Some embodiments provide a non-transitory machine-readable medium that stores a program. The program identifies a first data structure having a first type. The first data structure is configured to store a set of geometries. The program further identifies a second data structure associated with the first data structure. The second data structure is configured to store modifications to the set of geometries. The program also perform a merge operation on the first data structure and the second data structure to form a third data structure.