  Mass models of galactic disks traditionally rely on axisymmetric density and
rotation curves, paradoxically acting as if their most remarkable asymmetric
features, such as lopsidedness or spiral arms, were not important. In this
article, we relax the axisymmetry approximation and introduce a methodology
that derives 3D gravitational potentials of disk-like objects and robustly
estimates the impacts of asymmetries on circular velocities in the disk
midplane. Mass distribution models can then be directly fitted to asymmetric
line-of-sight velocity fields. Applied to the grand-design spiral M99, the new
strategy shows that circular velocities are highly nonuniform, particularly in
the inner disk of the galaxy, as a natural response to the perturbed
gravitational potential of luminous matter. A cuspy inner density profile of
dark matter is found in M99, in the usual case where luminous and dark matter
share the same center. The impact of the velocity nonuniformity is to make the
inner profile less steep, although the density remains cuspy. On another hand,
a model where the halo is core dominated and shifted by 2.2-2.5 kpc from the
luminous mass center is more appropriate to explain most of the kinematical
lopsidedness evidenced in the velocity field of M99. However, the gravitational
potential of luminous baryons is not asymmetric enough to explain the
kinematical lopsidedness of the innermost regions, irrespective of the density
shape of dark matter. This discrepancy points out the necessity of an
additional dynamical process in these regions: possibly a lopsided distribution
of dark matter.
