Contains a line with two perpendicular intersects.  All pairs of points on the intersects that are are opposite sides of the original line are co-linear with a point on the original line. 

Trying to create cases where no points need to move, however finding what path to use to minimize the case.  
200 all have to change (looking in wrong dimension.)
201 all but 2 have to change (all looking at origin, except origin looking towards adjacent point.)
202 lines point to next points along themselves, end points point to start of another line.  points on two lines use original line for direction they are looking.

For 202, we can change the direction the drones at, to in the direction:
0 2 0      2 1 0
0 4 0      -1 -1 0
-2 3 0     1 -6 0
0 -4 0     2 1 0

The above is if one cycle is needed, which it isn't, thus three changes can solve this case:
0 -4 0   to look at   2 -3 0
0 2 0    to look at   -1 -3 0
-2 3 0   to look at   -1 3 0