Geography Reference
In-Depth Information
It is important to consider the pseudo-dimensionality of both an object and the field (the space) in which
it resides. A point on a line is a zero-dimensional object in one-dimensional space. A line segment on a
plane is a one-dimensional object in two-dimensional space. A polygon is a two-dimensional object in a
two-dimensional space. A point in a volume is a zero-dimensional object in three-dimensional space.
The dimensionality of the object must be less than, or equal to, the dimensionality of the space in which
it resides.
This issue of dimensionality comes into play here because great economies of computer storage are
achievable if an object is considered to have fewer dimensions than it actually does. For example,
describing a fire hydrant as a complex three-dimensional spatial object would be an arduous task and
involve many numbers and much text. If it is considered a zero-dimensional object, its location can be
described (very precisely, but still inexactly) with three numbers, perhaps representing the latitude,
longitude, and altitude of some point on the hydrant or, perhaps, its center of mass.
The spatial dimensions of a spatial pseudo-zero-dimensional object are insignificant with respect
to the context or environment in which it resides. A theoretical geometric point is the prototypical
example. Examples of such zero-dimensional objects on maps or in a GIS could be streetlights, parking
meters, oil wells, census tracts, or cities—depending on the spatial extent of other objects or features in
the database.
A spatial pseudo-one-dimensional object or feature has no more than one significant dimension or is
made up of essentially one-dimensional objects. A straight-line segment is the prototypical example. In
terms of making a one-dimensional object up from component parts, consider the example of a telephone
wire strung from one pole to the next to the next and so on. It is considered a one-dimensional object,
even though the poles may not be in a straight line, so that the phone line zigzags over a two-dimensional
field. (The line itself sags and persists in time—and therefore exists in a four dimensional context—but
these facts notwithstanding, it can be simplified or generalized into a one-dimensional feature—saving
us lots of computer storage, processing time, and conceptual complication.) Roads, school district
boundaries, pipes for fluid transportation, and contour lines on a topographic map are all examples of
pseudo one-dimensional entities.
You can disregard the up-down dimension in a spatial-pseudo-two dimensional object. Plain areas such as
voting districts and soybean fields are examples. Such pseudo-areas lack vertical components—variability in
altitude—that can be important. The true surface area of hilly terrain may be considerably underrepresented
by the plane area within the borders of the plane figure that represents it.
You must consider all dimensions of a spatial three-dimensional object in order to represent it. Three-
dimensional features are volumes—say, a coal seam or a building.
Relative to each other, positions of features that we record with a GIS do not move, or do not move
quickly, with respect to each other. Sometimes we want to know how conditions change or object move.
The representation of the objects may be zero-, one-, two-, or three-dimensional. At its most complex,
GIS would involve all four dimensions. Most GIS operations and data sets are two-dimensional; the data
are assumed to pertain to moments in time, or stable phenomena or conditions over a period of time.
Three-dimensional GIS could involve either three spatial dimensions (such as representing the volume
of a limestone quarry) or two spatial dimensions and varying time (showing historical changes in a
landscape). Rarely will you use four-dimensional GIS.
Results from a GIS are always only an approximation of reality. One of the reasons, among others to be
discussed later, is that we simplify objects by reducing their dimensionality.
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