Edge orientation and cube coordinates

[bulerias]

The cube coordinate systems I've seen define corner and edge orientation with respect to one axis. I'd like to be able to compute the edge orientation with respect to the other two axes, but it's not obvious to me how to do this with this type of coordinate. Kociemba says (here)

It is possible to give another definition for the edge-orientations, so that the full symmetry group can be used with the edge orientation coordinate. But we prefer the usual definition which is better suited for the two-phase algorithm.

which sounds like the kind of thing I'm looking for, but I can't find any information about these alternative EO coordinates.

What are these coordinates, and how does one compute EO with respect to all three axes (is there some formula in the usual coordinates, for instance)?

 

[Herbert Kociemba]

The cube coordinate systems I've seen define corner and edge orientation with respect to one axis. I'd like to be able to compute the edge orientation with respect to the other two axes, but it's not obvious to me how to do this with this type of coordinate. Kociemba says (here)

which sounds like the kind of thing I'm looking for, but I can't find any information about these alternative EO coordinates.

What are these coordinates, and how does one compute EO with respect to all three axes (is there some formula in the usual coordinates, for instance)?

You can define the orientation of an edge at a certain position to be 0 if it takes an even number of quarter turns to move it to this position from its home position and 1 if it takes an odd number of quarter turns.