  We present a method to constrain galaxy parameters directly from
three-dimensional data cubes. The algorithm compares directly the data with a
parametric model mapped in $x,y,\lambda$ coordinates. It uses the spectral
lines-spread function (LSF) and the spatial point-spread function (PSF) to
generate a three-dimensional kernel whose characteristics are instrument
specific or user generated. The algorithm returns the intrinsic modeled
properties along with both an `intrinsic' model data cube and the modeled
galaxy convolved with the 3D-kernel. The algorithm uses a Markov Chain Monte
Carlo (MCMC) approach with a nontraditional proposal distribution in order to
efficiently probe the parameter space. We demonstrate the robustness of the
algorithm using 1728 mock galaxies and galaxies generated from hydrodynamical
simulations in various seeing conditions from 0.6" to 1.2". We find that the
algorithm can recover the morphological parameters (inclination, position
angle) to within 10% and the kinematic parameters (maximum rotation velocity)
to within 20%, irrespectively of the PSF in seeing (up to 1.2") provided that
the maximum signal-to-noise ratio (SNR) is greater than $\sim3$ pixel$^{-1}$
and that the ratio of the galaxy half-light radius to seeing radius is greater
than about 1.5. One can use such an algorithm to constrain simultaneously the
kinematics and morphological parameters of (nonmerging) galaxies observed in
nonoptimal seeing conditions. The algorithm can also be used on adaptive-optics
(AO) data or on high-quality, high-SNR data to look for nonaxisymmetric
structures in the residuals.
