Towards a 3D kinetic tomography of Taurus clouds: I -- Linking neutral
  potassium and dust
  Results. We illustrate our profile-fitting technique and present the K\,{\sc
i} velocity structure of the dense ISM along the paths to all targets. As a
validation test of the dust map, we show comparisons between distances to
several reconstructed clouds with recent distance assignments based on
different techniques. Target star extinctions estimated by integration in the
3D map are compared with their K\,{\sc i} 7699 A absorptions and the degree of
correlation is found comparable to the one between the same K\,{\sc i} line and
the total hydrogen column for stars distributed over the sky that are part of a
published high resolution survey. We show images of the updated dust
distribution in a series of vertical planes in the Galactic longitude interval
150-182.5 deg and our estimated assignments of radial velocities to the opaque
regions. Most clearly defined K\,{\sc i} absorptions may be assigned to a dense
dust cloud between the Sun and the target star. It appeared relatively
straightforward to find a velocity pattern consistent will all absorptions and
ensuring coherence between adjacent lines of sight, at the exception of a few
weak lines. We compare our results with recent determinations of velocities of
several clouds and find good agreement. These results demonstrate that the
extinction-K\,{\sc i} relationship is tight enough to allow linking the radial
velocity of the K\,{\sc i} lines to the dust clouds seen in 3D, and that their
combination may be a valuable tool in building a 3D kinetic structure of the
dense ISM. We discuss limitations and perspectives for this technique.
