Map Projections
 The world according to the equatorial aspect of Lambert's azimuthal equal-area projection. Unprojected original satellite data by NASA

## Summary

Several approaches attempt to classify projections. Most are orthogonal, thus any single projection may belong simultaneously to different categories. In others, like biology-inspired Maurer's, a branching taxonomy is applied.

Please note that, for ease of definition and visualization, some categories and projections are informally described below in terms of parallels and meridians, thus some properties may seem to depend on the particular aspect used for the map. For instance, the coordinate lines in cylindrical maps cross at right angles in equatorial, but not in polar or oblique maps, although all other properties still hold; after all, the coordinate grid is only a set of conventional lines.

### Projections Classified by Geometry

 Category Properties Azimuthal Also called zenithal. Shows true directions (azimuths) from a single point; in polar aspects all parallels are circular, and meridians are straight lines uniformly spaced and concurring at a point; an unclipped world map is a disc. Cylindrical Defined by analogy to a cylinder as an intermediate projection surface; in the equatorial aspect all parallels and meridians are straight lines; meridians are orthogonal to parallels and uniformly spaced; an unclipped world map is rectangular Conic By analogy to a conic intermediate projection surface; in the polar aspect all parallels are concentric arcs of circle, while meridians are straight lines perpendicular to every parallel, uniformly spaced by less than on Earth; unclipped maps are circular or annular sectors Pseudocylindrical In the equatorial aspect all parallels are straight parallel lines; meridians are arbitrary curves, equally spaced along every parallel Pseudoconic In the polar aspect all parallels are concentric circular arcs, while meridians are arbitrary curves Arbitrary or compromise Parallels and meridians are arbitrary curves; usually no purely geometric construction is defined. Some authors call "arbitrary", "conventional" or "compromise" any projection not derived from geometric devices, but custom-fit to a purpose

In a sense, the cone includes as extreme cases both the cylinder (a cone with vertex at the infinite) and the plane (a cone with zero height). Therefore, the conic group generalizes the azimuthal and cylindrical and, broadly, pseudocylindrical and pseudoconic projections. Also, some consider a polyconic group to include projections where parallels are derived from circles, including modified azimuthals like Hammer's and Aitoff's. Actually, many so-called "azimuthal", "conic" or "cylindrical" projections are not built on a pure projective process using solids, but are so classified due to geometrical properties of the mapped coordinate grid.

Also, a projective, geometric or perspective projection can be described in exact analogy to a geometric set-up of light rays connecting the original surface to the map surface. Some authors call other projections "mathematical".

 In azimuthal projections, the angles between straight lines radiating from the center of projection (which may or may not coincide with the center of the map) are the same for the corresponding lines on Earth. On the azimuthal equidistant map on the left, distances along those lines are also directly proportional to those on Earth. On the equal-area sinusoidal map (top right), for any two identical boundaries (like the blue squares), their counterparts on Earth will enclose the same area, although they will not necessarily have the same shape. That pseudocylindrical projection preserves angles only along the two axes (green); it is equidistant (red) only along those axes and all lines perpendicular to the minor axis. Unlike almost every other conformal projections, Eisenlohr's (bottom right) preserves small angles at every point: the green lines are perpendicular on both Earth and map. Areal and distance distortion are large, but less than in typical conformal maps.

### Projections Classified by Property

 Category Properties Equal-area Any region in the map has area directly proportional to the corresponding region on the sphere; also called equivalent or authalic. Generally more useful for statistical comparisons and didactic purposes. Equidistant On the map there are two sets of points A and B, such that, along a selected set of lines (not necessarily straight), distances from any point in A to another in B are proportional to the distances between corresponding points on the sphere, again along those corresponding lines.  In other words, scale is constant on those lines, which are called standard.  Most projections have such sets but few are actually called "equidistant". Conformal In any* small region of the map, two concurrent lines have the same angle as corresponding lines on the sphere, thus shapes are locally preserved. Also called orthomorphic or autogonal. Most important for navigational purposes and large-scale mapping, especially in the ellipsoidal case. *In almost every conformal projection, at least one point (frequently a pole is chosen) either can not be represented or fails conformality. Aphylactic Some authors use this name for those projections which are neither conformal nor equivalent.

### Projections in a Nutshell

Projections enumerated below are described in further detail. This is just a small sample of all existing designs, not necessarily the most important or most commonly used; as such, the selection is necessarily subjective. Equally arbitrary is whether changing the aspect or another minor detail is enough to justify a separate entry (cf. e.g., Cassini's v. equidistant cylindrical, Gauss transverse v. Mercator and Petermann v. Berghaus).