104 THe geOgRaPHiC anD
CaRTOgRaPHiC FRaMeWORK
poorly represented (Figure 6.14). This is a very useful group of projections for much
thematic map work.
Projection surface
A second common way to classify projections is by the projection surface. Surfaces
that can be cut and flattened without distortion
or tearing are called developable
surfaces. The sphere is not a developable surface; it cannot be flattened without dis-
tortion or tearing. If, however, the graticule is transformed
onto a surface that is
developable, that surface can be flattened without any additional distortion (Figure
6.15). A cone can be placed on a globe, the graticule projected onto it, and the cone
then unrolled into a plane. The cylinder and the plane may also be used as projection
surfaces; the cylinder can be flattened and the plane is already flat. The cylinder and
plane may be thought of as extreme cases of a cone. A cone that touches the equator
and has therefore an infinitely high apex is a cylinder, and as cones are placed on
higher
and higher parallels, they approach the plane.
Projection, in theory, is a two-stage process. First, an imaginary globe is created
at the intended scale. The imaginary globe is called the
generating globe or
reference
Mollweide
Mercator
fIgURe 6.13.
The Mollweide projection is equal area and the Mercator is conformal. Com-
pare the size of Greenland and South America on the two projections.
The earth’s graticule and Projections 105
globe. The scale of the map projection is called the
defined scale or the
nominal scale
and is the same as that of the generating globe. The second stage is to project the
globe onto a plane.
If we imagine one of the developable forms placed on a transparent reference
globe with a light source inside, we can then visualize the earth’s graticule being pro-
jected onto the developable surface. The name of each group of projections is taken
from the surface upon which the map is projected. Consequently, we have cylindri-
cal, conic, and plane projections. A final group of projections is made up of those
that cannot in any way be imagined as projected onto one of these surfaces. Various
names are given to these last, the most common being
mathematically devised or
conventional projections.
Of course, projections are not normally created by a light source and a globe;
this would be done only for demonstration or teaching purposes. They are created
mathematically and drawn by a computer or, in the past, manually constructed geo-
metrically or from tables (Figure 6.16). Only a limited
number of projections can
actually be projected by light or by geometric projection (these are called
perspective
projections); but if a projection has the general appearance characteristics of a cylin-
drical projection, for example, it is placed in this class.
