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augmented with spatial and time-dependent types. Therefore, a spatio-temporal
data warehouse is a warehouse that supports ST-OLAP queries.
As we have stated in the introduction, a trajectory data warehouse is a par-
ticular case of spatio-temporal data warehouse, where the facts are trajectories,
part of trajectories, or some aggregation of trajectories or parts of trajectories.
4.5 Continuous Fields
Continuous fields are phenomena that change continuously in space and/or time.
Examples include altitude and temperature, where the former varies only on
space and the later varies on both space and time. Continuous fields have been
extensively studied in GIS, although multidimensional analysis of continuous
fields is a novel area of research. We will show in this section that combining tra-
jectory data with continuous field data provides additional analysis capabilities
for decision making.
At a conceptual level continuous fields can be represented as a function that
assigns to each point of space (and possibly in time) a value of a particular domain
(e.g., integer for altitude). However, at a logical level , continuous fields must be
represented in a discrete way. For this, we need first to discretize the space, that
is, to partition the spatial domain into a finite number of elements (what is called
a tessellation ), and then assign a value of the field to a representative point in each
partition element. Furthermore, because values of the field are known only at a
finite number of points (called sampled points ), the values at other points must
be inferred using an interpolation function . In practice, different tessellations
and different interpolation functions may be used. The most popular represen-
tation is the raster tessellation, which partitions the space in regular elements
(squares, cubes, etc.) and assigns the same value to each point belonging to an
element.
We extend next our conceptual model with continuous fields, independently of
their underlying implementation. Fields can be seen as two- or three-dimensional
cubes with a single measure. For example, a time-dependent field representing
temperature can be seen as a spatio-temporal cube that associates a real value
to any given point in space and time. This view of fields as cubes allows us
to seamlessly combine fields with regular cubes composed of fact relationships
and dimensions. As we will see in the queries below, relating fields to fact
relationships or to dimensions is performed through spatial or spatio-temporal
operators. Fields can also be included as measures in fact relationships, although
this is beyond the scope of this chapter.
Figure 4.4 extends our example with continuous fields. Nontemporal fields are
identified by the f( ) pictogram, while time-dependent ones are identified by the
f( ,) pictogram. There are two nontemporal fields, Elevation and LandUse .
The former could be used, for example, for analyzing the correlation between
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