Most space-partitioning systems use planes (or, in higher dimensions, hyperplanes) to divide space: points on one side of the plane form one region, and points on the other side form another.
Space partitioning is particularly important in computer graphics, especially heavily used in ray tracing, where it is frequently used to organize the objects in a virtual scene.
Storing objects in a space-partitioning data structure (k-d tree or BSP tree for example) makes it easy and fast to perform certain kinds of geometry queries—for example in determining whether a ray intersects an object, space partitioning can reduce the number of intersection test to just a few per primary ray, yielding a logarithmic time complexity with respect to the number of polygons.
There is also a usage in collision detection: determining whether two objects are close to each other can be much faster using space partitioning.
The number of components in a space partition plays a central role in some results in probability theory.
In the context of Cartography and GIS - Geographic Information System, is common to identify cells of the partition by standard codes.
Common space-partitioning systems include: Suppose the n-dimensional Euclidean space is partitioned by
The largest number of components is attained when the hyperplanes are in general position, i.e, no two are parallel and no three have the same intersection.