- #1
Septimra
- 27
- 0
So I have been heavily trying to understand rotations.
Rotations as i understand is a planar phenomenon. You need at least two dimensions.
That is why rotations cannot work in dim 1.
With 2 dimensions, rotations happen in the only plane that exists: XY. However the axis of rotation cannot actually be described in ℝ2 you have to go to ℝ3to define the primary axis of rotation.
In ℝ3 is different because there are 3 planes of rotation: XY, XZ, YZ.
The problem comes from properly and effectively interpolating and combining rotations.
So just like we did in 2D we can define an axis or plane in ℝ4 all X,Y, and Z vectors rotate around. Or the planes XY, XZ, YZ rotate around. This is the w axis/component.
So now if my intuition is correct then can you please explain how exactly quaternions fit into this and why we do not quaternions defined for 2D rotation like 3D rotation.
A complex number is sufficient for a rotation in 2d because there is only one plane, and a combination of planes are not require, right?
So should there not be a way to define a 2d rotation in terms of an 3d axis like 4-vector quaternion does not 3d?
Thank you so much!
Rotations as i understand is a planar phenomenon. You need at least two dimensions.
That is why rotations cannot work in dim 1.
With 2 dimensions, rotations happen in the only plane that exists: XY. However the axis of rotation cannot actually be described in ℝ2 you have to go to ℝ3to define the primary axis of rotation.
In ℝ3 is different because there are 3 planes of rotation: XY, XZ, YZ.
The problem comes from properly and effectively interpolating and combining rotations.
So just like we did in 2D we can define an axis or plane in ℝ4 all X,Y, and Z vectors rotate around. Or the planes XY, XZ, YZ rotate around. This is the w axis/component.
So now if my intuition is correct then can you please explain how exactly quaternions fit into this and why we do not quaternions defined for 2D rotation like 3D rotation.
A complex number is sufficient for a rotation in 2d because there is only one plane, and a combination of planes are not require, right?
So should there not be a way to define a 2d rotation in terms of an 3d axis like 4-vector quaternion does not 3d?
Thank you so much!