Examples of cubic monotonic interpolations in cell faces intersected by a short-characteristic, for a ray propagating in the first octant, i.e., along increasing x, y, and z. Two configurations are possible. The first one is displayed in the top panel, where all the quantities are known in the grid points neighboring the cell face. This situation always occurs for the upwind and downwind source functions and opacities (S_u,χ_u), (S_d,χ_d). But, for the upwind specific intensity I_u, it occurs only when horizontal faces f_z:z =  ± Δz_k or boundary faces are intersected. The second configuration is displayed in the bottom panel. It impacts the determination of I_u when vertical non-boundary faces, f_x:x =  ± Δx_i or f_y:y =  ± Δy_j, are intersected. In this case, the upwind specific intensity is not known in all the grid points neighboring the cell face. See Sect. 5.1 for detailed explanations.