Upwind cell (top) and downwind cell (bottom), for the short-characteristic M_uM_c displayed in Fig. 1. In this example, the direction of propagation of the radiation, n, is in the first octant, which corresponds to (θ,ϕ) ∈  [0,π/2 [×  [0,π/2 [. The local coordinate system is defined by (M_c,e_x,e_y,e_z). The upwind end point M_u belongs to the cell face f_z:z = −Δz_k. However, depending on (θ,ϕ) in this octant, M_u may belong to f_x:x = −Δx_i, or to f_y:y = −Δy_j. In the general case, Δx_i ≠ Δy_j, Δx_i ≠ Δz_k, Δy_j ≠ Δz_k, though equalities are possible. The downwind end point M_d belongs to f_z:z = Δz_k + 1. However, depending on (θ,ϕ) in this octant, M_d may belong to f_x:x = Δx_i + 1 or to f_y:y = Δy_j + 1. See Sect. 3.2 for more details.