Re:How to Fix Gimbal Lock in N-Dimensions
by Jasper_ on Saturday August 29, 2020 @01:50AM
(#24313935)
So the thing that made Gimbal Lock click is a combination of two things: rotations are ordered, and euler angles (and fixed angles, its counterpart) are a combination of three different rotation motions.
Effectively, since you have XYZ, one of them is nested within the others. If you instead have a nested set of gimbals, like XYZX2Y2*Z2, then you avoid gimbal lock since you can always "escape" to the other gimbal.
Also, orientations are not rotations. Gimbal lock doesn't prevent you from finding a set of values that gives you an orientation, it prevents you from finding a good path from one orientation to another.
That you can't cover all rotations with three nested gimbals is a demonstration of the fact that rotations are a not obvious space. See also the Dirac belt trick.
Effectively, since you have XYZ, one of them is nested within the others. If you instead have a nested set of gimbals, like XYZX2Y2*Z2, then you avoid gimbal lock since you can always "escape" to the other gimbal.
Also, orientations are not rotations. Gimbal lock doesn't prevent you from finding a set of values that gives you an orientation, it prevents you from finding a good path from one orientation to another.
That you can't cover all rotations with three nested gimbals is a demonstration of the fact that rotations are a not obvious space. See also the Dirac belt trick.