Comparision of Axis-angle and Euler-Angles contradicting?

Question

I used SpinCalcVis to compare axis-angle against the euler-angles and think the angle signs of both are contradicting. I used q = -1 0 0 0 as input. Using the euler-angles it is fine to rotate superimposing frame B around x-axis of frame A with a right-hand helix looking along the x direction. So far so good.
With the axis-angle values it only makes sense when rotating with the positive angle in a right hand helix around the pink vector, but looking into the coordinates origin. Is this the right way to interprete the positive angle for axis-angle or whats the convention there?

Screenshot

Answer 1

The unclarity came from the 180 degree, where one could rotate around +pi or -pi still having same results. A positive rotation angle for the axis-angle construct is positive clockwise looking into the direction of the axis away from the origin. The convention of spincalcviz is congruent to the robotics/aerosim package. Verified by this image and the internal implementation here.

Answer 2

I do not have a specific knowledge on the software you are using. But I know for sure that matlab uses the JPL convention for quaternions (they are part of the aerosim package) therefore are left handed and the rotation matrix and euler angles that you extract from a quaternion using matlab is the opposite you would expect to obtain.

Apologies, I was terribly wrong. According to this matlab page the quaternion seems to be Hamiltonian and represented as $ \mathbf{q} = [\eta, \vec{v}]$.

Apologies for the mistake.