  Context. The Vela complex is a region of the sky that gathers several stellar
and interstellar structures in a few hundred square degrees. Aims. Gaia data
now allows us to obtain a 3D view of the Vela interstellar structures through
the dust extinction. Methods. We used the FEDReD (Field Extinction-Distance
Relation Deconvolver) algorithm on near-infrared 2MASS data, cross-matched with
the Gaia DR2 catalogue, to obtain a 3D cube of extinction density. We applied
the FellWalker algorithm on this cube to locate clumps and dense structures.
Results. We analysed 18 million stars on $450~\mathrm{deg}^2$ to obtain the
extinction density of the Vela complex from 0.5 to 8~kpc at
$\ell\in[250\degr,280\degr]$ and $b\in[$-10$\degr,5\degr]$. This cube reveals
the complete morphology of known structures and relations between them. In
particular, we show that the Vela Molecular Ridge is more likely composed by
three substructures instead of four, as suggested by the 2D densities. These
substructures form the shell of a large cavity. This cavity is visually aligned
with the Vela supernova remnant but located at a larger distance. We provide a
catalogue of location, distance, size and total dust content of ISM clumps that
we extracted from the extinction density cube.
