Geography Reference
In-Depth Information
coni guration of streets in Manhattan, New York. Manhattan distances are the sum of
distances along each grid segment connecting the start and end points. Network dis-
tances are distances along networks. An example is distances along a road network,
using the kind of vector structures detailed in Section 2.2. h is topic details a variety
of ways of representing distances. h ese include friction surfaces, whereby the 'cost' of
moving over a particular area of land is taken into account (see Section 10.6).
Measuring lengths and perimeters
4.3
With raster grids, lengths can be measured along cells (as outlined above) or in terms
of Euclidean distances between, for example, cell centroids. In the former case, mea-
surement requires information on the spatial resolution of cells and their number.
In a simple case, if we are measuring the length along the side of i ve cells and their
spatial resolution is 10 m, then clearly the distance is 5 ¥ 10 = 50 m. Another way of
dealing with distance travelled over raster grids, the use of friction (cost) surfaces, is
discussed in Section 10.6. Measurement of lengths of vector features is discussed next.
4.3.1 Length of vector features
Lines can be measured simply by calculating the length of each line segment using
Pythagoras' theorem (see Section 4.2) and summing the lengths of each segment
that makes up a line. Perimeters of polygons can be measured in the same way by
working from one polygon node, around the polygon, and back to the same node.
Measurement of line lengths is a common task in GIS contexts. As an example, appli-
cations concerning road networks (see Chapter 6) ot en make use of information on
the length of road networks.
Measuring areas
4.4
Measurement of areas with raster grids is straightforward. If n cells belong to a given
class then the area of a cell (given by the spatial resolution squared) is simply multi-
plied by n to get the total area covered by pixels in that class. Measurement of the areas
of vector polygons is outlined in the following section. Many applications require
information on the areas of zones. As an example, to compute population density in
an area both the total population and the area of the zone are required.
4.4.1 Areas of polygons
h e area of a polygon can be calculated by:
n
Â
A
0.5
y
¥ -
(
x
x
)
(4.2)
i
i
+
1
i
-
1
i
=
1
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