Quaternions really are very natural for representing rotations when they're not being unnecessarily obfuscated. The three "imaginary" -bivector- terms are pretty understandable; they're the 3 basis axes / basis planes and all of them do 180° rotations (with 2-sided rotations). The scalar then has absolutely nothing to do with 4D space and _everything_ to do with _doing absolutely nothing._ A quaternion is just a weighted sum of rotations around each of the three basis axes plus the action of doing nothing. I will briefly mention the existence of "dual quaternions," which let you encode the transformation as a multiplication just like the rotations, and then you can just translate from the object to the origin, apply a rotation, and then translate back as TRT¯¹ (assuming you're composing from right to left), and the whole thing will perform a rotation around the origin of the object in the same plane as R. It's basically what you did manually with addition, but more composable.

using cub to do quaternion explanation is just genius. many thanks

Haven’t really needed to use this before because I’ve been in 2D, but this was fascinating and a good explanation of something I’ve always heard people explain as “something you don’t really need to understand yet”

I’ve been using Quaternion.Identity and Quaternion.LookRotation for a couple years but but never understood how they worked until watching your video. Thanks for this!

This is a very unique take on the path to understand what quaternions are. It helps a lot . Thank you

This is a very clever presentation that does a great job of making the non-commutitive nature of Q's intuitive.

This was pretty helpful! As a guy who hates dealing with Quaternions - thank you.

Just what I needed :) I've been struggling to understand quaternions mathematically, so just to understand how to use the tool is good enough for me for now.

This is super helpful as a visualization tool. Thank you!

I cannot believe that a 10-minute video, that was made with paint and a Rubix cube explained Quaternions better than 3blue1grey and their fancy graphics. Thank you!

This is a very good tip on how to visualise these damn things! Not there yet but this certainly helps a ton!

This helped me get through a problem on the last day of my internship! Thanks!

Thanks a lot! maybe in a few hours i can understand the concept of quaternion, if my brain don't explode before it

This is great! I find that most of the time when I use quaternions I'm thinking of them in the way you talked about right at the end, either as a Quaternion.LookRotation (forward vector, up vector) or as an angle around an axis vector with Quaternion.AngleAxis (angle, axis vector), which works like a shish kebab as you described.

When you make a sonic fan-game and your character need to have a tube based movement system this is perfect

Solid explanations and examples

The end of this video was enlightening I thank you !

Dude oh my god, thank you so much for this, first time its ever clicked for me!

You just made Quaternions easy for me.

instructions unclear solved a rubik's cube with quaternions

Im still confused.....

That's abbsolutely brilliant. Thank you!

legend

to really understand quaternions you need : direction cosine matrix, euler rotation matrix --> rodrigues rotation formula, finally quaternions. when you use euler rotation matrix, you will see why we need quaternions really bad

In case it's helpful to anyone stuck using 3x3 rotation matrices, for everything in this video Quaternion can be replaced with 3x3 rotation matrix and its all still true. They are interchangeable in this conversation. But I guess "quaternion" is easier to say than "3D rotation" all the time.

5:21 şiş kebap dediği yerde koptum 😅güzel betimleme olmuş

can someone explain me how to interpretate the components in a cuaternion? like a + ib + jc + kd i can only think about a, b, c, d as a 4d vector, like (a, b, c, d), how does that ends up being a rotation?

Excellento

Example at 9:17 helps understanding how quaternions inverses can be used but I'd probably just add to pos_A some offset_vector multiplied by transform_matrix_A. Or it can even be just 1 basis vector from transform_matrix_A multiplied by offset magnitude (in case if we're sure about the axis). Unsure though how much quaternions more efficient than matrix multiplication. Multiplying matrix by vector typically takes 9 multiplications and 3 adds, don't know about the quats. PS Love the shish kebab metaphor 😂

it's frustrating that it's all about the gimbal lock. People need to start thinking about whether they can rotate at points other than the x y or z axis with a gimbal.

Really cool to use rubik cube

i like the title

Me want know how make quaternion relative to other quaternion

that rubiks website or game please

Are you related to mike rose?

Geometric algebra >>

A vector also has a magnitude 🤓

tNice tutorials software

You are comparing how multiplication works in quaternions with how addition works in 3D vectors. But the quaternions still also have addition with an additive identity and additive inverses and behave just like 4D vectors in that sense. You saying that quaternions have multiplication "instead" of addition will make people feel they understand things when they'll just get horribly confused if they delve any deeper. Also, the two systems do not have different notions of an "origin". You are confusing the idea of an origin in the sense of (0,0,0) or (0,0,0,0), i.e., a coordinate system, with the idea of identity with respect to some transformation. When we say that one times two equals two, and two times 1/2 equals one, we don't call "one" the "origin". It's the same in any higher-dimensional number system. I like the Rubik's Cube demo though.

Why have all the kiddies started talking in that weird exaggerated wayje

you didn't explained quaternions at all, you explained basic rotations, and transformations, the whole point of quaternions is avoid gimbal lock, so it never ever happen, you introduced your videos with that premise and the whole time you didn't tackle the subject.

The puzzle cube adds unnecessary complexity.