102 THe geOgRaPHiC anD
CaRTOgRaPHiC FRaMeWORK
1.
Equivalence of area. Maps that preserve area scale are called
equal-area or
equivalent projections.
2.
Preservation of angles or of shape of small areas. Projections that have this
proporty
are called conformal or
orthomorphic projections.
3.
Linear scale. Projections that preserve the linear scale for some part of the
map are called
equidistant projections.
4.
Direction, specifically azimuths. These projections are called
azimuthals or
zenithals.
There are various other properties, such as showing great circles as straight lines
and the like, but these have no specific category. A last category is a
compromise
group that has no special properties, but presents a good general appearance that is
not terribly distorted in any of the properties.
eQUiVaLenT PROJeCTiOns
A uniform area scale is maintained on equivalent or equal-area projections. Equiva-
lence is obtained by matching stretching with compression. That is, if there is stretch-
ing in one dimension, there must be equal compression in the orthogonal (at right
angles) dimension. To do this, angles may be distorted, which means that shape is
sacrificed. The shapes in Figure 6.11 all have the same area. It is possible to maintain
equivalence throughout the projection.
COnFORMaL PROJeCTiOns
These
are also called orthomorphic projections. Often conformal projections are
incorrectly described as true-shape projections, but the shape quality is limited. Con-
formal projections preserve angles with infinitely short sides; therefore, only small
features, such as a bay or peninsula, retain correct shape; larger areas, such as coun-
tries or continents, are distorted in overall configuration.
Conformality is achieved by meeting two conditions: (1) parallels and meridians
must cross at right angles, and (2) scale must be the same in all directions about a
