  We present a reanalysis of reverberation-mapping data from 2005 for the
Seyfert galaxy NGC 4151, supplemented with additional data from the literature
to constrain the continuum variations over a significantly longer baseline than
the original monitoring program. Modeling of the continuum light curve and the
velocity-resolved variations across the H$\beta$ emission line constrains the
geometry and kinematics of the broad line region (BLR). The BLR is well
described by a very thick disk with similar opening angle ($\theta_o \approx
57^{\circ}$) and inclination angle ($\theta_i \approx 58^{\circ}$), suggesting
that our sight line towards the innermost central engine skims just above the
surface of the BLR. The inclination is consistent with constraints from
geometric modeling of the narrow line region, and the similarity between the
inclination and opening angles is intriguing given previous studies of NGC 4151
that suggest BLR gas has been observed temporarily eclipsing the X-ray source.
The BLR kinematics are dominated by eccentric bound orbits, with $\sim10$% of
the orbits preferring near-circular motions. With the BLR geometry and
kinematics constrained, the models provide an independent and direct black hole
mass measurement of $\log M_{\rm BH}/M_{\odot} = 7.22^{+0.11}_{-0.10}$ or
$M_{\rm BH}=1.66^{+0.48}_{-0.34}\times10^7 M_{\odot}$, which is in good
agreement with mass measurements from stellar dynamical modeling and gas
dynamical modeling. NGC 4151 is one of the few nearby broad-lined Seyferts
where the black hole mass may be measured via multiple independent techniques,
and it provides an important test case for investigating potential systematics
that could affect the black hole mass scales used in the local Universe and for
high-redshift quasars.
