Does anyone know if it is possible/easy to convert between these two conventions?
https://github.com/JuliaGeometry/Rotations.jl/issues/281
We need to express some rotations using the intrinsic convention but Rotations.jl uses the extrinsic convention. Is there an easy conversion rule?
can't you just multiply the rotations, one after the other?
i.e., rot_total = RotX * RotY * RotZ
should apply RotZ
first, followed by RotY
(around the new Y axis), followed by RotX
if you then have rot_total * myVec
, you should end up with the composed rotation
Isn't RotZYX equivalent to this multiplication? The problem is that RotY still refers to the original Y axis not the Y axis moving with the object.
I think the ReferenceFrameRotations.jl package rotates the coordinate system and therefore is extrinsic if we flip the signs of the angles. I'll perform some tests. It would be great to be able to convert between the two conventions.
https://math.stackexchange.com/questions/1137745/proof-of-the-extrinsic-to-intrinsic-rotation-transform has a conversion
Isn't RotZYX equivalent to this multiplication?
No, RotZYX
is Z * Y * X
Will use the theorem tomorrow, thanks for the link
I'm a bit confused about this extrinsic vs intrinsic convention though. To my understanding, that's just a difference in order of operations, no?
i.e., whether you apply the overall rotation from the right or left, if I'm not mistaken
https://dominicplein.medium.com/extrinsic-intrinsic-rotation-do-i-multiply-from-right-or-left-357c38c1abfd seems to agree too, and has a longer derivation if the stackexchange one is too terse
I'm a bit confused about this extrinsic vs intrinsic convention though. To my understanding, that's just a difference in order of operations, no?
That's a very non-obvious result of some interesting calculations though
I always found it super counter intuitive that it worked
If I tell you to rotate about 3 Euler angles from my perspective, then you in your rotating perspective can just re-use the angles I gave you and reverse the order of operations and do the rotations from your own perspective and end up in the same place
yeah, I knew about the difference in perspective, I just never knew that this was called intrinsic vs. extrinsic
we had a few assignments in my first linear algebra course that had a much more elegant solution if you knew about this shift in perspective
basically, if you view any matrix multiplication as a coordinate transform, multiplying from the left vs. from the right is exactly equivalent to transforming the entire world vs. local space only
if you parenthesize your expressions properly, you can quite cleanly write down a rotation about the world axis, followed by a translation along a local axis, followed by another rotation in world coordinates. In total, that would be a higher dimensional shear
Last updated: Nov 06 2024 at 04:40 UTC