A very fast method for calculating line shapes in the presence of an external magnetic field accounting for charge particle dynamics is proposed. It is based on a reformulation of the frequency fluctuation model, which provides an expression of the dynamic line shape as a functional of the static distribution function of frequencies. In the presence of an external magnetic field, the distribution of intensity and polarization of the emission depends on the angle between the observation line and the magnetic field's direction. Comparisons with numerical simulations and experimental results for various plasma conditions show very good agreement. Results on hydrogen lines in the context of magnetic fusion and the Lyman-α line, accounting for fine structure, emitted by argon in the context of inertial fusion, are also presented.