A map is a
transformation between the curved surface of the earth and the flat
plane of the map. Distortions always result from this transformation.
They may affect conformality, distance, direction, scale, or area
When the scale of a map at any point on the map is the
same in any direction, the projection is conformal. Meridians (lines
of longitude) and parallels (lines of latitude) intersect at right
angles. Shape is preserved locally on conformal maps; scale may
change from point-to-point.
A map is equidistant when it accurately portrays great
circle distances from the center of the projection to any other place
on the map. An equidistant map cannot accurately show great circle
distances from all points to all other points.
A map preserves direction when azimuths (angles from a
point on a line to another point) are portrayed correctly in all
Scale is the relationship between a distance portrayed
on a map and the same distance on the Earth. Azimuthal maps accurately
show true directions from one point to all other points on the map.
Azimuthal maps accurately show directions accurately only from a
single central point (or sometimes two central points).
When a map portrays areas over the entire map so that
all mapped areas have the same proportional relationship to the areas
on the Earth that they represent, the map is an equal-area map.
Projections seek to minimize distortions of one
or more of these factors, but they do so only at the expense of
distortions of other factors. For example, in Mercator's projection, a
course from one point to another can be represented as a straight line
between the two points, which makes the projection very useful for
navigation. But it does not preserve the relationship of areas, so
that the size of Greenland is much larger on the map than in reality.