Geometry of a scattering event used for the analytical validation in Sect. 4. A photon arrives from the right side of the grain with some initial north direction d_N,init (red). Grain symmetry axis o and angle of incidence α are shown in black. The photon package initial direction k, the plane of incidence, and the north direction in the frame of the grain d_N are shown in orange. Scattering angles θ and φ and north directions d_N,sca, during the scattering process are in blue. The direction of the scattered photon k′, exit angle γ, plane of departure, and outgoing north direction d′_N is shown in green.