Editing Map projection (section)

==Projections by preservation of a metric property==

===Conformal===
{{Main|Conformal map projection}}
[[File:Usgs map stereographic.PNG|thumb|upright=2|A [[stereographic projection]] is conformal and perspective but not equal area or equidistant.]]
[[Conformal map|Conformal]], or orthomorphic, map projections preserve angles locally, implying that they map infinitesimal circles of constant size anywhere on the Earth to infinitesimal circles of varying sizes on the map. In contrast, mappings that are not conformal distort most such small circles into [[Tissot's indicatrix|ellipses of distortion]]. An important consequence of conformality
is that relative angles at each point of the map are correct, and the local scale (although varying throughout the map) in every direction around any one point is constant. These are some conformal projections:
* [[Mercator projection|Mercator]]: [[Rhumb line]]s are represented by straight segments
* [[Transverse Mercator projection|Transverse Mercator]]
* [[Stereographic projection in cartography|Stereographic]]: Any [[circle of a sphere]], great and small, maps to a circle or straight line.
* [[Roussilhe oblique stereographic projection|Roussilhe]]
* [[Lambert conformal conic projection|Lambert conformal conic]]
* [[Peirce quincuncial projection]]
* [[Adams hemisphere-in-a-square projection]]
* [[Guyou hemisphere-in-a-square projection]]

===Equal-area===<!-- [[Equiareal]] links to here -->
{{Main|Equal-area projection}}
[[File:Mollweide projection SW.jpg|thumb|300px| The equal-area [[Mollweide projection]]]]

Equal-area maps preserve area measure, generally distorting shapes in order to do so. Equal-area maps are also called ''equivalent'' or ''authalic''. These are some projections that preserve area:

{{div col|colwidth=25em}}
* [[Albers conic projection|Albers conic]]
* [[Boggs eumorphic projection|Boggs eumorphic]]
* [[Bonne projection|Bonne]]
* [[Bottomley projection|Bottomley]]
* [[Collignon projection|Collignon]]
* [[Cylindrical equal-area projection|Cylindrical equal-area]]
* [[Eckert II projection|Eckert II]], [[Eckert IV projection|IV]] and [[Eckert VI projection|VI]]
* [[Equal Earth projection|Equal Earth]]
* [[Gall–Peters projection|Gall orthographic]] (also known as Gall–Peters, or Peters, projection)
* [[Goode homolosine projection|Goode's homolosine]]
* [[Hammer projection|Hammer]]
* [[Hobo–Dyer projection|Hobo–Dyer]]
* [[Lambert azimuthal equal-area projection|Lambert azimuthal equal-area]]
* [[Lambert cylindrical equal-area projection|Lambert cylindrical equal-area]]
* [[Mollweide projection|Mollweide]]
* [[Sinusoidal projection|Sinusoidal]]
* [[Strebe 1995 projection|Strebe 1995]]
* [[Snyder equal-area projection|Snyder's equal-area polyhedral projection]], used for [[geodesic grid]]s.
* [[Tobler hyperelliptical projection|Tobler hyperelliptical]]
* [[Werner projection|Werner]]
{{div col end}}

===Equidistant===
[[File:Two-point equidistant projection SW.jpg|thumb|right|A [[two-point equidistant projection]] of Eurasia]]
If the length of the line segment connecting two projected points on the plane is proportional to the geodesic (shortest surface) distance between the two unprojected points on the globe, then we say that distance has been preserved between those two points. An '''equidistant projection''' preserves distances from one or two special points to all other points. The special point or points may get stretched into a line or curve segment when projected. In that case, the point on the line or curve segment closest to the point being measured to must be used to measure the distance.
* [[Plate carrée projection|Plate carrée]]: Distances from the two poles are preserved, in equatorial aspect.
* [[Azimuthal equidistant projection|Azimuthal equidistant]]: Distances from the center and edge are preserved.
* [[Equidistant conic projection|Equidistant conic]]: Distances from the two poles are preserved, in equatorial aspect.
* [[Werner cordiform projection|Werner cordiform]] Distances from the [[North Pole]] are preserved, in equatorial aspect.
* [[two-point equidistant projection|Two-point equidistant]]: Two "control points" are arbitrarily chosen by the map maker; distances from each control point are preserved.

===Gnomonic===
[[File:Usgs map gnomic.PNG|thumb|upright=2|The [[Gnomonic projection]] is thought to be the oldest map projection, developed by [[Thales]] in the 6th century BC]]

[[Great circle]]s are displayed as straight lines:
* [[Gnomonic projection]]

===Retroazimuthal===
Direction to a fixed location B (the bearing at the starting location A of the shortest route) corresponds to the direction on the map from A to B:
* [[Littrow projection|Littrow]]—the only conformal retroazimuthal projection
* [[Hammer retroazimuthal projection|Hammer retroazimuthal]]—also preserves distance from the central point
* [[Craig retroazimuthal projection|Craig retroazimuthal]] ''aka'' Mecca or Qibla—also has vertical meridians

===Compromise projections===
[[File:Usgs map robinson.PNG|thumb|upright=2|The [[Robinson projection]] was adopted by ''[[National Geographic (magazine)|National Geographic]]'' magazine in 1988 but abandoned by them in about 1997 for the [[Winkel tripel projection|Winkel tripel]].]]

Compromise projections give up the idea of perfectly preserving metric properties, seeking instead to strike a balance between distortions, or to simply make things look right. Most of these types of projections distort shape in the polar regions more than at the equator. These are some compromise projections:
* [[Robinson projection|Robinson]]
* [[Van der Grinten projection|van der Grinten]]
* [[Miller cylindrical projection|Miller cylindrical]]
* [[Winkel tripel projection|Winkel Tripel]]
* [[Dymaxion map|Buckminster Fuller's Dymaxion]]
* [[Bernard J. S. Cahill|B. J. S. Cahill's Butterfly Map]]
* [[Kavrayskiy VII projection]]
* [[Wagner VI projection]]
* [[Chamberlin trimetric projection|Chamberlin trimetric]]
* [[Oronce Finé]]'s cordiform
* [[AuthaGraph projection]]