# Map Projection

A map projection is a mathematical set of equations for taking a position on the three dimensional earth onto a flat map.  For the Mercator projection, this keeps parallels and meridians perpendicular.  The only way to do this is to increase the scale in north-south direction because the meridians should be converging toward the poles.  To keep the angles and local distances on the map correct, the east-west dimensions increase by the same amount.  This scaling factor increases from 1 at the equator to ¥ at the poles (which can thus never appear on a Mercator map).

The x and y coordinates on the map can be plotted like a regular graph.  They may or may not actually appear on the map?for ground maps used by the Army and Marines they are the preferred way to report positions, although with a UTM projection and  not with a Mercator projection.  The actual equations, especially for an elliptical earth, can be quite messy.

• Projection(lat, long, earth radius)  à Map(x,y)

• InverseProjection(Map x,y) à Earth(lat, long, earth radius)

last revision 1/11/2017