As long as we retain the critical point or isoset p, we can coalesce cells within a zone component up to the limits given by the zone structure, and not change the resulting topology of any isosurface component extracted from the zone (the topology will still conform to the zone boundaries). In this manner we can reduce the tiling complexity of the resulting isosurfaces, prior to actually extracting them. This is different from topologically correct triangle decimation, (See [25]), where we start with a rendered triangular mesh, and remove or merge traingles in a manner that preserves the topology of the complex.
This means that we can manage the level of detail rendering, within zones, in a very simple fashion. For example, for 3 dimensional regularly gridded data within a given zone component let us suppose that we have rendered an isosurface using large coalesced cells. We can divide each large cell into 8 smaller cubes, by adding back an interior data point (which will be part of the zone component read into memory). We can now recursively refine the rendering in those smaller cubic regions that are of interest (e.g. have large volume gradient).
We can further simplify the dataset by eliminating smaller zone components (merging them with larger zones), if we feel that the associated criticality represents an inessential feature. This will, of course, depend on the application.