Combine multiple rotation matrixes in 3D

Question

I have calculated an axis angle rotations for each axis. If I only apply one of the three rotations, the objects rotates as expected.

If I multiply the rotation matrixes, as you would normally do it if you combine rotations I don't get the desired result, cause the first rotation affects the others and therefore the end result is not what I'm looking for.

I want to apply each rotation to the object as if it wasn't rotated before.

I guess this is a simple task, but it seems that I'm not searching for the right keywords. (Also the title is not perfect ... (open for suggestions))

Thanks for every hint / help.

Answer 1

You're experiencing gimbal lock. It's not a maths problem, it's a logical fallacy. Try it with, for the sake of description, your phone:

1. put it on your desk face up, with the charging connector at the bottom.
2. rotate clockwise around z by 90 degrees. So the charging connector is now to the left.
3. rotate around x (which will be the longer axis of the phone assuming the charging port is on the top or bottom) by 180 degrees.
4. the phone is now upside down, with the charging port on the left.

But:

1. put it on your desk face up, with the charging connector at the bottom.
2. rotate around x by 180 degrees. So the charging connector is now at the top.
3. rotate clockwise around z by 90 degrees.
4. the phone is now upside down, with the charging port on the right.

Which of those is incorrect if the instruction was to rotate 180 degrees around x and 90 degrees clockwise around z? Neither is incorrect. The instructions were ambiguous.

The order of individual rotations always matters, because the second affects the work done in the first, the third affects the work done in the first and second, etc. Shuffling the order just changes which affects which.

Orientation is normally stored directly as a matrix or as a quaternion because it's unambiguous and because it keeps the order of actions properly ordered.