Projections - Families / Distortion Control
The picture given on the last page showed a cylinder of paper standing vertically around the earth. Lines were projected from the center of the earth to the paper. When the projection is finished, the paper is cut and the cylinder unrolled to make the map. This is the Mercator projection. It is true along the equator, good near the equator but distorted at high latitudes. The poles are off the map. But the map is conformal (angles are true).
This is a common projection for world maps. But it has a lot of distortion. Compare Greenland and South America on a Mercator projection (Greenland is bigger) and on a globe.
Families
Originally when projections had a geometric interpretation, they were grouped into families. The grouping was according to the shape of the paper.
The bold lines on the cylindrical and conic cases represent standard lines. These are where the scale of the map is true. In these cases the lines are where the paper touches the earth. The scale is not true away from these lines, and generally get worse the further you go from the tangent lines. One way to control the distortion is to "depress the paper" into the earth. Now there will be two standard lines, where the paper cuts the earth. Several common projections do this. They generally have the standard lines about 10 percent from the edge.
The most common map projection from the United States is the Lambert conformal conic. It does this. The military favor the Universal Transverse Mercator (UTM) projection. This also depresses the paper into the earth to control the maximum distortion.
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