  We present synthetic dust polarization maps of simulated molecular clouds
(MCs) with the goal to systematically explore the origin of the relative
orientation of the magnetic field ($\bf{B}$) with respect to the MC
sub-structures identified in density ($n$; 3D) and column density ($N$; 2D).
The polarization maps are generated with the radiative transfer code POLARIS,
including self-consistently calculated efficiencies for radiative torque
alignment. The MCs are formed in two sets of 3D MHD simulations: in (i)
colliding flows (CF), and (ii) the SILCC-Zoom simulations. In 3D, for the CF
simulations with an initial field strength below $\sim$5 $\mu$G, $\bf{B}$ is
oriented parallel or randomly with respect to the $n$-structures. For CF runs
with stronger initial fields and all SILCC-Zoom simulations, which have an
initial field strength of 3 $\mu$G, a flip from parallel to perpendicular
orientation occurs at high densities of $n_\text{trans}$ $\simeq$ 10$^2$ -
10$^3$ cm$^{-3}$. We suggest that this flip happens if the MC's mass-to-flux
ratio, $\mu$, is close to or below the critical value of 1. This corresponds to
a field strength around 3 - 5 $\mu$G. In 2D, we use the Projected Rayleigh
Statistics (PRS) to study the orientation of $\bf{B}$. If present, the flip in
orientation occurs at $N_\text{trans}$ $\simeq$ 10$^{21 - 21.5}$ cm$^{-2}$,
similar to the observed transition value from sub- to supercritical magnetic
fields in the ISM. However, projection effects can reduce the power of the PRS
method: Depending on the MC or LOS, the projected maps of the SILCC-Zoom
simulations do not always show the flip, although expected from the 3D
morphology. Such projection effects can explain the variety of recently
observed field configurations, in particular within a single MC. Finally, we do
not find a correlation between the observed orientation of $\bf{B}$ and the
$N$-PDF.
