Directions are relative to viewpoint of object
The directions front/back, right/left, and up/down are relative to the viewpoint of the object.
They are not relative to the viewpoint of the viewer.
The right/left, front/back, and up/down directions relative to the viewpoint of that object don't change.
If I were to rotate
the cube in Figure 1 so as to turn it "upside down", the green axis would then
point downward, but that would still be the top of the cube
relative to the cube's viewpoint.