  We extract local current distributions from interatomic currents calculated
using a fully relativistic quantum mechanical scattering formalism by
interpolation onto a three-dimensional grid. The method is illustrated with
calculations for Pt$|$Ir and Pt$|$Au multilayers as well as for thin films of
Pt and Au that include temperature-dependent lattice disorder. The current flow
is studied in the "classical" and "Knudsen" limits determined by the sample
thickness relative to the mean free path $\lambda$, introducing current
streamlines to visualize the results. For periodic multilayers, our results in
the classical limit reveal that transport inside a metal can be described using
a single value of resistivity $\rho$ combined with a linear variation of $\rho$
at the interface while the Knudsen limit indicates a strong spatial dependence
of $\rho$ inside a metal and an anomalous dip of the current density at the
interface which is accentuated in a region where transient shunting persists.
