The definition of the Hausdorff distance between U and V is

.

In everyday language, what that means is this. You look for the furthest distance from V that a point of U can be. Then you look for the furthest distance from U that a point of V can be. Finally, you take the larger of those two distances.

For the example in the picture, the furthest distance from V that you can get while remaining in U is 2 (all the points on the right-hand edge of U are distance 2 from V). The furthest distance from U that you can get while remaining in V is 1 (all the points on the bottom edge of V are distance 1 from U). The maximum of the numbers 2 and 1 is 2. Therefore .

In that calculation, it makes no difference whether or not the intersection of U and V is empty.