May 28 2024

See the Question & Answer section below for more info.

r =

↓
r

The space of "

The space of

First, note that a 3D rotation by a certain amount around a vector is the same as a 3D rotation by the negative of that amount around the vector pointing in the opposite direction.

Second, axis/lines are like vectors, but unlike vectors they point in both directions, so they are their own opposite.

So, in order for the input to not have any jumps in the rotation it represents, the rotation amount must be negated when the axis selector point wraps around the edge of the input. The shadow point is there to show you what negative rotation amount you are close to by wrapping around the edge of the circle.

I thought of two ways this could be visualized as the rotation amount decreases: 1. by shrinking the spherical inputs and leaving the point the same size, or 2. by making the point grow to fill the whole spherical input. I previously went with 2, but have changed the input to use approach 1. Do you know another way this could be visualized?

The new input is updated so that there is only

I also updated the question and answer section to match the redone input.

⚠️ Math-y and frustrated notes folow. Continue at your own risk. What is
going on with how people work with 3D rotations ⚠️ 😵💫 ?

The spaces listed in the question are popular for working with 3D rotations. I believe I understand that they are all the same

Unit Quaternions ≅ Geometric Algebra Rotors ≅ SU(2) ≅ Spin(3) ≅ 3-sphere are overly complicated for working with 3D rotations in that sense.

I still don't really understand why the listed spaces are more popular to work with than SO(3). Is it because they have nicer algebraic properties? Is it because they can more easily be interpolated? Is it because they are easier to represent?