In this demonstration, the "Function Graph" window shows the graph of f color coded by the sign of the partials derivatives.

Purple represents f_r > 0 and f_θ > 0.
Pink represents f_r > 0 but f_θ < 0.
Blue represents f_θ > 0 but f_r < 0.
White repsesents f_r < 0 and f_θ < 0.

In the second window, "Fold Sets", the fold set in the r-direction is colored in pink, and the fold set in the θ-direction is colored in blue.  The intersections of these fold sets are the critical points.