Illustration of the geometry and the octree grid structures for the three test models: the logarithmic spiral galaxy (top row), the AGN torus (middle row), and the galaxy from an SPH simulation (bottom row). In each row, the left column represents a cut through the dust density. For the two galaxy models, this cut corresponds to the xy plane; for the AGN torus model it is a cut through the xz plane. The central and right columns are cuts through the octree grids corresponding to the same planes, and correspond to the regular and barycentric subdivision recipes, respectively. The different shades of gray in the middle and right columns illustrate the density of the cells: darker gray means higher density.