## The Three Main Families of Map Projections

### Unwrapping the Sphere to a Plane

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. 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.

### Cylindrical Projections

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

#### Pseudocylindrical Map Projections

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

### Conic Projections

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

### Azimuthal Projections

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