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If you were
told that some object A was
perfectly (or somewhat, or not at all) in some direction d (e.g., west, above-right) of some
reference object B, where in
space would you look for A?
Cognitive experiments suggest that you would mentally build a spatial
template. Using essentially angular deviation, you would partition the
space into regions where the relationship “in direction d of B” holds (to various extents) and
regions where it does not hold. You would then be able to locate the
objects for which the relationship holds best, and find A. Spatial templates, therefore,
represent directional spatial relationships to reference objects (e.g.,
“east of the post office”). Note that other names can also be found in
the literature (e.g., fuzzy landscape, applicability structure,
potential field). There exists a very simple and yet cognitively
plausible way to mathematically model a spatial template without
sacrificing the geometry of the reference object (i.e., the object is
not approximated through its centroid or minimum bounding rectangle).
In case of 2D raster data, exact calculation of the model can easily be
achieved but is computationally expensive, and tractable approximation
algorithms were proposed. In case of 2D vector data, exact calculation
of the model is not conceivable. In previous work, we introduced the
concept of the F-template. We discussed the case of 2D raster data and
designed, based on this concept, an efficient approximation algorithm
for spatial template computation. The algorithm is faster, gives better
results, and is more flexible than its competitors. Here, comparable
advances are presented in the case of 2D vector data. These advances
are of particular interest for spatial query processing in Geographic
Information Systems.
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