Axis-aligned Minimum Bounding Box
The axis-aligned minimum bounding box for a given point set is its minimum bounding box subject to the constraint that the edges of the box are parallel to the (Cartesian) coordinate axes. It is simply the Cartesian product of N intervals each of which is defined by the minimal and maximal value of the corresponding coordinate for the points in S.
Axis-aligned minimal bounding boxes are used to an approximate location of an object in question and as a very simple descriptor of its shape. For example, in computational geometry and its applications when it is required to find intersections in the set of objects, the initial check is the intersections between their MBBs. Since it is usually a much less expensive operation than the check of the actual intersection (because it only requires comparisons of coordinates), it allows to quickly exclude from checks the pairs that are far apart.
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