  The near-Earth space weather is driven by the quick release of magnetic free
energy in the solar corona. Probing this extremely hot and rarified region of
the extended solar atmosphere requires modeling the polarization of forbidden
and permitted coronal lines. To this end, it is important to develop efficient
codes to calculate the Stokes profiles that emerge from given three-dimensional
(3D) coronal models, and this should be done taking into account the symmetry
breaking produced by the presence of magnetic fields and non-radial solar wind
velocities. We have developed such a tool with the aim of theoretically
predicting and interpreting spectropolarimetric observations of the solar
corona in permitted and forbidden lines. In this paper we show the results of a
theoretical investigation of the linear polarization signals produced by
scattering processes in the H I Ly-${\alpha}$ line at 1216 A and in the He II
Ly-${\alpha}$ line at 304 A using 3D coronal models by Predictive Science Inc.
These spectral lines have very different critical magnetic fields for the onset
of the Hanle effect (53 G and 850 G, respectively), as well as different
sensitivities to the Doppler effect caused by the solar wind velocities. We
study under which circumstances simultaneous observations of the scattering
polarization in these Ly-${\alpha}$ lines can facilitate the determination of
magnetic fields and macroscopic velocities in the solar corona.
