what are the eight directions?
Firstly if you look up any Aikido terminology starting with the word Happo then you will see.
Doing much Aikitaiso I learned what was called happo undo. Through the bokken happo giri.
One is eight direction ikkyo and one was eight direction cutting.North, south, east, west, north east, south east, south west, north west. ( any eight direction aikitaiso exercise we classed as happo undo for we also did eight direction funakogi undo)
Happo on it's own is to do with attention or ki out in all directions or you may say another way of saying zanshin.
Then a study of the foot and leg (knee) motion in shihonage, along with centre and centre line etc and the utilization of four directions which later you have to do in eight directions. Eight paths of least resistance.
I could go on and take it further but hopefully you get the picture.
Basically it gets the body used to turning or moving comfortably in all directions. Ki wise in that discipline it gets you used to directing in one direction and changing to other directions with ease. Etc.
Now what I don't know but think may be the case is that Tomiki Aikido use these principles in one form or another but I may be wrong there.