Low- and intermediate-κ_s lensing regimes of the ellipsoidal NFW lens mapped in its parameter space, as described in Sect. 4.4.2 and Sect. 4.4.3. Eccentricity e is marked on the right vertical axes; ellipticity $1-\sqrt{1-e^2}$ on the left vertical axes; convergence parameter on the horizontal axis up to κ_s = 2.1 in the left panel and up to κ_s = 8 in the right panel. Plotted boundaries mark the following transitions: cusp piercing (bold solid black); tangential peanut (thin dashed green); radial peanut (thin solid purple); hyperbolic umbilic (dashed black); tangential bulge (thin dotted green); butterfly metamorphosis (bold dashed green). Parameter combinations of the critical-curve and caustic examples presented in Figs. 7 and 9 are marked by red and blue dots, respectively. Cyan dotted circles mark combinations for which image-orientation plots are presented in Fig. 16; the green dot marks the branching point of the tangential-bulge boundary from the tangential-peanut boundary. Vertical dashed lines: κ_s values for which critical-curve and caustic dimensions are plotted in Figs. 11 and 13, respectively. Horizontal dashed lines: e values for which the image-plane analysis is demonstrated in Figs. C.1 and C.2.