We present phase-resolved spectroscopy of the bright, eclipsing polar HU Aqr obtained with high time (~30sec) and spectral (1.6 A) resolution when the system was in a high accretion state. The trailed spectrograms reveal clearly the presence of three different line components with different width and radial velocity variation. By means of Doppler tomography their origin could be located unequivocally (a) on the secondary star, (b) the ballistic part of the accretion stream (horizontal stream), and (c) the magnetically funnelled part of the stream (vertical stream). For the first time we were able to derive a (near-)complete map of the stream in a polar. We propose to use Doppler tomography of AM Herculis stars as a new tool for the mass determination of these binaries. This method, however, still needs to be calibrated by an independent method. The asymmetric light curve of the narrow emission line originating on the mass-donating companion star reveals evidence for significant shielding of 60% of the leading hemisphere by the gas between the two stars.