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 Bezier 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.
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