Cartography

Cartography is the study and practice of mapmaking.

Map projections can be grouped into several categories, not all disjoint. The projections are described in terms of placing a gigantic sheet of paper in contact with the earth, followed by an implied scaling operation.

Azimuthal projections

These projections touch the earth to a plane at a tangent point; angles from that tangent point are preserved, and distances from that point are computed by a function independent of the angle.

• Azimuthal equidistant projection is used by amateur radio operators to know the direction to point their antennas toward a point and see the distance to it. Distance from the tangent point on the map is equal to surface distance on the earth.
• Azimuthal equal-area projection. Distance from the tangent point on the map is equal to straight-line distance through the earth.
• Azimuthal conformal projection is the same as stereographic projection.
• Azimuthal orthographic projection maps each point on the earth to the closest point on the plane.

Conformal projections

Conformal map projections preserve angles.

• Mercator projection wraps a cylinder around the earth; the distance from the equator on the map is ln(tan(lat/2+pi/4)). (Someone please check this)
• Stereographic projection touches a plane to the earth and projects each point in a straight line from the antipode of the tangent.

Equal-area projections

These projections preserve area.

• Gall-Peters projection wraps a cylinder around the earth and maps each point on the earth to the nearest point on the cylinder.
• Azimuthal equal-area: see above.
• Cordiform projection designates a pole and a meridian; distances from the pole are preserved, as are distances from the meridian (which is straight) along the parallels.

Shape of the Earth

The projection is also affected by how the shape of the earth is approximated. In the above discussion, I assumed a sphere, but the Earth is not exactly spherical.

For more accurate coordinates, the Earth can be represented by a spheroid that "squashes" the sphere into a regular oval-shaped solid.

Even more accuracy can be gained by representing the Earth as a geoid, which takes the spheroid and adds irregularities to it to better match the Earth?s actual shape.

The projection is also affected by the geographic datum that is used.

See also: Cartographer, GIS, Gall-Peters projection, Van der Grinten projection, Mercator projection, Robinson projection, Winkel Tripel projection