Spacing

The spacing from a set of coordinates A to another set B, is the largest distance d (in that coordinates system) such that all the following are true for the circle of diameter d centered at the center of A:

• the circle contains no point of B; and
• either B contains an horizontal rectangle with width and height at least d, or the circle does not intersect a similar circle of diameter d centered at the center of B.

Where the center of a set of coordinate is the intersection of the diagonals of the smallest horizontal rectangle that contains the set.