Graphics Programs Reference
In-Depth Information
This projection does not preserve shapes. Landmasses away from the central merid-
ian are sheared, making them look extremely deformed or even unrecognizable.
An interrupted version of this projection reduces distortions considerably because
(1) the scale on the equator is uniform, (2) the meridians cross it at right angles, and
(3) the vertical scale of the projection does not vary along the equator for different
longitudes.
It is worth mentioning that the sinusoidal and Mollweide projections handle polar
regions in complementary ways; while the former crowds them together, the latter results
in widely spaced meridians, which leads to more pronounced angular distortion. These
two projections are combined in Goode's homolosine projection.
The Eckert IV equal-area world map projection (Figure 4.58) is the fourth in a
set of six projections developed in the 1920s by Max Eckert as a pseudocylindrical
compromise projection to obtain equal areas. The projection is in the form of a capsule,
similar to an ellipse but larger, with curved lines of longitude (see also Figure 4.27).
The outer meridians are semicircles, and the inner meridians are elliptical arcs. The
central meridian is straight and its height is identical to the length of the equator.
Figure 4.58: Eckert IV Projection.
The mathematical expression of this projection starts with a point with longitude
θ and latitude φ on the sphere. The point is mapped by this projection to the point
θ 0 )(1 + cos α )and y =2 π
2
π (4 + π )
x =
( θ
4+ π sin α
on the map, where θ 0 is the longitude at the center of the map and α is the solution to
the equation α +sin α cos α +2sin α =(2+ π/ 2) sin α .
 
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