Context. Observations and theoretical calculations have shown the importance of non-spherically symmetric structures in supernovae. Thus, the interpretation of observed supernova spectra requires the ability to solve the transfer equation in 3-D moving atmospheres. Aims. We present an implementation of the solution of the radiative transfer equation in 3-D homologously expanding atmospheres in spherical coordinates. The implementation is exact to all orders in v/c. Methods. We use the methods that we have developed in previous papers in this series as well as a new a. ne method that makes use of the fact that photons travel on straight lines. The a. ne method greatly facilitates delineating the characteristics and can be used in the case of strong-gravitational and arbitrary-velocity fields. Results. We compare our results in 3-D for spherically symmetric test problems with high velocity fields (up to 87\% of the speed of light) and find excellent agreement, when the number of momentum space angles is high. Our well-tested 1-D results are based on methods where the momentum directions vary along the characteristic (co-moving momentum directions). Thus, we are able to verify both the analytic framework and its numerical implementation. Additionally, we have been able to test the parallelization over characteristics. Using 5122 momentum angles we ran the code on 16 384 Opteron processors and achieved excellent scaling. Conclusions. It is now possible to calculate synthetic spectra from realistic 3D hydro simulations. This should open an era of progress in hydro modeling, similar to that that occurred in the 1980s when 1-D models were confronted with synthetic spectra.