Geography Reference
In-Depth Information
estimations of distances and directions are better for nearby objects [ 39 ] . Also,
wayfinding and other spatial activities seem to be easier for parts of the environment
that are nearby and familiar: “For an individual there is not an equal probability of
behavior occurring in all sections of the environment. There is a spatial bias for
behavior close to his residence owing to least effort considerations” ([ 6 ] , p. 368).
That things near to each other are more correlated than distant things was an
observation made originally by Tobler for geographic space [ 56 ] , and later also
confirmed as a mental default assumption [ 41 ] . As a design choice Voronoi diagrams
provide an unambiguous set of relationship s 5 and an efficient reasoning on a small
number of links between likely correlated objects.
A number of properties follow from this design choice:
￿
Objects in one configuration can belong to different object classes (e.g., the
variety of objects within a city), but they must be spatially separable (non-
overlapping), i.e., from the same level in a hierarchy of spatial granularities. For
example, one configuration can consist of cities (in the context of representing the
geographic space of a country), and another configuration can consist of salient
buildings within a city (in the context of representing the geographic space of the
city), but a configuration cannot contain a city and a building of that city. The city
is an agglomerate of buildings (hence, the building is contained by the city), and
accordingly, city and buildings belong to different levels of spatial granularity.
￿
The objects of a configuration form a context via contrast [ 63 ] . The spatial
meaning of a locative expression can be specified by its current contrast set. For
example, the locative expression “[at / pass] the church” can have a meaning in
a configuration of f (this) church, city hall, museum, cinema g , and it would have
another spatial meaning in
f (this)church, the other church north of it, and the
third church south of it g .
The Voronoi diagram associates always the nearest landmark for a localization task.
“I am near the church” describes my location anchored by the church (in some
appropriate contrast set). “I am in Zurich” anchors my location at another level of
granularity and also evokes a different contrast set.
Choosing Voronoi diagrams is of course a simplifying heuristic, which brings in
uncertainty at two levels:
￿
The application of a Voronoi diagram is a (heuristic) simplification of a more
complex geographic reality. For example, a configuration of all European capitals
provides a stable Voronoi diagram to locate other objects in this reference frame.
However, the Voronoi diagram is only a poor reflection of the nations' boundaries
and hence may produce non-preferred nearness relationships.
5 Mathematically there are exceptions: relationships become ambiguous when nearest neighbors
are arranged on a line or in a rectangle. But practically this nearly never happens in geographic
space.
 
 
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