Kick Quat out of VectorSpace

[mweatherley]

Follow-up for #12747

I have filed this as a bug, but it's really more of a matter of philosophy than anything (and it's not really an enhancement...).

What is the issue?

Currently, Quat implements VectorSpace; however, glam's Quat type is supposed to represent unit quaternions (i.e. versors), which do not meaningfully form a vector space over the reals, even though the full quaternion algebra does form a real vector space.

The reason that this is bad is because a lot of vector space operations really don't make sense for Quat; chief among these is VectorSpace::ZERO, which always produces an invalid quaternion, but in general, vector space operations will cause unit quaternions to denormalize. In other words, VectorSpace is at best a collection of convenience methods for quaternions, but they have extremely poor semantics.

What is the alternative?

Let's fall in line with the philosophy we landed on for colors: Unit quaternions are not a vector space, and if you want to pretend they are, you can embed them in Vec4 and perform explicit conversions. e.g.:

let sum_quat = Quat::from_vec4(Vec4::from(quat1) + Vec4::from(quat2)).normalize()

[BD103]

Not sure how to label this kind of design issue, so I'm going to leave it marked as bug. :)

[rlidwka]

glam's Quat type is supposed to represent unit quaternions (i.e. versors), which do not meaningfully form a vector space over the reals

Unit quaternions are isomorphic to rotations, and rotations do form a perfectly valid vector space.

edit: sorry, I said dumb thing, 3d rotations don't commute

[mweatherley]

In particular, unit quaternions form a vector space over R, where zero vector is x=0, y=0, z=0, w=1, vector addition is quaternion multiplication, and multiplication of vector by scalar is exponentiation of quaternion by said scalar.

For this to produce anything like a vector space, the quaternions would have to be Abelian. They are not; in fact, SU(2) has rank 1, and its Lie algebra su(2) doesn't even have any Lie subalgebras of dimension 2 (hence no Abelian ones). In other words: it has to be a miracle for addition between two elements to even commute.

[SolarLiner]

So the action here is to remove the VectorSpace impl from Quat, right? If so, I'm marking this as a good first issue as the changes are straightforward, and the impl hasn't been there long enough for it to be an effective breaking change.

[mweatherley]

So the action here is to remove the VectorSpace impl from Quat, right? If so, I'm marking this as a good first issue as the changes are straightforward, and the impl hasn't been there long enough for it to be an effective breaking change.

Yep! Technically NormedVectorSpace too, but it's all in one place. We did release a version with Quat as a Point, so it's breaking in that sense (at least, either way it should probably be mentioned in release notes).