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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 made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
) or set of objects within its
coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...
; in other words , , , {{math, max(''y''). The MBR is a 2-dimensional case of the minimum bounding box. MBRs are frequently used as an indication of the general position of a geographic feature or dataset, for either display, first-approximation spatial query, or spatial indexing purposes. The degree to which an "overlapping
rectangle In Euclidean geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that a ...
s" 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. If the MBR is full or nearly so (for example, a mapsheet aligned with axes of
latitude In geography, latitude is a geographic coordinate system, geographic 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 t ...
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 lett ...
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 R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found s ...
method of spatial indexing.


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, i.e.
metadata Metadata (or metainformation) is "data that provides information about other data", but not the content of the data itself, such as the text of a message or the image itself. There are many distinct types of metadata, including: * Descriptive ...
that describes spatial (geographic) objects; examples includ
DCMI Box
as an extension to the
Dublin Core 140px, Logo of DCMI, maintenance agency for Dublin Core Terms The Dublin Core vocabulary, also known as the Dublin Core Metadata Terms (DCMT), is a general purpose metadata vocabulary for describing resources of any type. It was first developed ...
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 I ...
). 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 The Open Geospatial Consortium (OGC) is an international voluntary consensus standards organization that develops and maintains international standards for geospatial content and location-based services, sensor web, Internet of Things, Geographi ...
(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.


See also

* Bounding parallelogram * C-squares * Darboux integral * Elongatedness *
Geographic information system A geographic information system (GIS) consists of integrated computer hardware and Geographic information system software, software that store, manage, Spatial analysis, analyze, edit, output, and Cartographic design, visualize Geographic data ...
* Geospatial metadata * Largest empty rectangle, also known as maximal empty rectangle * Minimum bounding box *
R-tree R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found s ...
* Shapefile * Spatial index *
Convex hull In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, ...


References


External links


Geospatial Methods website
Cartography Geometric algorithms