Comparison of the grid quality metrics for octree and k-d-tree based grids of our three test cases (stars correspond to octree grids, dots to k-d tree grids, and the different colours correspond to the three different test models). The top left panel shows N_cells, the total number of cells in the grid, as a function of the threshold mass fraction δ_max. For a given threshold value, octree grids require up to more than double the number of cells compared to the corresponding k-d tree. The other panels show the average number of cells crossed per path ⟨ N_cross ⟩, the density quality metric Δρ, and the optical depth quality metric Δτ as a function of N_cells.