Transformations - Spatial Mathematics: Theory and Practice through Mapping - page 64

shopping centers. This is an example of a many-to-many relationship. In sum-
mary, you should join two tables when the data in the tables have a one-to-
one or a many-to-one relationship, and you should relate two tables when the
data in the tables have a one-to-many or many-to-many relationship.
3.1.3 QR codes
Bar codes, and their two-dimensional counterpart, QR codes, permit a trans-
formation from print to electronic format. We use them extensively through-
out this topic to explain concepts with animations, applets, extra color, and
so on either when those concepts cannot be included using standard print
media or when they are difficult or expensive to include in a different for-
mat. The Smartphone, loaded with an appropriate QR code reader, performs
the transformation. A few years ago, we might not even have dreamt of this
possibility; now this transformation is commonplace: QR codes appear in
advertising on buses or subways, on hospital wrist bands, on cemetery mark-
ers (W. E. Arlinghaus, 2011), and a host of unexpected spots. Where have you
seen them? Where might you see them? What sorts of applications might you
consider for them?
What is important is that one QR code might link to one location or many
different QR codes might link to a single location. The transformation is a
function. A single QR code, however, may not link to multiple locations—a
good thing! For example, a memorial QR code on a cemetery marker might
link to obituary text; another QR code posted in a local newspaper might also
link to the same obituary. That pattern would be fine; however, it would not
be fine to have the single QR code on the cemetery marker link to obituaries
of two different people! What sorts of far-reaching transformations might you
imagine?
3.2 Partition: Point-line-area transformations
3.2.1 Buffers
Often in spatial analysis, we seek to determine proximity—how far things
are from each other. Zones of proximity often involve a GIS concept known
as “buffering.” Around a point, a buffer of a specified distance becomes a
circle. Around a line segment, a buffer becomes a sausage-like shape, while
around a polygon, a buffer takes the shape of the polygon but appears rather
“inflated” or “puffy.”
Whether one considers accessibility to railroad service using linear buf-
fers of tracks, counts population in buffered bus routes, or selects minority
groups from within circular buffers intersecting census tracts, the buffer
has long served, and continues to serve, as a basis for making decisions
from maps. Buffers have a rich history in geographical analysis—long before
the advent of GIS software. Mark Jefferson (Jefferson, 1928) rolled a circle