Editing Map projection (section)

{{short description|Systematic representation of the surface of a sphere or ellipsoid onto a plane}}
[[File:Claudius Ptolemy- The World.jpg|thumb|upright=1.35|A medieval depiction of the [[Ecumene]] (1482, Johannes Schnitzer, engraver), constructed after the coordinates in Ptolemy's [[Geography (Ptolemy)|''Geography'']] and using his second map projection]]
In [[cartography]], a '''map projection''' is any of a broad set of [[Transformation (function) | transformation]]s employed to represent the curved two-dimensional [[Surface (mathematics)|surface]] of a [[globe]] on a [[Plane (mathematics)|plane]].<ref>{{cite book |last1=Lambert |first1=Johann |last2=Tobler |first2=Waldo |title=Notes and comments on the composition of terrestrial and celestial maps |date=2011 |publisher=ESRI Press |location=Redlands, CA |isbn=978-1-58948-281-4}}</ref><ref>{{cite book |last1=Richardus |first1=Peter |last2=Adler |first2=Ron |title=map projections |date=1972 |publisher=American Elsevier Publishing Company, inc. |location=New York, NY |isbn=0-444-10362-7}}</ref><ref>{{cite book |last1=Robinson |first1=Arthur |last2=Randall |first2=Sale |last3=Morrison |first3=Joel |last4=Muehrcke |first4=Phillip |title=Elements of Cartography |date=1985 |publisher=Wiley |isbn=0-471-09877-9 |edition=fifth}}</ref> In a map projection, [[coordinates]], often expressed as [[latitude]] and [[longitude]], of locations from the surface of the globe are transformed to coordinates on a plane.<ref name='Snyder1453'>{{cite book
 |author1      = Snyder, J.P.
 |author1-link = John P. Snyder
 |author2      = Voxland, P.M.
 |title        = Album of Map Projections
 |chapter = An album of map projections
 |publisher    = United States Government Printing Office
 |date         = 1989
 |url          = https://pubs.usgs.gov/pp/1453/report.pdf
 |series       = U.S. Geological Survey Professional Paper
 |volume       = 1453
 |access-date  = 8 March 2022
 |doi          = 10.3133/pp1453
}}</ref><ref name="EGmap">{{Cite journal|last=Ghaderpour|first=E.|date=2016|title=Some equal-area, conformal and conventional map projections: a tutorial review|journal=Journal of Applied Geodesy|volume=10|issue=3|pages=197–209|doi=10.1515/jag-2015-0033|arxiv=1412.7690|bibcode=2016JAGeo..10..197G|s2cid=124618009}}</ref>
Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography.

All projections of a sphere on a plane necessarily distort the surface in some way.<ref>{{cite book |last1=Monmonier |first1=Mark |title=How to lie with maps |date=2018 |publisher=The University of Chicago Press |isbn=978-0-226-43592-3 |edition=3rd}}</ref> Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections.<ref name="SnyderFlattening">
{{cite book
  | author    = Snyder, John P.
  | author-link = John P. Snyder
  | title     = Flattening the earth: two thousand years of map projections
  | publisher = [[University of Chicago Press]]
  | year      = 1993
  | isbn      = 0-226-76746-9
  }}
</ref>{{rp|1}}
More generally, projections are considered in several fields of pure mathematics, including [[differential geometry]], [[projective geometry]], and [[manifold]]s. However, the term "map projection" refers specifically to a [[Cartography|cartographic]] projection.

Despite the name's literal meaning, projection is not limited to [[3D projection#Perspective projection|perspective projections]], such as those resulting from casting a shadow on a screen, or the [[rectilinear projection|rectilinear]] image produced by a [[pinhole camera]] on a flat film plate. Rather, any mathematical function that transforms coordinates from the curved surface distinctly and smoothly to the plane is a projection. Few projections in practical use are perspective.{{cn|date=November 2019}}

Most of this article assumes that the surface to be mapped is that of a sphere. The [[Earth]] and other large [[celestial bodies]] are generally better modeled as [[oblate spheroid]]s, whereas small objects such as [[asteroid]]s often have irregular shapes. The surfaces of planetary bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid.<ref>{{Citation|last1=Hargitai|first1=Henrik|title=Map Projections in Planetary Cartography|date=2017|pages=177–202|publisher=Springer International Publishing|isbn=978-3-319-51834-3|last2=Wang|first2=Jue|last3=Stooke|first3=Philip J.|last4=Karachevtseva|first4=Irina|last5=Kereszturi|first5=Akos|last6=Gede|first6=Mátyás|series=Lecture Notes in Geoinformation and Cartography |doi=10.1007/978-3-319-51835-0_7}}</ref>

The most well-known map projection is the [[Mercator projection]].<ref name="SnyderFlattening"/>{{rp|45}} This map projection has the property of being [[Conformal map projection|conformal]]. However, it has been criticized throughout the 20th century for enlarging regions further from the equator.<ref name="SnyderFlattening"/>{{rp|156{{ndash}}157}} To contrast, [[equal-area projection]]s such as the [[Sinusoidal projection]] and the [[Gall–Peters projection]] show the correct sizes of countries relative to each other, but distort angles. The [[National Geographic Society]] and most atlases favor map projections that compromise between area and angular distortion, such as the [[Robinson projection]] and the [[Winkel tripel projection]].<ref name="SnyderFlattening" /><ref>{{cite news |title=Which is the best map projection? |url=https://geoawesomeness.com/best-map-projection/ |work=Geoawesomeness |date=25 April 2017 |first=Ishveena |last=Singh}}</ref>