  Context: Knowledge about hot, massive stars is usually inferred from
quantitative spectroscopy. To analyse non-spherical phenomena, the existing 1D
codes must be extended to higher dimensions, and corresponding tools need to be
developed. Aims: We present a 3D radiative transfer code that is capable of
calculating continuum and line scattering problems in the winds of hot stars.
By considering spherically symmetric test models, we discuss potential error
sources, and indicate advantages and disadvantages by comparing different
solution methods. Further, we analyse the UV resonance line formation in the
winds of rapidly rotating O stars. Methods: We consider both a (simplified)
continuum model including scattering and thermal sources, and a UV resonance
line transition approximated by a two-level-atom. We applied the
short-characteristics (SC) method, using linear or monotonic B\'ezier
interpolations, to solve the equation of radiative transfer on a non-uniform
Cartesian grid. To calculate scattering dominated problems, our solution method
is supplemented by an accelerated $\Lambda$-iteration scheme. Results: For the
spherical test models, the mean relative error of the source function is on the
$5-20\,\%$ level, depending on the applied interpolation technique and the
complexity of the considered model. All calculated line profiles are in
excellent agreement with corresponding 1D solutions. The predicted line
profiles from fast rotating stars show a distinct behaviour as a function of
rotational speed and inclination. This behaviour is tightly coupled to the wind
structure and the description of gravity darkening and stellar surface
distortion. Conclusions: Our SC methods are ready to be used for quantitative
analyses of UV resonance line profiles. When calculating optically thick
continua, both SC methods give reliable results, in contrast to the alternative
finite-volume method.
