Martin Erwig and Markus Schneider
—This paper investigates temporal changes of topological relationships and thereby integrates two important research areas:
First, two-dimensional topological relationships that have been investigated quite intensively and, second, the change of spatial
information over time. We investigate spatio-temporal predicates, which describe developments of well-known spatial topological
relationships. A framework is developed in which spatio-temporal predicates can be obtained by temporal aggregation of elementary
spatial predicates and sequential composition. We compare our framework with two other possible approaches: one is based on the
observation that spatio-temporal objects correspond to three-dimensional spatial objects for which existing topological predicates can
be exploited. The other approach is to consider possible transitions between spatial configurations. These considerations help to
identify a canonical set of spatio-temporal predicates.
—Time in geographic information, spatio-temporal data types, representation of spatio-temporal objects, changes of
spatial predicates, developments of spatial objects.
affinity of spatial and temporal phenomena has been
recognized for a long time in literature. Both phenom-
ena deal with “spaces” or “dimensions” of some kind and
are thus closely related. The (regained) awareness of their
deep relationships has led, both in spatial and in temporal
data modeling, to an increased interest in integrating both
directions into a common research branch called
temporal data modeling
and in constructing
. Their underlying basic entities are called
and are ubiquitous in everyday life.
Consider the flight of an airplane, the migration of whales,
the raging of a storm, or the spreading of a fire region.
Characteristic features of all these objects are that they are
spatial entities changing over time
and that these changes are
. Changes refer to the motion, shrinking, growing,
shape transformation, splitting, merging, disappearing, or
reappearing of spatio-temporal objects. In particular, the
capability of incorporating
change of spatial
objects over time belongs to the most challenging require-
ments of spatio-temporal data modeling. In the meantime,
some spatio-temporal data models (which will be described
later) have already been proposed.
Temporal changes of spatial objects induce modifications
of their mutual topological relationships over time. For
example, at one time, two spatio-temporal objects might be
disjoint whereas, some time later, they might intersect.
These modifications usually proceed continuously over
time but can, of course, also happen in discrete steps.