We can remove details that do not contribute significantly to the rendered surface safely if they are contained within a particular zone. We can also remove zones nested within that particular zone. Such a circumstance would be if the detail rendered to a small fraction of the size of a pixel when projected in screen space. We can manage detail at the topologic level and then at the geometric level. We can ultimately reduce any surface enclosed within a zone up to the required degree of geometric detail.
For example, for 3-dimensional data within a given zone let us suppose that we have rendered an iso-surface using very few data points. We divide each large cube into 8 smaller cubes, by adding back an interior lattice point. We can now recursively refine the rendering in those smaller cubic regions that have large volume gradient, since this gradient corresponds to geometric features.