  Accurate simulations of the 21-cm signal from the Epoch of Reionization
require the generation of maps at specific frequencies given the values of
astrophysical and cosmological parameters. The peculiar velocities of the
hydrogen atoms producing the 21-cm radiation result in a shift in the observed
frequency of the 21-cm radiation and changes the amplitude of the signal
itself. This is not an effect we can remove but instead needs to be accurately
modelled to ensure we infer the correct physical parameters from an
observation. We describe the full calculation of the distortion of the 21-cm
signal, and propose a new code that integrates the 21-cm intensity along the
line of sight for each individual light cone pixel to fully capture the
intensity contributions from multiple redshifts. This algorithm naturally deals
with the typical divergences found in standard approaches, allowing for large
optical depths and 21-cm absorption events at high redshifts. We find the new
method results in up to a 60% decrease in power on the largest scales on the
sky, and an increase of over 80% on the smallest scales on the sky. We find
that the new implementation of the light cone results in a longer tail of
bright temperatures in the brightness temperature distribution, as a result of
the successful circumventing of a previous cap that had to be implemented to
avoid a divergence in the brightness temperature. We conclude that this full
treatment of the evolution of the light cone pixel can be an important effect.
