  Generalised Complex Geometry provides a natural interpretation of the
$\mathcal{N}=1$ supersymmetry conditions for warped solutions of type II
supergravity as differential equations on polyforms on the internal manifold.
Written in this language the supersymmetry conditions correspond to calibration
conditions for probe D-branes: D-string, domain-wall or space-filling branes,
depending on the directions they span in the non-compact four-dimensional
space. The BPS condition corresponding to the calibration of space-filling
D-branes has been reformulated by Tomasiello, eliminating the explicit
dependence on the metric. We generalise this derivation to the case of
non-supersymmetric backgrounds violating the domain-wall and D-string
calibration conditions. We use this reformulation to derive constraints that
the ten-dimensional solutions with BPS space-filling sources must respect in
order to dimensionally reduce to solutions of four-dimensional $\mathcal{N}=1$
supergravity with non-vanishing F-terms and potentially non-vanishing D-terms.
We give the equations of motion for the class of type II vacua satisfying these
constraints in the language of pure spinors. We investigate how restrictive
these constraints are for the class of type IIB SU$(3)$ backgrounds with BPS
space-filling O5-planes.
