The left panel shows the time required to produce the image displayed on the right as a function of grid size, N_grid, comparing a single grid approach (dot-dashed line) with the proposed nested grids method (solid line), with N_h = 8. The single grid method scales as ﹩{N}_{{\rm{grid}}}^{2}﹩, as expected (dashed line); the nested grids method, on the other hand, depends weakly on N_grid for large numbers of cells. The middle panel shows the typical error of the recovered projected density relative to the single grid method as a function of the assumed N_h, for N_grid = 4096. For N_h = 8, the relative (σ) error is ≈1%, while achieving a speed-up of ≈30.