  The magnetic field dependent critical current $I_{\text{c}}(B)$ of a
Josephson junction is determined by the screening currents in its electrodes.
In macroscopic junctions, a local vector potential drives the currents,
however, in thin film planar junctions, with electrodes of finite size and
various shapes, they are governed by non-local electrodynamics. This
complicates the extraction of parameters such as the geometry of the effective
junction area, the effective junction length and, the critical current density
distribution from the $I_{\text{c}}(B)$ interference patterns. Here we provide
a method to tackle this problem by simulating the phase differences that drive
the shielding currents and use those to find $I_{\text{c}}(B)$. To this end, we
extend the technique proposed by John Clem [Phys. Rev. B, \textbf{81}, 144515
(2010)] to find $I_{\text{c}}(B)$ for Josephson junctions separating a
superconducting strip of length $L$ and width $W$ with rectangular, ellipsoid
and rhomboid geometries. We find the periodicity of the interference pattern
($\Delta B$) to have geometry independent limits for $L \gg W$ and $L \ll W$.
By fabricating elliptically shaped S$-$N$-$S junctions with various aspect
ratios, we experimentally verify the $L/W$ dependence of $\Delta B$. Finally,
we incorporate these results to correctly extract the distribution of critical
currents in the junction by the Fourier analysis of $I_{\text{c}}(B)$, which
makes these results essential for the correct analysis of topological channels
in thin film planar Josephson junctions.
