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Aspatial relation[1][2] 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 abounding box.
InAnatomy 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.
Inspatial databases andgeospatial topology thespatial relations are used forspatial analysis and constraint specifications.
Incognitive development for walk and for catch objects, orfor understand objects-behaviour; inrobotic Natural Features Navigation; and many other areas,spatial relations plays a central role.
Commonly used types ofspatial relations are:topological,directional anddistance relations.
TheDE-9IM model expresses importantspace relations which are invariant torotation,translation andscaling transformations.
For any two spatial objectsa andb, that can be points, lines and/or polygonal areas, there are 9 relations derived fromDE-9IM:
| Equals | a =b Topologicallyequal. Also (a ∩b =a) ∧ (a ∩b =b) |
|---|---|
| Disjoint | a ∩b = ∅ a andb are disjoint, have no point in common. They form a set ofdisconnected geometries. |
| Intersects | a ∩b ≠ ∅ |
| Touches | (a ∩b ≠ ∅) ∧ (aο ∩bο = ∅) a touchesb, they have at least one boundary point in common, but no interior points. |
| Contains | a ∩b =b |
| Covers | aο ∩b =b b lies in the interior ofa (extendsContains). Other definitions: "no points ofb lie in the exterior ofa", or "Every point ofb is a point of (the interior of)a". |
| CoveredBy | Covers(b,a) |
| Within | a ∩b =a |
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.
Distance relations specify how far is the object away from the reference object.
Reference objects represented by abounding box or another kind of "spatial envelope" that encloses its borders, can be denoted with the maximum number ofdimensions of this envelope: '0' forpunctual objects, '1' forlinear objects, '2' forplanar objects, '3' forvolumetric objects. So, any object, in a2D modeling, can by classified aspoint,line orarea according to its delimitation. Then, atype of spatial relation can be expressed by the class of the objects that participate in the relation:
Morecomplex modeling schemas can represent an object as a composition ofsimple sub-objects. Examples: represent in anastronomical map a star by apoint and abinary star bytwo points; represent ingeographical map a river with aline, for itssourcestream, 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 andmulti-area) and heterogeneous composition (points+lines as "object of dimension 1",points+lines+areas as "object of dimension 2").
Two internal components of acomplex object can express (the above)binary relations between them, andternary relations, using the whole object as aframe of reference. Some relations can be expressed by an abstract component, such thecenter of mass of the binary star, or a center line of the river.
For human thinking, spatial relations include qualities like size, distance, volume, order, and, also, time:
Time is spatial: it requires understanding ordered sequences such as days of the week, months of the year, and seasons. A person with spatial difficulties may have problems understanding “yesterday,” “last week,” and “next month”. Time expressed digitally is just as spatial as time expressed by moving clock hands, but digital clocks remove the need to translate the hand position into numbers.
— Stockdale and Possin
Stockdale and Possin[3] discusses the many ways in which people with difficulty establishing spatial and temporal relationships can face problems in ordinary situations.