Michael Junger and William Pulleyblank ("Geometric dualing and combinatorial optimization", in Jahrbuch Uberblicke Mathematik, Viewig, 1993) described a nice way to visualize a certain lower-bound on the tour length of Euclidean TSP instances. In the picture below, any tour must have length at least twice the sum of the radii of the red "zones" plus twice the sum of the widths of the blue "moats"; this proves that the indicated tour is optimal.