Trajectory Databases - Mobility Data - page 48

atinstant: mpoint × instant → ipoint

inst: ipoint → instant

val: ipoint → point

at: mbool × bool → mbool

deftime: mbool → periods

atperiods: mpoint × periods → mpoint

The operation atinstant returns a data type intime ( point ), ipoint for short.
The type represents a pair ( i, p ) consisting of an instant and a point . From
such pairs one can determine the two components using the operations inst and
val. Operation at reduces a time-dependent Boolean value to the times when it
assumes the second argument. deftime works for type mbool in the same way
as for mpoint .
The need to reduce a moving object to the times when it fulfills certain
properties occurs frequently. For a moving object x , the expression

x atperiods deftime( predicate ( x ) at TRUE)

can be abbreviated to x when[ predicate ( x )] using operator when with sig-
nature

when: mpoint × mbool → mpoint

Hence we can write the previous query more simply, as

query trajectory(train7 when[speed(train7) > (50 * kmh)])

It goes without saying that all the operations presented can be used in set-
oriented queries, that is, in the select or where clause of an SQL query.
We also need some predicates to determine whether a moving object passes
through a certain area or is defined at a given time. The following query finds
all trains passing through mehringdamm and determines the times when they
arrive at or leave this station.

select Id, Line, Up,
inst(initial(Trip at mehringdamm)) as ArrivalTime,
inst(final(Trip at mehringdamm)) as DepartureTime
from Trains
where Trip passes mehringdamm

Here operations are used:

mpoint × point

→ bool

passes:

→ ipoint

initial, final: mpoint

at: mpoint × point → mpoint