Minimum bounding rectangle: Difference between revisions

Revision as of 21:08, 19 July 2020

Revision as of 01:28, 9 June 2022

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{{Short description|Smallest rectangle which encloses some planar set of points}}

[[File:Minimum bounding rectangle.svg|thumb|A series of geometric shapes enclosed by its minimum bounding rectangle]]

TheIn [[computational geometry]], the '''minimum bounding rectangle''' ('''MBR'''), also known as '''bounding box''' ('''BBOX''') or '''envelope''', is an expression of the maximum extents of a 2two-dimensional object (e.g. [[Point (geometry)|point]], [[Line (geometry)|line]], [[polygon]]) or set of objects within its (or their) 2{{mvar|x-D (x, y)}} [[Cartesian coordinate system|coordinate system]],; in other words {{math|min(''x'')}}, {{math|max(''x'')}}, {{math|min(''y'')}}, {{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 [[geography|geographic]] feature or dataset, for either display, first-approximation spatial query, or [[Spatial database|spatial indexing]] purposes.

The degree to which an "overlapping [[rectangle]]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]] and [[longitude]] 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]]ing.