
Case 1: e_{xy} > 0 and e_{x} > e_{y} 


The principal axes are counterclockwise to the current axes (because e_{xy} > 0) and no more than 45º away (because e_{x} > e_{y}).


Case 2: e_{xy} < 0 and e_{x} > e_{y} 


The principal axes are clockwise to the current axes (because e_{xy} < 0) and no more than 45º away (because e_{x} > e_{y}).


Case 3: e_{xy} > 0 and e_{x} < e_{y} 


The principal axes are counterclockwise to the current axes (because e_{xy} > 0) and between 45º and 90º away (because e_{x} < e_{y}).


Case 4: e_{xy} < 0 and e_{x} < e_{y} 


The principal axes are clockwise to the current axes (because e_{xy} < 0) and between 45º and 90º away (because e_{x} < e_{y}).


Case 5: e_{xy} = 0 and e_{x} > e_{y} 


The principal axes are aligned with the current axes (because e_{x} > e_{y} and e_{xy} = 0).


Case 6: e_{xy} = 0 and e_{x} < e_{y} 


The principal axes are exactly 90° from the current axes (because e_{x} < e_{y} and e_{xy} = 0).
