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A spatial relation specifies how some object is located in space in relation to some reference object. Since the reference object is usually 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 (oblique or axis-parallel).

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 use for spatial analysis and constraint specifications.

Commonly used spatial relations are: topological, directional and distance relations.

## Topological relations

Examples of topological spatial relations.
Main article DE-9IM.

The DE-9IM model express important space relations because they are formally specified, and are invariant to rotation, 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:

 Equals a = b Topologically equal. Also (a ∩ b = a) ∧ (a ∩ b = b) Disjoint a ∩ b = ∅ a and b are disjoint, have no point in common. They form a set of disconnected geometries. Intersects a ∩ b ≠ ∅ Touches (a ∩ b ≠ ∅) ∧ (a ∩ b = ∅) a touches b, they have at least one boundary point in common, but no interior points. Covers b lies in the interior of a (extends Contains). Other definitions: "no points of b lie in the exterior of a", or "Every point of b is a point of (the interior of) a". Contains a ∩ b = b CoveredBy Covers(b,a) Within a ∩ b = a

## 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

## References

1. J Freeman (1975), "The modelling of spatial relations", Computer Graphics and Image Processing, Elsevier. Freeman75.pdf

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Information source: wikipedia.org

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