Minimum bounding rectangle

In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two-dimensional object (e.g. point, line, polygon) or set of objects within its x-y coordinate system; in other words min(x), max(x), min(y), max(y).

The degree to which an "overlapping rectangles" query based on MBRs will be satisfactory (in other words, produce a low number of "false positive" hits) will depend on the extent to which individual spatial objects occupy (fill) their associated MBR.

On the other hand, if the MBR describes a dataset consisting of a diagonal line, or a small number of disjunct points (patchy data), then most of the MBR will be empty and an "overlapping rectangles" test will produce a high number of false positives.

It is also (as "boundingBox") an element in Geography Markup Language (GML), that is utilised by a range of Web Service specifications from the Open Geospatial Consortium (OGC).

In the ISO 19107 Spatial Schema (ISO/TC 211), MBR appears as the datatype GM_Envelope that is returned by the envelope() operation on the root class GM_Object.