Illustration on how the density dispersion criterion q_max solves the problem of sharp edges in models such as the AGN torus. In this example we used an octree grid. The left panel represents a cut through the true dust density in xz plane, and the central panel shows the grid density as obtained without a density dispersion criterion with about 3 million cells. The edges of the torus are clearly poorly resolved. The right panel shows the grid density after adding the density dispersion criterion q_max = 0.99 and a maximum subdivision level of 10. The edges are now extremely well resolved using about 7 million of additional cells.