Two segments intersect iff endpoints of one straddle the line of the other (orientation test). Need crossing, not just collinear.

Reduce: does a line through two pumps separate two reservoirs onto opposite sides? Or vice versa. Convex hull of each set helps prune candidates.

O(n log n) solution: for each set, find extreme directions from centroid. Only O(1) candidate pump pairs needed — hull's antipodal pairs.