Transformations - Spatial Mathematics: Theory and Practice through Mapping - page 66

buffers, also generates the bisector AB ( Figure 3.5b ) . The GIS notion of buffer,
or proximity, captured the Euclidean construction of perpendicular bisector.
3.2.3 Buffers build bisectors and proximity zones
If there are more than two points in a given distribution, and if one wishes
to find perpendicular bisectors within the whole set, the matter can quickly
become tedious. Mapping software again offers a quick and accurate way to
calculate bisector positions. We illustrate the conceptual basis on which this
might be done using circular buffers around a distribution of 25 Canadian cit-
ies (viewed as points). Figure 3.6 shows a pattern of circular Euclidean buf-
fers surrounding these points. The underlying multi-colored mesh of polygons
arises from the construction of perpendicular bisectors associated with these
buffers. The bisectors are edges of the polygons, and the polygons serve as
proximity zones. The reader may find other names used for such zones or
Figure 3.6. Buffers build bisectors and proximity zones around a set of points and
these bisectors in turn create proximity zones. QR code links to an associated ani-
mation. Source: Arlinghaus, S. L. 2001. Base Maps, Buffers, and Bisectors. Solstice:
An Electronic Journal of Geography and Mathematics. Vol. XII, No. 2. Ann Arbor:
Institute of Mathematical Geography. Source of base map: Esri software. http://
www-personal.umich.edu/%7Ecopyrght/image/solstice/win01/sarhaus