106 THe geOgRaPHiC anD
CaRTOgRaPHiC FRaMeWORK
Zone of Least Deformation
0
o
Zone of Least
Deformation
Standard
Parallel
Zone of Least
Deformation
CYLINDRICAL
PROJECTION
AZIMUTHAL
PROJECTION
CONIC
PROJECTION
fIgURe 6.15.
Developable surfaces and zones of best representation.
60°
45°
30°
15°
0°
15°
30°
45°
60°
0°
90°
180°
270°
360°
fIgURe 6.16.
A simple cylindrical projection can be created geometrically.
The earth’s graticule and Projections 107
entire earth is represented on a flat map, the distortions become obvious and trouble-
some. Since many thematic maps are of countries or the entire earth, the selection of
a projection becomes of paramount importance. The cartographer must choose the
projection with the most advantages for the problem at hand and one for which the
distortions are least intrusive.
There are several ways of analyzing projection distortions. Tissot’s indicatrix,
which permits quantification of distortion, is frequently used. It is also possible to
draw
isoanamorphic lines (lines of equal distortion) on a projection to show distor-
tions graphically. Because this chapter is a nonmathematical introduction to projec-
tions,
I will take a more intuitive, if less rigorous, approach.
Scale varies from point to point on any projection, and at any point the scale may
vary in different directions. The variations can be measured by a
scale factor (SF).
The SF is equal to the scale on the reference globe at the point divided by the defined
scale. If SF = 1.0, there is no distortion.
Distortion is not random on projections; it follows a definite, orderly pattern for
each projection. On every projection there is a point (or points) or line(s) that is (are)
correct, that is, the SF is 1.0. These are called
standard points and
standard lines.
For a short distance away from the point or line, there is an area of minimum distor-
tion. This is called the
area of least deformation or the
zone of best representation.
By matching this zone with the area to be represented and considering the desirable
properties, the cartographer can choose a suitable projection.
In the discussion of
projection types that follows, the zone of best representation for the various groups
will be designated. Figure 6.15 shows the pattern of these zones for the major catego-
ries of projections.
