Overhaul Quaternion documentation

[Mickeon]

Closes godotengine/godot-docs#6271

This PR aims to completely overhaul the Quaternion type.
The reasoning and changelog are extremely similar to the "Overhaul Basis Documentation" PR, so I'm not sure I should bother repeating them twice.

More specific notes:

• Specify that the quaternions in Godot use the Hamilton convention, not JPL;
  • Closes Godot uses JPL style quaternions instead of Hamilton godot-docs#6271. I still am very, very unsure on what it means, but for users that do care, they can now know.
• Mention https://quaternions.online/ and https://github.com/iwatake2222/rotation_master as point of reference;
  • I hope these websites use the Hamilton convention, it would be a shame if they don't.
• Mention that quaternions are 32-bit by default.
• Mention "Basis to Quaternion" conversion caveats.
• Made the extra line about not messing with the quaternions' components a note
• ...

---

I started this ASAP after seeing the "overwhelmingly" positive reception of the prior PR after a few mere hours. Feedback is very, very welcome. Quaternions are a very complicated concept to digest and comprehend.

This PR may contain multiple versions of the same line I was not sure about, denoted with "??". Reviewing of these lines is heavily appreciated.

Sources:

• https://quaternions.online/
• https://fzheng.me/2017/11/12/quaternion_conventions_en/

[Zireael07]

A great resource I just found https://github.com/iwatake2222/rotation_master

[Mickeon]

Definitely looks like a great website. However, as far as introductions go, it's extremely unfriendly. There's a lot data present all at once. The web version could be added as another link in the tutorial section, perhaps.

[Zireael07]

The web version could be added as another link in the tutorial section, perhaps.

Please do!

[Mickeon]

It's done in the current version of this PR

[0awful]

Man I wish this was a thing a week ago when I took on handling quaternion code in rust's gdextension. That being said. I've got a few things I discovered that aren't covered here. #87422. I propose that I merge after yours to incorporate the nitty gritty of what happens when you break the rules.

[fire]

I wanted to mention that the JPL and HAMILTON conversions differ by x*-1,y*-1,z*-1,w. Assuming that w is the real. Sometimes x is the real component. Like one.

I am certain this is incomprehensible :(

[Mickeon]

I have understood it in part from the sources I looked up. I am still struggling to visualize the difference in practice, however, as well as providing a simpler explanation to fit in Quaternion's description. Hence I cannot tell if the provided websites use the same convention as Godot or not.

[Mickeon]

I have once and for all clarified it's the Hamilton convention. Now, for more to review if there is

[aaronfranke]

I urge you to please test things and review your work for factual accuracy. Nicer wording is useless if the words are not correct.

[Mickeon]

I took all of the feedback at heart and addressed it. Hopefully I have not forgotten anything.
While I am not fully satisfied with the leading description it does feel good enough.

[aaronfranke]

Looks great!

[akien-mga]

Thanks!

[akien-mga]

Cherry-picked for 4.2.2.
Cherry-picked for 4.1.4.