Mapmakers have developed hundreds of map projections, over several
thousand years. Three large families of map projection, plus several
smaller ones, are generally acknowledged. These are based on the types
of geometric shapes that are used to transfer features from a sphere
or spheroid to a plane. As described above, map projections are based
on *developable surfaces*, and the three traditional
families consist of cylinders, cones, and planes. They are used to
classify the majority of projections, including some that are not
analytically (geometrically) constructed. In addition, a number of
map projections are based on polyhedra. While polyhedral projections
have interesting and useful properties, they are not described in
this guide.

Which developable surface to use for a projection depends on what region is to be mapped, its geographical extent, and the geometric properties that areas, boundaries, and routes need to have, given the purpose of the map. The following sections describe and illustrate how the cylindrical, conic, and azimuthal families of map projections are constructed and provides some examples of projections that are based on them.

A *cylindrical* projection is produced by
wrapping a cylinder around a globe representing the Earth. The map
projection is the image of the globe projected onto the cylindrical
surface, which is then unwrapped into a flat surface. When the cylinder
aligns with the polar axis, parallels appear as horizontal lines and
meridians as vertical lines. Cylindrical projections can be either
equal-area, conformal, or equidistant. The following figure shows
a regular cylindrical or *normal aspect* orientation
in which the cylinder is tangent to the Earth along the Equator and
the projection radiates horizontally from the axis of rotation. The
projection method is diagrammed on the left, and an example is given
on the right (equal-area cylindrical projection, normal/equatorial
aspect).

For a description of projection aspect, see Projection Aspect.

Some widely used cylindrical map projections are

Equal-area cylindrical projection

Equidistant cylindrical projection

Mercator projection

Miller projection

Plate Carrée projection

Universal transverse Mercator projection

All cylindrical projections fill a rectangular plane. *Pseudocylindrical* projection
outlines tend to be barrel-shaped rather than rectangular. However,
they do resemble cylindrical projections, with straight and parallel
latitude lines, and can have equally spaced meridians, but meridians
are curves, not straight lines. Pseudocylindrical projections can
be equal-area, but are not conformal or equidistant.

Some widely-used pseudocylindrical map projections are

Eckert projections (I-VI)

Goode homolosine projection

Mollweide projection

Quartic authalic projection

Robinson projection

Sinusoidal projection

A *conic* projection is derived from the
projection of the globe onto a cone placed over it. For the *normal
aspect*, the apex of the cone lies on the polar axis of
the Earth. If the cone touches the Earth at just one particular parallel
of latitude, it is called *tangent*. If made smaller,
the cone will intersect the Earth twice, in which case it is called *secant*.
Conic projections often achieve less distortion at mid- and high latitudes
than cylindrical projections. A further elaboration is the *polyconic* projection,
which deploys a family of tangent or secant cones to bracket a succession
of bands of parallels to yield even less scale distortion. The following
figure illustrates conic projection, diagramming its construction
on the left, with an example on the right (Albers equal-area projection,
polar aspect).

Some widely-used conic projections are

Albers Equal-area projection

Equidistant projection

Lambert conformal projection

Polyconic projection

An *azimuthal* projection is a projection
of the globe onto a plane. In polar aspect, an azimuthal projection
maps to a plane tangent to the Earth at one of the poles, with meridians
projected as straight lines radiating from the pole, and parallels
shown as complete circles centered at the pole. Azimuthal projections
(especially the orthographic) can have equatorial or oblique aspects.
The projection is centered on a point, that is either on the surface,
at the center of the Earth, at the antipode, some distance beyond
the Earth, or at infinity. Most azimuthal projections are not suitable
for displaying the entire Earth in one view, but give a sense of the
globe. The following figure illustrates azimuthal projection, diagramming
it on the left, with an example on the right (orthographic projection,
polar aspect).

Some widely used azimuthal projections are

Equidistant azimuthal projection

Gnomonic projection

Lambert equal-area azimuthal projection

Orthographic projection

Stereographic projection

Universal polar stereographic projection

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