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If the azimuth value from a to b is the same on a map as on the
Earth, then the map preserves direction from a to b. An azimuthal
projection is one that preserves direction for all straight lines passing
through a single, specified point. No map has true direction
everywhere.
Figure 6.4. A few projections with different properties.
The Lambert Conformal Conic preserves shape. The Mollweide
preserves area. (Compare the relative sizes of Greenland and South
America in one and then the other.) The Orthographic projection
preserves direction. The Azimuthal Equidistant preserves both
distance and direction. The Winkel Tripel is a compromise projection.
Measuring distortion using Tissot's Indicatrix
In the nineteenth century, Nicolas Auguste Tissot developed a
method to analyze map projection distortion (figure 5.5.). An
infinitely small circle on the earth's surface will be projected as an
infinitely small ellipse on any given map projection. The resulting
ellipse of distortion, or indicatrix, shows the amount and type of
distortion at the location of the ellipse. For example, if an indicatrix is
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