godot for a while and this video helped me understand the why my rotations weren't working as expected. Getting down to the physics of it was super useful.
you are awesome! thank you so much for making this. I remember trying to understand quaternions so many times in the past and just give up and just use it cuz it "just works". You made it so easy for me to visualize it and understand it in under 20 minutes!
Yeah you finally were able to make me understand. All other explanations tried to explain quats as some four dimensional object. its just a vector and a rotation value
Great vid. Good explanation that helped me understand gimbal lock and usage of quaternions in practice. You're right the 4D stuff about how they work is quite involved, will go watch the 3B1B vids if I ever have a need to understand their implementation.
you can also use if is_equal_approx(0, interpolated_quat.angle_to(quat_box.quaternion)): at line 78 in quinternion_demo it will check for mild over and under shoot
Wow, you have a new follower, thank you for the explanation, I was not understanding why my rotation sometimes didn't work. I was searching a local rotation function 😂.
Nice presentation on Quaternions.Can you tell me please what program you used to do your demo? I am trying to understand how quaternions function. The program you presented evidently has functions which compute the steps required. Access to your source code for your example would be much appreciated. I am not a programmer but am very much interested in comparing the Euler approach with the Quaternion approach when rotating objects. This is an excellent program to do this comparison ! ! The code would help me understand the math involved. THANK YOU !!!!
The sliders are just a vector3 and are pre-normalized. Once I have my numbers I want, I normalize this (make it length of 1), and build a new quaternion in global space using Quaternion(ijk, w). I then apply it to the box when I'm ready to rotate. I, J, and K are aligned with the X, Z, and Y axis in world space.
I didn't even know what Gimbal Lock was before, Now I have a base understanding of quarternions. But I have a question, Wouldn't Euler XYZ be equivalent to Global ZYX?
I'm not 100% sure what you mean by that. If you're talking about the Cartesian coordinate system, then yes, Godot uses Y as up instead of Z as up. Afaik, Godot is consistent internally, but other programs or equations might swap the axis.
This is a good idea and structure for a video, but you're speeding up around the key points instead of slowing down. You should focus a little more on the specific information that you're trying to communicate, maybe with stricter editing. When you fiddle around and improvise with the demonstrations, it makes it difficult to follow the point you're trying to illustrate. If I had no concept of Gimbal Lock, I don't think that section of the video would clarify it for me, and that's supposed to be the main conflict of the story.
I don't understand how someone may lock the rotation using this method, if possible. Assuming you start using quaternions for a players camera for some reason... If you want to lock it to 30 degrees from the top and bottom so the player doesn't start flipping when going to far. I assume euler would fit this purpose better?
Yeah, I'd probably use Euler. You can actually change the ordering, so if you are doing a camera, you can set it to rotate Y, then X, then Z. In the camera code, you can rotate Y and rotate X within limits, and Z is never needed. If your camera needs roll for some reason, then you might want to use quats instead.
@@SDGGames True. If you *are* using roll it's also probably safe to say you don't need to limit the camera or can at least devise a system for it since roll is complicated
Where i job we've got quinoa buns. You wouldn't believe how hard it is for some people to pronounce quinoa. From Kinoya, to Kichinoa or my all time favorite Kinocchio I've heard so many funny names.
Yeah, at least that's the primary use in game engines specifically. Other fields might use them exclusively for expressing any rotation. There are some other ways of dealing with rotations in Godot that I'll cover in my next video.
SORRY !! I did not realize that Godot was a programming language and the source code was available. I have to learn Godot. I do not know how to execute the Quaternion program yet. If you could give me a quick procedure on how this is accomplished I would appreciate it. THANK YOU !!!
Godot is a game engine, you can download it for free and run the scene in it. If you download the source code from the GitLab link in the description, you can play around with the quaternion demo scene. There is a lot of stuff that Godot does automatically, so I'm not sure how useful the code will be as an example for other languages. I did try uploading the project to Itch, but web support isn't quite there yet for Godot. I'll keep an eye on it and try to get the demo up when I can.
Thank you for the very nice and visual explanation. Even though quaternions are obviously superior in functionality, godot makes it a little too hard to use them. You mentioned that multiplying quaternions is the same as adding eulers. How are we supposed to know that? Why isn't there a "combine_with(....)" function on the quaternion class that properly deals with the math and exposes it in a language a non-mathematician can deal with? Not your fault of course :)
It's a hard balance to strike. If you re-invent the wheel, then the math people get upset because the function doesn't match reality. But, if you don't study the math, the game engine functions don't make much sense. I'm not sure what the ideal solution would be...
I'm not sure what it uses under the hood, but that function sets the rotation directly on the node. You can see the final rotation expressed as a quaternion, but I think the actual data is stored as a Basis.
It's definitely an issue with the system, but I wonder how many teachers actually understand these concepts themselves. If you get a degree in teaching, then you will never have the practical knowledge that comes from using math in a career. If you get a degree as an engineer or programmer, then you can make at least 3X a teacher's salary by not teaching. I feel like schools should welcome retired professionals to help teach the advanced concepts. Most of my college professors had a lot of experience in the workplace, and it showed. They were 10X easier to understand than the math professor because they were able to go beyond the theory and root the concepts in real projects they worked on. All that to say, the system is broken, but I don't think it's malicious. Just underfunded and overregulated
One big hurdle in understanding the slightest bit about quaternions is the naming of the components of a quaternion. Naming three of the four components x y and z implies concepts that are nothing like anything you know so far
but why normalze the 4d vektor? wouldn't it be much easyer to use with our 3d brains if we just keep it as a vektor and an angle instead of representing it as a 4d vektor?
It's not really designed for mere mortals to understand. I think I linked the 3Blue1Brown video on the topic. We use it for math reasons, not for convenience. Euler angles are more convenient, until gimbal lock kicks in
You must be doing something very wrong. You're videos are very right, top of the line. Really great content. But you must be doing something wrong to have only 5k views on a video like this, when the video itself is so good.
the explanation of the concept of quaternions is very helpful but your code example in godot is very confusing as you don't explain much of the godot specific syntax, as well as having several variables that aren't explained
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
Quick Corrections:
5:43 I was referring to the commutative property (I misspoke and said cumulative.) You can google "associative, commutative, and distributive" for more details on "basic" algebraic properties. But, yeah, some laws can break in higher dimensions.
you spelled gimbal wrong sometimes, also in 16:19 you spelled quaternion with an extra n
@@felicaamiko "quanternion" is also how he pronounces it throughout the video
Goddamnit. The gatekeepers have kept such a crazy simple concept behind "bro too complicated" doors.Thank you so much for clarifying this!
Bro not everything is gatekeeping just because people aren't giving you a personal lesson on mathematics.
imagine having a mind where you think everything's a conspiracy and that people are out to keep you down instead of, maybe, just maybe, you didn't put enough effort in to understanding a little bit of math. wow. just wow.
"Genius is making complex topics simple"
Thanks for making quaternions finally click for me 🤯
ok but what if ur not a genius...
Very well done explaining Quaternions, so wish I saw this video years ago. Would like to see a video with this type of explanation of Transform3D/Basis too. I know many solutions (and other engines) use Quaternions, however, Godot uses T3D/Basis "under the hood"; the inspector Euler angles are just for ease-of-viewing, and the Quaternion methods are wrappers that interact with the underlying T3D/Basis variant.
Good catch! I'm working on a general Variant video now. I'm not sure if anything else will need to break out like Quaternions did, but I'll definitely be looking into T3Ds in more detail this week.
a) really great tutorial. Saved for linking to others when needed.
b) one of the great results of Quaternions is that you can lerp from one random rotation to another and it won't do something weird as it would with eulers.
Thank You! I have been trying to wrap my head around quats for ages. This finally made sense. +100 knowledge!
Great explanations, awesome tutorial.
And icing on the cake, sources available on git !
Thank you for making this video.
Have a wonderful day.
This gives me a different perspective on quaternions - that I really appreciate.
First video that gives the intuition of quaternion real fast.
Lol chatgpt being a waste of time is to be expected.
Excellent video! I finally understood how to use quaternions in godot. Thank you!
thank you so much! I loved every minute of it. Was trying at this for hours trying to find out how quaternions work in godot so your source code really helps
Thanks for the video! I had been stuck on 3d rotations in Godot for a while and this video helped me understand the why my rotations weren't working as expected. Getting down to the physics of it was super useful.
Excellent video, thank you for taking the time to put this all together!
you are awesome! thank you so much for making this. I remember trying to understand quaternions so many times in the past and just give up and just use it cuz it "just works". You made it so easy for me to visualize it and understand it in under 20 minutes!
Okay well, I haven’t even watched the video yet but that story telling at the beginning was INCREDIBLE
Yeah you finally were able to make me understand. All other explanations tried to explain quats as some four dimensional object. its just a vector and a rotation value
Well thats the best explanation of quaternions )
Thanks a lot )
Great vid. Good explanation that helped me understand gimbal lock and usage of quaternions in practice. You're right the 4D stuff about how they work is quite involved, will go watch the 3B1B vids if I ever have a need to understand their implementation.
Excellent work and good job on the visual explanation
dude this is the best tutorial ive seen thank you so much i can understand now!
Hey, thanks a lot! 👍 This really helped me get the random spread on my projectiles working.
Thank you so much!! I really need it
I love your channel so much!! i just found it today and it's amazing
Ooh, yeah. My script said communitive, but those long C words all jumble together sometimes!
Good vid! Also looking forward to the Variant video :)
Excellent video and work! Fantastic reference! Thank you!
you can also use if is_equal_approx(0, interpolated_quat.angle_to(quat_box.quaternion)): at line 78 in quinternion_demo it will check for mild over and under shoot
That's a good trick, thanks!
a beast of a vid. thank you!
How was I not using this before? Thank you so much!
Extremly helpful! thank you. this will save me a lot of frustration
Wow, you have a new follower, thank you for the explanation, I was not understanding why my rotation sometimes didn't work. I was searching a local rotation function 😂.
Nice presentation on Quaternions.Can you tell me please what program you used to do your demo?
I am trying to understand how quaternions function. The program you presented evidently has functions which compute the steps required. Access to your source code for your example would be much appreciated. I am not a programmer but am very much interested in comparing the Euler approach with the Quaternion approach when rotating objects. This is an excellent program to do this comparison ! ! The code would help me understand the math involved. THANK YOU !!!!
Nice
will use them when I can
You have saved me hours of work thank you so much!
That was really useful!
Quaternions embody the phrase "Sit on it and spin!" - that's how I've always described them! haha
You are the best!!
Good useful. Thank you! 👍
this video is beautiful
Thank you i guess now i understood very well explained
Great vídeo! One thing that is not clear to me in the your code: How are you obtaining this ijk value? Are you using local or global basis?
The sliders are just a vector3 and are pre-normalized. Once I have my numbers I want, I normalize this (make it length of 1), and build a new quaternion in global space using Quaternion(ijk, w). I then apply it to the box when I'm ready to rotate. I, J, and K are aligned with the X, Z, and Y axis in world space.
I didn't even know what Gimbal Lock was before, Now I have a base understanding of quarternions.
But I have a question, Wouldn't Euler XYZ be equivalent to Global ZYX?
I'm not 100% sure what you mean by that. If you're talking about the Cartesian coordinate system, then yes, Godot uses Y as up instead of Z as up. Afaik, Godot is consistent internally, but other programs or equations might swap the axis.
There were no planes when the mathmagician discovered quaternion, since that was something in the 1800's.
what if I have array of Vector3 points - whith I want rotate around... center of mass?
This is a good idea and structure for a video, but you're speeding up around the key points instead of slowing down. You should focus a little more on the specific information that you're trying to communicate, maybe with stricter editing. When you fiddle around and improvise with the demonstrations, it makes it difficult to follow the point you're trying to illustrate. If I had no concept of Gimbal Lock, I don't think that section of the video would clarify it for me, and that's supposed to be the main conflict of the story.
Thanks for the feedback! This one was a bit of an experiment, but I'll keep your advice in mind in case I do another video like this
I don't understand how someone may lock the rotation using this method, if possible.
Assuming you start using quaternions for a players camera for some reason... If you want to lock it to 30 degrees from the top and bottom so the player doesn't start flipping when going to far. I assume euler would fit this purpose better?
Yeah, I'd probably use Euler. You can actually change the ordering, so if you are doing a camera, you can set it to rotate Y, then X, then Z. In the camera code, you can rotate Y and rotate X within limits, and Z is never needed. If your camera needs roll for some reason, then you might want to use quats instead.
@@SDGGames True. If you *are* using roll it's also probably safe to say you don't need to limit the camera or can at least devise a system for it since roll is complicated
Where i job we've got quinoa buns. You wouldn't believe how hard it is for some people to pronounce quinoa. From Kinoya, to Kichinoa or my all time favorite Kinocchio I've heard so many funny names.
So, how did I do? I used to say quan-tern-eeon, until I realized there was no "N' in the middle...
So... The point of quaternions is that they make it easy to rotate around a vector, right?
Yeah, at least that's the primary use in game engines specifically. Other fields might use them exclusively for expressing any rotation. There are some other ways of dealing with rotations in Godot that I'll cover in my next video.
Mathemagician
can someone explain how to apply this to a camera?
SORRY !! I did not realize that Godot was a programming language and the source code was available. I have to learn Godot. I do not know how to execute the Quaternion program yet. If you could give me a quick procedure on how this is accomplished I would appreciate it. THANK YOU !!!
Godot is a game engine, you can download it for free and run the scene in it. If you download the source code from the GitLab link in the description, you can play around with the quaternion demo scene. There is a lot of stuff that Godot does automatically, so I'm not sure how useful the code will be as an example for other languages.
I did try uploading the project to Itch, but web support isn't quite there yet for Godot. I'll keep an eye on it and try to get the demo up when I can.
THANK YOU !! I was able to run the source code.@@SDGGames
thanks man shit helped a lot
Thank you for the very nice and visual explanation. Even though quaternions are obviously superior in functionality, godot makes it a little too hard to use them. You mentioned that multiplying quaternions is the same as adding eulers. How are we supposed to know that? Why isn't there a "combine_with(....)" function on the quaternion class that properly deals with the math and exposes it in a language a non-mathematician can deal with? Not your fault of course :)
It's a hard balance to strike. If you re-invent the wheel, then the math people get upset because the function doesn't match reality. But, if you don't study the math, the game engine functions don't make much sense. I'm not sure what the ideal solution would be...
Does the look_at() function use a quaternion?
I'm not sure what it uses under the hood, but that function sets the rotation directly on the node. You can see the final rotation expressed as a quaternion, but I think the actual data is stored as a Basis.
I have serious questions about an education system that seems to go out of its way to hide this from most studentd becaude "its too complex"
It's definitely an issue with the system, but I wonder how many teachers actually understand these concepts themselves. If you get a degree in teaching, then you will never have the practical knowledge that comes from using math in a career. If you get a degree as an engineer or programmer, then you can make at least 3X a teacher's salary by not teaching.
I feel like schools should welcome retired professionals to help teach the advanced concepts. Most of my college professors had a lot of experience in the workplace, and it showed. They were 10X easier to understand than the math professor because they were able to go beyond the theory and root the concepts in real projects they worked on.
All that to say, the system is broken, but I don't think it's malicious. Just underfunded and overregulated
Ro ro rotate your owl 🎵
Ghin Baal L'qeh does sound ominous
One big hurdle in understanding the slightest bit about quaternions is the naming of the components of a quaternion. Naming three of the four components x y and z implies concepts that are nothing like anything you know so far
but why normalze the 4d vektor? wouldn't it be much easyer to use with our 3d brains if we just keep it as a vektor and an angle instead of representing it as a 4d vektor?
It's not really designed for mere mortals to understand. I think I linked the 3Blue1Brown video on the topic. We use it for math reasons, not for convenience. Euler angles are more convenient, until gimbal lock kicks in
You must be doing something very wrong.
You're videos are very right, top of the line. Really great content.
But you must be doing something wrong to have only 5k views on a video like this, when the video itself is so good.
1:20 W
It happens to the best of us... ¯\_ (ツ)_/¯
Like and Subscribe! Great work 👍
the explanation of the concept of quaternions is very helpful but your code example in godot is very confusing as you don't explain much of the godot specific syntax, as well as having several variables that aren't explained
Yeah, I probably should have broken down the code a bit more. Thanks for the feedback!
I refuse to call Euler, OIL-er
Yeah, I forgot to check. YOU'LL-er sounds like a Christmas drink to me, but it might be more correct
@@SDGGames I think the way you prounounced it is the correct way. I just still refuse lol
So I do I apply this to godot trash animation playernso it shuts up and leaves me alone