  Superconducting vortex cores have been extensively studied for magnetic
fields applied perpendicular to the surface by mapping the density of states
(DOS) through Scanning Tunneling Microscopy (STM). Vortex core shapes are often
linked to the superconducting gap anisotropy---quasiparticle states inside
vortex cores extend along directions where the superconducting gap is smallest.
The superconductor 2H-NbSe$_2$ crystallizes in a hexagonal structure and
vortices give DOS maps with a sixfold star shape for magnetic fields
perpendicular to the surface and the hexagonal plane. This has been associated
to a hexagonal gap anisotropy located on quasi two-dimensional Fermi surface
tubes oriented along the $c$ axis. The gap anisotropy in another,
three-dimensional, pocket is unknown. However, the latter dominates the STM
tunneling conductance. Here we measure DOS in magnetic fields parallel to the
surface and perpendicular to the $c$ axis. We find patterns of stripes due to
in-plane vortex cores running nearly parallel to the surface. The patterns
change with the in-plane direction of the magnetic field, suggesting that the
sixfold gap anisotropy is present over the whole Fermi surface. Due to a slight
misalignment between the vector of the magnetic field and the surface, our
images also show outgoing vortices. Their shape is successfully compared to
detailed calculations of vortex cores in tilted fields. Their features merge
with the patterns due to in plane vortices, suggesting that they exit at an
angle with the surface. Measuring the DOS of vortex cores in highly tilted
magnetic fields with STM can thus be used to study the superconducting gap
structure.
