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odd-numbered addresses are on the east side of the north-south streets. Suppose
you have been directed to find an even address on Woodlawn, somewhere “near”
57th Street, on the left side of Woodlawn. If you begin at the node, head north
on Woodlawn, look on the left side of Woodlawn and find it is not there (even
though you are looking at even numbers that are perhaps too low), then proceed
back past the node along the indicated path, as you look on the left, you will now
be looking at the odd-numbered addresses. You will not be able to execute with
accuracy. Again, the problem is solved by removing the node.
Thus, when working with digital maps, it is important to know that the digi-
tizing process did not introduce any polygons that cross themselves, and, that
any nodes that produce such crossings were removed in the digitizing pro-
cess. The examples above are straightforward; it is not always that straightfor-
ward when actually digitizing a complicated street map. Fortunately, digital
maps made since 1990 and the release of the first TIGER/Line files providing
nationwide street centerline coverage of the United States (US Census Bureau,
2012), are free from this difficulty.
However, the USGS Digital Line Graphs (DLG), another commonly used vector
data set, have no standard about the order of digitizing. Therefore, adjacent
line segments may start and end in different orders and thus contain differ-
ent directions as part of their attributes. When one wishes to select a certain
polygon, therefore, through the use of these line segments, one needs to use
statements like “select line segment A where the left side polygon = 1 OR the
right side polygon = 1,” to account for the different directions in which a line
segment was digitized. Not including the “OR” statement can lead to a smaller
number of polygons being selected, potentially skewing the resulting analysis.
Therefore, it remains relevant to understand the sort of unintended conse-
quence that a lack of attention to underlying geometry, and order within that
geometry, might cause. One must have the Jordan Curve Theorem built into
the software if geocoding is to work on address, color, or other assignment
problems matching data to spatial units. This process that involves “order” is
critical, but unseen by most readers of maps.
Try your hand at the Esri geocoding exercise linked at the end of this chapter.
Geocoding, in one form, is the process of associating geographic location to
street addresses. It can involve, therefore, concepts such as “all of the even
numbers lie along the west side of the street.” As you work the exercise, think
about what sorts of problems might have arisen if considerations involving
digitizing order and the Jordan Curve Theorem had not been integrated into
the software background.
6.5 Making something from nothing?
The Thiessen polygons in Chapter 3 illustrated one way to create polygons
from a scatter of points. There are a variety of others, as well, that permit the
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