Trajectory Data Warehouses - Data Warehouse Systems: Design and Implementation - page 474

a b c

t

v

v

v

t

t

t

field(temporal(·))

y temporal(field(·))

x

Fig. 12.5 Three possible ways to conceptualize temporal fields

a value of type temporal(field(real)) , which defines a function f : instant →

( point real ), can be used to represent temperature, which varies in

time and space. Notice that the types temporal(field(real)) (Fig. 12.5 b) and
field(temporal(real)) (Fig. 12.5 c) are equivalent, that is, they associate a real
value to a point in a spatiotemporal space.
All operations defined for temporal types apply for temporal fields,
although some of them must be redefined, as we will see next. Suppose that
Temperature is a temporal field defined over Belgium and covering the period
[2010-01-01, 2012-12-31]. DefTime(Temperature) yields the period above, and
RangeValues(Temperature) yields the range defined by the minimum and max-
imum temperature at all instants in the period above and all points located
in Belgium. Similarly, AtInstant(Temperature, 2011-01-01 08:00) yields a non-
temporal field corresponding to the temperature at that particular instant,
while AtPeriod(Temperature, [2012-04-01, 2012-04-03]) returns a temporal
field projected over the given interval. Finally, InitialInstant(Temperature) and
InitialValue(Temperature) return the first instant for which a temperature is
defined, along with the nontemporal field corresponding to that instant.
We have seen that the operations AtMin and AtMax reduce the function
defining a temporal value to the instants when its value is minimal or
maximal, respectively. These operations have as argument a temporal value
and return a temporal value. As temporal fields vary both on space and time,
two versions of these operations must be considered, depending on whether
the operation is applied instant by instant or point by point. For example,
AtMin t applied to a temporal(field(real)) (see Fig. 12.5 b) operates instant by
instant and applies the operation AtMin to the field of reals valid at that
instant, thus restricting it to the points in space where its value is minimum.
On the other hand, AtMin s applied to a field(temporal(real)) (see Fig. 12.5 c)
operates point by point and applies the operation AtMin to the temporal
real valid at that point, thus restricting it to the instants where its value is
minimum.
Similarly, lifted aggregation operations must be renamed to differentiate
those that operate on space or on time. For example, Sum s and Sum t
correspond to the Sum operation lifted in space and in time, respectively.

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