Spatial Data Warehouses - Data Warehouse Systems: Design and Implementation - page 421

extent” without any commitment to a specific spatial data type. Like
SimpleGeo , Geo is an abstract type. It can be used, for instance, to represent
the administrative regions of a country, where regions may be either a Surface
or a SurfaceSet .
It is worth noting that empty geometries are allowed, that is, geometries
representing an empty set of points. This is needed in particular to express
the fact that the intersection of two disjoint geometries is also a geometry,
although it may be an empty one.
Spatial data types have a set of operations, which can be grouped in classes.
Table 11.1 shows the most common operations.

Table 11.1 Classes of operations on spatial types
Class Operations
Topological operations Intersects, Disjoint, Equals, Overlaps, Contains,
Within, Touches, Covers, CoveredBy, Crosses

Predicates IsEmpty, OnBorder, InInterior

Unary operations Boundary, Buffer, Centroid, ConvexHull

Binary operations Intersection, Union, Difference, SymDifference

Numeric NoComponents, Length, Area, Perimeter

Distance, Direction

Topological operations are based on the well-known topological relation-
ships , which specify how two spatial values relate to each other. They are
extensively used in spatial applications since they can be used to test, for
instance, whether two states have a common border, a highway crosses a
state, or a city is located in a state.
The definitions of the topological relationships are based on the definitions
of the boundary, the interior, and the exterior of spatial values. Intuitively,
the exterior of a spatial value is composed of all the points of the underlying
space that do not belong to the spatial value. The interior of a spatial value is
composed of all its points that do not belong to the boundary. The boundary
is defined for the different spatial data types as follows. A point has an empty
boundary, and its interior is equal to the point. The boundary of a line is
given by its extreme points, provided that they can be distinguished (e.g.,
a closed line has no boundary). The boundary of a surface is given by the
enclosing closed line and the closed lines defining the holes.

Intersects/Overlaps Disjoint

Equals Contains/Within

Covers/CoveredBy Touches

Crosses

Fig. 11.2 Icons for the various topological relationships