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If you are looking on a world map and someone asks you where Geneva is, you will probably move your attention to the European continent, in particular to Swizerland (provided you know where Geneva approximately lies). Then you will try to locate successively smaller and smaller regions, where Geneva should and gradually narrowing until you identify the city at lake Geneva in the southwest of Switzerland.
Whilst searching for Geneva you decomposed the space into sectors. You discarded the ones which aren’t pertinent to your task and you subdivided the candidate region to contain the city recursively. You partitioned the map (space), for instance.
Another example: You forgot the phone number of a friend. To find it out you will probably look in the directories. Actually looking for Mr. Jones, you won’t begin at the first page of the directories going through until you find it. Surely you will use the index and begin your search by the letter ‘j’ and then slip through all the pages until you find ‘jo’ and so on. In other words you make use of the indexing applied to the structured information contained in the directories.
Hierarchical spatial data structures are based on the principle of recursive decomposition. They are attractive because they
are compact and depending on the nature of the data, they can save storage space as well as time and also facilitate operations
such as search.
This means that spatial data access methods (spatial indexing) in geodatabases, e.g. for spatial searches in geographic information
systems, provide fast access to spatial data.