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 In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two to ...

) or set of objects within its coordinate system; in other words , , , . The MBR is a 2-dimensional case of the

minimum bounding box In geometry, the minimum or smallest bounding or enclosing box for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure ...

. MBRs are frequently used as an indication of the general position of a

geographic Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...

feature or dataset, for either display, first-approximation spatial query, or spatial indexing purposes. The degree to which an "overlapping rectangles" query based on MBRs will be satisfactory (in other words, produce a low number of "

false positive A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test resul ...

" hits) will depend on the extent to which individual spatial objects occupy (fill) their associated MBR. If the MBR is full or nearly so (for example, a mapsheet aligned with axes of

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

and

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...

will normally entirely fill its associated MBR in the same coordinate space), then the "overlapping rectangles" test will be entirely reliable for that and similar spatial objects. 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. One system that attempts to deal with this problem, particularly for patchy data, is c-squares. MBRs are also an essential prerequisite for the R-tree method of

spatial index A spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most sp ...

ing.

As spatial metadata

Owing to their simplicity of expression and ease of use for searching, MBRs (frequently as "bounding box" or "bounding coordinates") are also commonly included in relevant standards for

geospatial metadata Geospatial metadata (also geographic metadata) is a type of metadata applicable to geographic data and information. Such objects may be stored in a geographic information system (GIS) or may simply be documents, data-sets, images or other object ...

, i.e. metadata that describes spatial (geographic) objects; examples includ
DCMI Box
as an extension to the

Dublin Core 220px, Logo image of DCMI, which formulates Dublin Core The Dublin Core, also known as the Dublin Core Metadata Element Set (DCMES), is a set of fifteen "core" elements (properties) for describing resources. This fifteen-element Dublin Core has ...

metadata scheme, "Bounding Coordinates" in th
(U.S.) FGDC metadata standard
and "Geographic Bounding Box" in the (2003–current) ISO 19115 Metadata Standard for geographic information (

ISO/TC 211 ISO/TC 211 is a standard technical committee formed within ISO, tasked with covering the areas of digital geographic information (such as used by geographic information systems) and geomatics. It is responsible for preparation of a series of Inte ...

). It is also (as "boundingBox") an element in

Geography Markup Language The Geography Markup Language (GML) is the XML grammar defined by the Open Geospatial Consortium (OGC) to express geographical features. GML serves as a modeling language for geographic systems as well as an open interchange format for geographi ...

(GML), that is utilised by a range of Web Service specifications from the

Open Geospatial Consortium The Open Geospatial Consortium (OGC), an international voluntary consensus standards organization for geospatial content and location-based services, sensor web and Internet of Things, GIS data processing and data sharing. It originated in 199 ...

(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. Web-accessible articles that deal further with the concept of the MBR include "Unlocking the Mysteries of the Bounding Box" by Douglas R. Caldwell, and "Geographic Database Search Interfaces and the Equatorial Cylindrical Equidistant Projection" by Ross S. Swick and Kenneth W. Knowles. The section on "searching" on th
Geospatial Methods
site is also well worth investigating. See also documentation for specific spatially enabled databases, e.g.ESRI, 1993. Understanding GIS: The Arc/Info method. John Wiley and Sons

References

External links

Geospatial Methods website
Cartography Geometric algorithms