In dual contouring, (as defined in here) terrain can be shown as an octree where the leaves contain a vertex of the mesh.
However in order to save memory the mesh needs to be minimized, or similar leaves are collapsed into a single, larger, leaf. The paper discusses this and it makes sense, however another problem arises;
if you want to modify the mesh, by carving it using some sort of shape, then you may need to split that larger node down again. The issue with this step is that when a node is split again, how would you then rebuild the 'hermite data' that those smaller nodes use?
The far edges of the larger node would already contain 'hermite data'; however the new edges, on that are inside of the larger node, would need to be generated somehow.
Please let me know if I'm doing this wrong or if you have any ideas!