A spatial relationD. M. Mark and M. J. Egenhofer (1994), "Modeling Spatial Relations Between Lines and Regions: Combining Formal Mathematical Models and Human Subjects Testing"
PDF
/ref> specifies how some object is located in space in relation to some reference object. When the reference object is much bigger than the object to locate, the latter is often represented by a point. The reference object is often represented by a

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 ...

. In

Anatomy Anatomy () is the branch of biology concerned with the study of the structure of organisms and their parts. Anatomy is a branch of natural science that deals with the structural organization of living things. It is an old science, having i ...

it might be the case that a spatial relation is not fully applicable. Thus, the degree of applicability is defined which specifies from 0 till 100% how strongly a spatial relation holds. Often researchers concentrate on defining the applicability function for various spatial relations. In

spatial database 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 s ...

s and

geospatial topology Geospatial topology is the study and application of qualitative spatial relationships between geographic features, or between representations of such features in geographic information, such as in geographic information systems (GIS). For examp ...

the ''spatial relations'' are used for

spatial analysis Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early deve ...

and constraint specifications. In

cognitive development Cognitive development is a field of study in neuroscience and psychology focusing on a child's development in terms of information processing, conceptual resources, perceptual skill, language learning, and other aspects of the developed adult bra ...

for walk and for catch objects, or for understand objects-behaviour; in robotic Natural Features Navigation; and many other areas, ''spatial relations'' plays a central role. Commonly used types of ''spatial relations'' are: ''topological'', ''directional'' and ''distance'' relations.

Topological relations

The DE-9IM model expresses important ''space relations'' which are invariant to

rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...

translation Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...

and scaling transformations. For any two spatial objects ''a'' and ''b'', that can be points, lines and/or polygonal areas, there are 9 relations derived from ''DE-9IM'':

Directional relations

Directional relations can again be differentiated into external directional relations and internal directional relations. An internal directional relation specifies where an object is located inside the reference object while an external relations specifies where the object is located outside of the reference objects. *Examples for internal directional relations: left; on the back; athwart, abaft *Examples for external directional relations: on the right of; behind; in front of, abeam, astern

Distance relations

Distance relations specify how far is the object away from the reference object. *Examples are: at; nearby; in the vicinity; far away

Relations by class

Reference objects represented by a

or another kind of "spatial envelope" that encloses its borders, can be denoted with the maximum number of

dimensions In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordin ...

of this envelope: '0' for punctual objects, '1' for linear objects, '2' for planar objects, '3' for volumetric objects. So, any object, in a 2D modeling, can by classified as ''point'', ''line'' or ''area'' according to its delimitation. Then, a ''type of spatial relation'' can be expressed by the class of the objects that participate in the relation: * point-point relations: ... * point-line relations: * point-area relations: * line-line relations: * line-area relations: * area-area relations: More ''complex'' modeling schemas can represent an object as a composition of ''simple sub-objects''. Examples: represent in an astronomical map a star by a ''point'' and a

binary star A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in ...

by ''two points''; represent in

geographical map Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an i ...

a river with a ''line'', for its

source Source may refer to: Research * Historical document * Historical source * Source (intelligence) or sub source, typically a confidential provider of non open-source intelligence * Source (journalism), a person, publication, publishing institute o ...

stream A stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long large streams ...

, and with an strip-''area'', for the rest of the river. These schemas can use the above classes, uniform composition classes (''multi-point'', ''multi-line'' and ''multi-area'') and heterogeneous composition (''points''+''lines'' as "object of dimension 1", ''points''+''lines''+''areas'' as "object of dimension 2"). Two internal components of a ''complex object'' can express (the above)

binary relations In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over sets and is a new set of ordered pairs consisting of elements in and in ...

between them, and ternary relations, using the whole object as a

frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both math ...

. Some relations can be expressed by an abstract component, such the

center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...

of the binary star, or a center line of the river.

Temporal references

For human thinking, spatial relations include qualities like size, distance, volume, order, and, also, time: Stockdale and PossinC. Stockdale and C. Possin (1998
Spatial Relations and Learning
discusses the many ways in which people with difficulty establishing spatial and temporal relationships can face problems in ordinary situations.

References

{{reflist Cognitive science Space