Projections - A Primer of GIS: Fundamental Geographic and Cartographic Concepts - page 86

valuable for sailors, who could use one single compass
heading to determine the direct route between two
points.

Stereographic The widely used stereographic projection is an azimuthal

projection developed in the 2nd century B.C.E. that pre-
serves directions; it is a further development of much
older stereographic projections. It additionally has the
particular quality of showing all great circle routes as
straight lines; however, directions are true from only one
point on the projection. It is used usually to show air-
plane navigation routes.

Robinson The Robinson projection is a compromise projection that

fails to preserve any projection properties. It is graphically
attractive; it was adopted by National Geographic in 1988
and is widely used elsewhere.

Fuller The Fuller projection was introduced in 1954 by

Buckminster Fuller. It transforms spherical latitude and
longitude coordinates to a 20-sided figure called the
icosahedron .

Calculating Projections

Examining the mathematics of projections is helpful for grasping how a pro-
jection transforms locations measured in three dimensions to two-dimen-
sional locations. You should always note that projections are never transfor-
mations between two two-dimensional coordinate systems, but between
locations found on or near the surface of the three-dimensional planet earth
to a two-dimensional coordinate system.
The three examples examined here are widely used. The sinusoidal pro-
jection is a pseudocylindrical projection developed in the 16th century; the
Lambert conformal conic projection is widely used around the world for
east-to-west-orientated areas; the Mercator projection is very common. How-
ever, the mathematics for each map projection discussed here are quite
straightforward, especially since these examples are based on spheroids.

Sinusoidal Projection
The sinusoidal projection is a simple construction that shows areas correctly,
but shapes are increasingly distorted away from the central meridian. Paral-
lels of latitude are straight and longitudinal meridians appear as sine or
cosine curves.
The equations for calculating the sinusoidal projection are quite simple.
You only need to remember to use radians for the angle measures of longi-
tude and latitude and to place a negative sign in front of longitude values
from the western hemisphere.