Add extrinsic euler rotations

[carbotaniuman]

Extrinsic rotations can be implemented by calling the intrinsic rotation with the first and last elements swapped and then manually swapping the elements, and would prove useful when interfacing with OpenCV.

EXTRINSIC_XYZ[0] = INTRINSIC_ZYX[2]
EXTRINSIC_XYZ[1] = INTRINSIC_ZYX[1]
EXTRINSIC_XYZ[2] = INTRINSIC_ZYX[0]

[bitshifter]

Hi @carbotaniuman , could you provide a bit more details here, I'm not totally clear on what you are asking for.

[carbotaniuman]

I was looking for extrinsic rotations, which was used for a visualization in the field I was working in. There's basically the extrinsic counterpart to the intrinsic rotations already present https://docs.rs/glam/latest/glam/enum.EulerRot.html, and according to https://pages.github.berkeley.edu/EECS-106/fa21-site/assets/discussions/D1_Rotations_soln.pdf

It turns out that extrinsic rotation is equivalent to an intrinsic rotation by the same angles but with
inverted order of elemental rotations, and vice-versa. Thus, a RPY transformation with roll, pitch, and
yaw angles of (γ, β, α) is equivalent to the ZYX Euler angle rotations of (α, β, γ).

[bitshifter]

Speculatively, what might an API for this look like in glam?

[carbotaniuman]

It would just be adding the new variants to this enum https://docs.rs/glam/latest/glam/enum.EulerRot.html, and handling them in the euler angle conversion code. I'm fairly confident that what I said in the first paragraph was an implementation technique where you map it to the intrinsic one and then swap some params, but it's been years since I looked at this so I don't really remember.