Two-dimensional histograms of simulated WCI and RBI (the darkest regions correspond to the highest frequencies). These indices were measured from simulated line profiles that arise from the BLR models KD, PW, and EW seen at an inclination of 34°, and with an emissivity ε = ε₀ (r_in/r)³. The simulations include the map orientations θ = [0°, 30°] (top panel), θ = [60°, 90°] (middle panel), and θ = [0°, 30°, 60°, 90°] (bottom panel) which is the combination of the top and middle panels. These histograms were built from the magnification maps used for the analysis of J1004+4112 (Hutsemékers et al. 2023). They show a particularly clear dependence on the map orientation. The simulations were restricted to 0.9 ≤ μ^BLR ≤ 1.1, and to a single value of the BLR size, r_in = 0.1r_E.