Quaternions and 3d rotation, explained interactively

An equally valuable form of support is to simply share some of the videos.

Previous video on Quaternions:

Nice explanation of Gimbal Lock:

Great videos comparing Euler angles and quaternions, from the perspective of an animator:

Music by Vincent Rubinetti:

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Various social media stuffs:

[dragonfiremalus]

I am a software engineer at a rocket company. There was a bug discovered in the code having to deal with interpreting rocket orientation in some simulation code originating from a mistake in the quaternion math. Despite having a physics degree, I was not at all familiar with quaternions so I turned to the internet for guidance. Your videos on quaternions helped me understand them enough to discover the mathematics mistakes and derive the correct formulae. Just thought you'd like to know this video helped launch rockets :)

[DarkCloud]

I don't say this lightly: Your videos and especially these interactive videos will pioneer the future of education.

I'm often disappointed in our school system ( here in germany but probably applies for other countries as well).
Schools don't use the potential of modern media thereby being inefficent and wasting the stundent's time and undermine their curiousity. As a teacher I try to work against that but get caught in the same fatigue rather often. But being confronted with new topics this way I become like a child again in the best sense : I'm curious and full of wonder. And it's fun to learn something new. I have regained hope that school can be like that most of the time for future generations of students.

[xavierinthetube]

Outstanding work. Together with Ben, you are setting the standard for how the next generation of educational material should look like. I'm very impressed by your work in general and I didn't imagine it was possible to go so much further. This is so good, I'm still in shock.

You are making humanity fundamentally richer. There is no telling how big an impact innovations in education like this one will have in our collective future.

I'm proud of being a patron, I just doubled my pledge.

[BradenEliason]

This is perhaps the highest quality content I've ever seen on the internet, not just on YouTube. Absolutely incredible work.

I just became a patreon contributor because of this video.

[auntie_alias]

After smashing my head against quaternions for almost a decade, this interactive simulation video has finally put things in some perspective.
Furthermore, the format of that platform is so powerful and SO smoothly executed.
Bravo, Grant and Ben. 👏 I am in awe!

[andy_lamax]

Being a software programmer, and a mathematician. I can tell the lengths 3b1b went for this video. No one has gone these lengths for a youtube video, I repeat. NO ONE

[francispicotte]

2:30 Me trying to tell my prof that singularities are features, not bugs.
Also: me, later, trying to tell my parents how an F is actually an A+ in 4D space.

[willstone]

This channel just keeps getting better!

3Blue & 1Brown takes a "Why?"
And, with logic disarmingly sly,
(Plus cool animation
And soothing narraration!)
Makes the complex as easy as Pi

--Best Wishes for Vivid Dreams & ongoing Flashes of Insight

[titouanparcollet]

I'm actually a second year PhD student working on "quaternion neural networks". I waited for this kind of visualization for year now, i even though of building my own software ... Thanks you so much !

[faiphei]

Can we just appreciate what a smart idea it was to put the first part of the explorable video on YouTube so that YouTube can recommend it to people?

[anthonyparfilko]

If you hold your mouse pointer in between the pi creature's eyes on the interactive video, it goes cross-eyed.

[AdvosArt]

>19th century versions of Wolverine and the old man from home alone

My sides

[skylxykt]

I just did the interactive thing and I feel genuinely enlightened lol.

As a hobby gamedev, quaternions have probably been the topic I've avoided most. Like all other topics I feel like I've been able to at least learn something about, but quaternions have always escaped me. I left it to "confusing computer math stuff I can't understand" and just used the functions that convert to and from euler angles. I saw another one of your videos, possibly a livestream, where my mind was blown by the simplicity of using cos(x) + i*sin(x) to represent 2d rotation, but seeing it apply to quaternions, where i just gets replaced with an axis for it to work in 3d is even more mind-blowing. I feel like I actually understand quaternions now, even enough to actually use them too. I cannot express the shear amount of confusion I went through trying to learn about them at first before giving up. This is the by far the best explaination and especially visualization ive seen for them! Awesome work!

[abstractvector]

What hyperdimensional aspect ratio should I watch this in?

[eraser]

0:52 "19th century versions of Wolverine and old man from Home Alone" LMFAO

[bobbiewu]

After watching this and the interactive videos, whenever I think of 3d rotations again, I cannot resist thinking in terms of the quaternions. There is just no other way that is more elegant than this!

[darshangupta]

Nowadays your teaching helps me in my other subjects too

[RVeda-vhon]

No question, Eater has done something truly remarkable with those explorable videos. Still going through them, taking all the time it needs. Thanks to you both.

[quahntasy]

You are a living legend. These animations are so cool its amazing.

Was worth the wait.

[bkboggy]

I am so happy you've created this. I work in VR and this is invaluable for me.