  In this work, we introduce the use of the differential geometry Frenet-Serret
equations to describe a magnetic line in a pulsar magnetosphere. These
equations, which need to be solved numerically, fix the magnetic line in terms
of their tangent, normal, and binormal vectors at each position, given
assumptions on the radius of curvature and torsion. Once the representation of
the magnetic line is defined, we provide the relevant set of transformations
between reference frames; the ultimate aim is to express the map of the
emission directions in the star co-rotating frame. In this frame, an emission
map can be directly read as a light curve seen by observers located at a
certain fixed angle with respect to the rotational axis. We provide a detailed
step-by-step numerical recipe to obtain the emission map for a given emission
process, and give a set of simplified benchmark tests. Key to our approach is
that it offers a setting to achieve an effective description of the system's
geometry {\it together} with the radiation spectrum. This allows to compute
multi-frequency light curves produced by a specific radiation process (and not
just geometry) in the pulsar magnetosphere, and intimately relates with
averaged observables such as the spectral energy distribution.
