Rotation in x, y axises follow Right Hand Rule

It doesn’t seem to be correct. X vector rotated 90 degrees around Z, does yields Y, BUT:
The Y vector, rotated positive around X, yields negative Z vector
The Z vector, rotated positive around Y, yields negative X vector

I need to work with quaternions and this brought some confusion. Obviously the coded maths works fine, it’s just a bit strange that indeed the left-hand rule is not consistently applied here. This is also visible in Henry Read’s formulas in #2 post.

See, pictures attached:

Identity (0 rotations)


Yaw = 90 degrees (rot around Z)

Roll = 90 degrees (rot around X)

Pitch = 90 degrees (rot around Y)

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