Spatial Data Warehouses - Data Warehouse Systems: Design and Implementation - page 423

Unary operations take one spatial value and return a new one. Boundary
returns the exterior ring of a surface. Buffer returns a geometry containing
all points whose distance to the geometry passed as parameter is less than
or equal to a given distance. Centroid returns the center point of a geometry.
ConvexHull returns the minimum convex geometry that encloses a geometry.
Binary operations take two (or more) spatial values and return a new
spatial value. Intersection , Union , Difference ,and SymDifference operate as
in usual set theory and return a geometry obtained by applying the
corresponding operation to the geometries given as argument.
Numeric operations take one or two geometries and return a numeric
value. NoComponents returns the number of disjoint maximal connected
subsets of a geometry, for instance, the number of points for a point set,
the number of connected components for a line set, or the number of faces
for a surface. Length returns the length of a line. Area returns the area of a
surface. Perimeter returns the length of the boundary of a surface. Distance
determines the minimum distance among all pairs of points of two geometries.
Finally, Direction returns the angle of the line between two points, measured
in degrees, that is, a value between 0 and 360.

11.1.2 Continuous Fields

Continuous fields are phenomena that change continuously in space and/or
time. Examples include altitude and temperature, where the former varies
only in space and the latter varies in both space and time. In this chapter,
we cover only nontemporal fields, leaving temporal fields for the next chapter.
At a conceptual level , a continuous field can be represented as a function that
assigns to each point in space a value of a domain, for example, an integer
for altitude. Continuous fields are represented with field types, which capture
the variation in space of base types (such as integers and reals). They are
obtained by applying a constructor field ( ). Hence, a value of type field ( real )

(e.g., representing altitude) is a continuous function f : point

·

real .
Notice that continuous fields are partial functions, that is, they could be
undefined at some points in space. Consider, for example, a field AltitudeBE
defining the altitude in Belgium. Since there are several enclaves and exclaves
between Belgium, the Netherlands, and Germany, the altitude of an enclave
of Germany within Belgium will be undefined.
Field types have associated operations, which can be grouped into several
classes, as shown in Table 11.2 . We discuss next some of these operations.
First, there are operations that perform the projection into the domain
and range .Operations DefSpace and RangeValues return, respectively, the
projection of a field type into its domain and range. For instance, Def-
Space(AltitudeBE) and RangeValues(AltitudeBE) will result, respectively, in
a region covering Belgium and the range of values [

→

− 4m , 694m].