Nonlinear Projections - Transformations and Projections in Computer Graphics - page 206

A distance measured along a meridian will have true scale because all the meridians
have the same length. Given a projection with such meridians, how can we draw the
latitudes so as to preserve scale along them too? There seems to be no solution to this
problem because the latitudes get shorter as we approach the poles and the only way
to fit shorter latitudes among the longitudes is to bend the longitudes. Thus, there is
no cylindrical projection that preserves distances along both dimensions.
Pseudocylindrical projections . All the cylindrical projections discussed here
(and also those not mentioned here) feature noticeable shape distortions at higher lati-
tudes (where area is normally also greatly exaggerated). The poles are either infinitely
stretched to lines or are impossible to include in the projection. Various pseudocylindri-
cal projections have therefore been developed in attempts to correct these shortcomings.
These projections feature (1) straight horizontal parallels, not necessarily equidistant,
and (2) arbitrary curves for meridians, equidistant along every parallel.
The horizontal parallels help to compute and predict phenomena that depend on
distance from the equator such as the lengths of day and night. The constant scale at
any point of a parallel makes it easy to measure distances in the direction of a latitude.
Parallels and meridians do not always cross at right angles in a pseudocylindrical
projection, which is why this type is nonconformal. Most pseudocylindrical projections
are known to cause severe shape distortions at polar regions.
Figure 4.56: Mollweide Projection.
The following are examples of pseudocylindrical projections:
The Mollweide projection (Figure 4.56) was created in 1805 by Karl Mollweide and
popularized by Jacques Babinet in 1857. This equal-area projection was designed to
inscribe the world into a 2: 1 ellipse, keeping the latitudes straight while still preserving
areas. It was developed for educational purposes. All meridians except the central one
are equally spaced semiellipses intersecting at the poles and concave toward the central