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"
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/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 Anatomy 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 databases and geospatial topology the ''spatial relations'' are used for spatial analysis and constraint specifications. In cognitive development 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 The Dimensionally Extended 9-Intersection Model (DE-9IM) is a topological Interpretation (logic), model and a Specification (technical standard), standard used to describe the spatial relations of two regions (two 2D geometric model, geometries ...

model expresses important ''space relations'' which are invariant to

rotation Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...

, translation 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 bounding box or another kind of "spatial envelope" that encloses its borders, can be denoted with the maximum number of dimensions 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 by ''two points''; represent in geographical map a river with a ''line'', for its source stream, 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 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 (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale have been specified in physical space. It ...

. 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 barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the d ...

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