And photoshop, for the vast majority of its life, has been a solely 2D image editing package with no "3 axis coordinate system". Its only the last couple of versions that some basic 3D support has been tacked on, none of which has any application to this purpose. If anything in "photoshop speak" layers represent the third axis most often.

In "computer graphics software" 3-axis coordinate systems are usually found in 3D packages such as Max, Maya, Blender et all which have no defined standard (and wouldnt be used for photo-retouching either).

Basically talking about a 3-axis coordinate system is of itself very "un-photoshop" and not typical of the field of image, its something specific to the fields of 3D modelling (ie games and VFX) rather than 2D image manipulation.