  Studying the feedback process of Active Galactic Nuclei (AGN) requires
characterising multiple kinematical components, such as rotating gas and
stellar disks, outflows, inflows, and jets. To compare the observed properties
with theoretical predictions of galaxy evolution and feedback models and to
assess the mutual interaction and energy injection rate into the interstellar
medium (ISM), one usually relies on simplified kinematic models. These models
have several limitations, as they often do not take into account projection
effects, beam smearing and the surface brightness distribution of the emitting
medium. Here, we present MOKA3D, an innovative approach to model the 3D gas
kinematics from integral field spectroscopy observations. In this first paper,
we discuss its application to the case of AGN ionised outflows, whose observed
clumpy emission and apparently irregular kinematics are only marginally
accounted for by existing kinematical models. Unlike previous works, our model
does not assume the surface brightness distribution of the gas, but exploits a
novel procedure to derive it from the observations by reconstructing the 3D
distribution of emitting clouds and providing accurate estimates of the
spatially resolved outflow physical properties (e.g. mass rate, kinetic
energy). As an example, we demonstrate the capabilities of our method by
applying it to three nearby Seyfert-II galaxies observed with MUSE at the VLT
and selected from the MAGNUM survey, showing that the complex kinematic
features observed can be described by a conical outflow with a constant radial
velocity field and a clumpy distribution of clouds.
