  We study geometries of galactic rotation curves from Dark Matter (DM) and
Modified Newtonian Dynamics (MOND) models in $(g_{\rm bar},g_{\rm tot})$-space
($g2$-space) where $g_{\rm tot}$ is the total centripetal acceleration of
matter in the galaxies and $g_{\rm bar}$ is that due to the baryonic (visible)
matter assuming Newtonian gravity. The $g2$-space geometries of the models and
data from the SPARC database are classified and compared in a rescaled
$\hat{g}2$-space that reduces systematic uncertainties on galaxy distance,
inclination angle and variations in mass to light ratios. We find that MOND
modified inertia models, frequently used to fit rotation curve data, are
disfavoured at more than 5$\sigma$ independent of model details. The
Bekenstein-Milgrom formulation of MOND modified gravity compares better with
data in the analytic approximation we use. However a quantitative comparison
with data is beyond the scope of the paper due to this approximation. NFW DM
profiles only agree with a minority of galactic rotation curves. Improved
measurements of rotation curves, in particular at radii below the maximum of
the total and the baryonic accelerations of the curves are very important in
discriminating models aiming to explain the missing mass problem on galactic
scales.
