  This is the first of a series of papers in which the kinematics of disk
galaxies over a range of scales is scrutinised employing spectroscopy. A
fundamental aspect of these studies is presented here: the new publicly
available software tool TiRiFiC
(http://www.astro.uni-bonn.de/~gjozsa/tirific.html) enables a direct fit of a
``tilted-ring model'' to spectroscopic data cubes. The algorithm generates
model data cubes from the tilted-ring parametrisation of a rotating disk, which
are automatically adjusted to reach an optimum fit via a chi-squared
minimisation method to an observed data cube. The structure of the new
software, the shortcomings of the previously available programs to produce a
tilted-ring model, and the performance of TiRiFiC are discussed. Our method is
less affected by the well-known problem of beam smearing that occurs when
fitting to the velocity field. Since with our method we fit many data points in
a data cube simultaneously, TiRiFiC is sensitive to very faint structures and
can hence be used to derive tilted-ring models significantly extending in
radius beyond those derived from a velocity field. The software is able to
parametrise HI disks of galaxies that are intersected by the line-of-sight
twice or more, i.e. if the disks are heavily warped, and/or with a significant
shift of the projected centre of rotation, and/or if seen edge-on. Furthermore,
our method delivers the surface-brightness profile of the examined galaxy in
addition to the orientational parameters and the rotation curve. In order to
derive kinematic and morphological models of disk galaxies, especially reliable
rotation curves, a direct-fit method as implemented in our code should be the
tool of choice.
