Fix quaternion keyframe optimization for collinear rotation over 180 degrees

[Dheatly23]

Fixes: #87813

Change the correct great-arc distance for 180 degrees rotation.

Bugsquad Edited:
Fixes #75159

[fire]

@TokageItLab I am not sure about this. What do you think?

[TokageItLab]

It sounds like it makes sense to check the angles before the axes check.

I remember there are a couple of issues related to this and will test to see if it works correctly (if it is possible to optimize without over thinning the keys) when I have time.

[Dheatly23]

After thinking about it, the original checks is sort-of correct. It just missing one key quirk of quaternion.

In short, unit quaternion is a double-covering of SO3 (rotation group). Rotating 360 degrees once brings a quaternion to it's negative. It requires 720 degrees rotation to bring it back to it's original state.

(See plate trick and quantum spin, if you'd like to know more)

So, doing a great arc distance (acos(q1.dot(q2))) gives half the angle rotated between the two quaternions. You can clearly tell by simply computing the distance between a quaternion and it's negative (360 degrees rotated). So 180 degrees rotation would be separated by PI/2, not PI.

PS: Arcsin is a bit numerically better than arccos, particularly with small angles.

[TokageItLab]

LGTM!

[akien-mga]

Thanks! And congrats for your first merged Godot contribution 🎉