Boundary conditions for rays propagating in the xz-plane at y-level (j) with three different directions n₁, n₂, n₃, and upwind points u₁, u₂, u₃. For point u₁, the intensity is set to and all remaining quantities are obtained by bilinear interpolation from points (i − 1, j, k − 1), (i, j, k − 1), (i − 1, j, k), and (ijk). The required quantities at point u₂ are found from Bézier interpolation using the values at (i − 2, j, k − 1), (i − 1, j, k − 1), (i, j, k − 1). The (unknown) quantities inside the core are indicated by red dots, and need to be reasonably approximated (see text). For direction n₃, the unknown intensity inside the core, , is directed inwards. Such situations occur only for ray directions (nearly) parallel to the spatial grid, and thus are relatively seldom.