> First of all i did not use the term 'ortholinear movement'.
The fact that you did not use the term, does not mean that it is not
what you are discussing. It is precisely the subject of this
discussion: whether units should be restricted to ortholinear movement,
or allowed to move along diagonals.
> I am concerned with the case where the 'most direct' route (ie. the shortest
> route) would be the diagonal and where the 2 possible orthogonal routes are
> of equal distance.
This is no different than the case that I described. I will say it
again. Suppose that you have to travel from aa01 to ab03, with diagonal
movement allowed. The "most direct" route would take you along a direct
line from aa01 to ab03, but that is not allowed. So you have to move
either from aa01 to aa02 to ab03, or from aa01 to ab02 to ab03. Both of
these are exactly the same length. You might therefore choose to move
from aa01 to aa02 to ab03, while a noble in ab03 might move from ab03 to
ab02 to aa01.
In other words: you are not allowed to move along the direct path. You
have two routes you could follow which are of equal length. If one
noble goes in one direction, and the other in the other direction, their
paths might not cross.
This is *exactly* the same as what happens in the example that you gave.
It is true in *any* movement system that one can reasonably suggest.