List of map projections

This is a summary of map projections that have articles of their own on Wikipedia or that are otherwise notable. Because there is no limit to the number of possible map projections,[1] there can be no comprehensive list.

Table of projectionsEdit

Projection Image Type Properties Creator Year Notes
Equirectangular
= equidistant cylindrical
= rectangular
= la carte parallélogrammatique
  Cylindrical Equidistant Marinus of Tyre 0120 c. 120 Simplest geometry; distances along meridians are conserved.

Plate carrée: special case having the equator as the standard parallel.

Cassini
= Cassini–Soldner
  Cylindrical Equidistant César-François Cassini de Thury 1745 Transverse of equidistant projection; distances along central meridian are conserved.
Distances perpendicular to central meridian are preserved.
Mercator
= Wright
  Cylindrical Conformal Gerardus Mercator 1569 Lines of constant bearing (rhumb lines) are straight, aiding navigation. Areas inflate with latitude, becoming so extreme that the map cannot show the poles.
Web Mercator   Cylindrical Compromise Google 2005 Variant of Mercator that ignores Earth's ellipticity for fast calculation, and clips latitudes to ~85.05° for square presentation. De facto standard for Web mapping applications.
Gauss–Krüger
= Gauss conformal
= (ellipsoidal) transverse Mercator
  Cylindrical Conformal Carl Friedrich Gauss

Johann Heinrich Louis Krüger

1822 This transverse, ellipsoidal form of the Mercator is finite, unlike the equatorial Mercator. Forms the basis of the Universal Transverse Mercator coordinate system.
Roussilhe oblique stereographic Henri Roussilhe 1922
Hotine oblique Mercator   Cylindrical Conformal M. Rosenmund, J. Laborde, Martin Hotine 1903
Gall stereographic
  Cylindrical Compromise James Gall 1855 Intended to resemble the Mercator while also displaying the poles. Standard parallels at 45°N/S.
Miller
= Miller cylindrical
  Cylindrical Compromise Osborn Maitland Miller 1942 Intended to resemble the Mercator while also displaying the poles.
Lambert cylindrical equal-area   Cylindrical Equal-area Johann Heinrich Lambert 1772 Standard parallel at the equator. Aspect ratio of π (3.14). Base projection of the cylindrical equal-area family.
Behrmann   Cylindrical Equal-area Walter Behrmann 1910 Horizontally compressed version of the Lambert equal-area. Has standard parallels at 30°N/S and an aspect ratio of 2.36.
Hobo–Dyer   Cylindrical Equal-area Mick Dyer 2002 Horizontally compressed version of the Lambert equal-area. Very similar are Trystan Edwards and Smyth equal surface (= Craster rectangular) projections with standard parallels at around 37°N/S. Aspect ratio of ~2.0.
Gall–Peters
= Gall orthographic
= Peters
  Cylindrical Equal-area James Gall

(Arno Peters)

1855 Horizontally compressed version of the Lambert equal-area. Standard parallels at 45°N/S. Aspect ratio of ~1.6. Similar is Balthasart projection with standard parallels at 50°N/S.
Central cylindrical   Cylindrical Perspective (unknown) 1850 c. 1850 Practically unused in cartography because of severe polar distortion, but popular in panoramic photography, especially for architectural scenes.
Sinusoidal
= Sanson–Flamsteed
= Mercator equal-area
  Pseudocylindrical Equal-area, equidistant (Several; first is unknown) 1600 c. 1600 Meridians are sinusoids; parallels are equally spaced. Aspect ratio of 2:1. Distances along parallels are conserved.
Mollweide
= elliptical
= Babinet
= homolographic
  Pseudocylindrical Equal-area Karl Brandan Mollweide 1805 Meridians are ellipses.
Eckert II   Pseudocylindrical Equal-area Max Eckert-Greifendorff 1906
Eckert IV   Pseudocylindrical Equal-area Max Eckert-Greifendorff 1906 Parallels are unequal in spacing and scale; outer meridians are semicircles; other meridians are semiellipses.
Eckert VI   Pseudocylindrical Equal-area Max Eckert-Greifendorff 1906 Parallels are unequal in spacing and scale; meridians are half-period sinusoids.
Ortelius oval   Pseudocylindrical Compromise Battista Agnese 1540

Meridians are circular.[2]

Goode homolosine   Pseudocylindrical Equal-area John Paul Goode 1923 Hybrid of Sinusoidal and Mollweide projections.
Usually used in interrupted form.
Kavrayskiy VII   Pseudocylindrical Compromise Vladimir V. Kavrayskiy 1939 Evenly spaced parallels. Equivalent to Wagner VI horizontally compressed by a factor of  .
Robinson   Pseudocylindrical Compromise Arthur H. Robinson 1963 Computed by interpolation of tabulated values. Used by Rand McNally since inception and used by NGS in 1988–1998.
Equal Earth   Pseudocylindrical Equal-area Bojan Šavrič, Tom Patterson, Bernhard Jenny 2018 Inspired by the Robinson projection, but retains the relative size of areas.
Natural Earth   Pseudocylindrical Compromise Tom Patterson 2011 Computed by interpolation of tabulated values.
Tobler hyperelliptical   Pseudocylindrical Equal-area Waldo R. Tobler 1973 A family of map projections that includes as special cases Mollweide projection, Collignon projection, and the various cylindrical equal-area projections.
Wagner VI   Pseudocylindrical Compromise K. H. Wagner 1932 Equivalent to Kavrayskiy VII vertically compressed by a factor of  .
Collignon   Pseudocylindrical Equal-area Édouard Collignon 1865 c. 1865 Depending on configuration, the projection also may map the sphere to a single diamond or a pair of squares.
HEALPix   Pseudocylindrical Equal-area Krzysztof M. Górski 1997 Hybrid of Collignon + Lambert cylindrical equal-area.
Boggs eumorphic   Pseudocylindrical Equal-area Samuel Whittemore Boggs 1929 The equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate.
Craster parabolic
=Putniņš P4
  Pseudocylindrical Equal-area John Craster 1929 Meridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 aspect.
McBryde–Thomas flat-pole quartic
= McBryde–Thomas #4
  Pseudocylindrical Equal-area Felix W. McBryde, Paul Thomas 1949 Standard parallels at 33°45′N/S; parallels are unequal in spacing and scale; meridians are fourth-order curves. Distortion-free only where the standard parallels intersect the central meridian.
Quartic authalic   Pseudocylindrical Equal-area Karl Siemon

Oscar Adams

1937

1944

Parallels are unequal in spacing and scale. No distortion along the equator. Meridians are fourth-order curves.
The Times   Pseudocylindrical Compromise John Muir 1965 Standard parallels 45°N/S. Parallels based on Gall stereographic, but with curved meridians. Developed for Bartholomew Ltd., The Times Atlas.
Loximuthal   Pseudocylindrical Compromise Karl Siemon

Waldo R. Tobler

1935

1966

From the designated centre, lines of constant bearing (rhumb lines/loxodromes) are straight and have the correct length. Generally asymmetric about the equator.
Aitoff   Pseudoazimuthal Compromise David A. Aitoff 1889 Stretching of modified equatorial azimuthal equidistant map. Boundary is 2:1 ellipse. Largely superseded by Hammer.
Hammer
= Hammer–Aitoff
variations: Briesemeister; Nordic
  Pseudoazimuthal Equal-area Ernst Hammer 1892 Modified from azimuthal equal-area equatorial map. Boundary is 2:1 ellipse. Variants are oblique versions, centred on 45°N.
Strebe 1995   Pseudoazimuthal Equal-area Daniel "daan" Strebe 1994 Formulated by using other equal-area map projections as transformations.
Winkel tripel   Pseudoazimuthal Compromise Oswald Winkel 1921 Arithmetic mean of the equirectangular projection and the Aitoff projection. Standard world projection for the NGS since 1998.
Van der Grinten   Other Compromise Alphons J. van der Grinten 1904 Boundary is a circle. All parallels and meridians are circular arcs. Usually clipped near 80°N/S. Standard world projection of the NGS in 1922–1988.
Equidistant conic
= simple conic
  Conic Equidistant Based on Ptolemy's 1st Projection 0100 c. 100 Distances along meridians are conserved, as is distance along one or two standard parallels.[3]
Lambert conformal conic   Conic Conformal Johann Heinrich Lambert 1772 Used in aviation charts.
Albers conic   Conic Equal-area Heinrich C. Albers 1805 Two standard parallels with low distortion between them.
Werner   Pseudoconical Equal-area, equidistant Johannes Stabius 1500 c. 1500 Parallels are equally spaced concentric circular arcs. Distances from the North Pole are correct as are the curved distances along parallels and distances along central meridian.
Bonne   Pseudoconical, cordiform Equal-area Bernardus Sylvanus 1511 Parallels are equally spaced concentric circular arcs and standard lines. Appearance depends on reference parallel. General case of both Werner and sinusoidal.
Bottomley   Pseudoconical Equal-area Henry Bottomley 2003 Alternative to the Bonne projection with simpler overall shape

Parallels are elliptical arcs
Appearance depends on reference parallel.

American polyconic   Pseudoconical Compromise Ferdinand Rudolph Hassler 1820 c. 1820 Distances along the parallels are preserved as are distances along the central meridian.
Rectangular polyconic   Pseudoconical Compromise U.S. Coast Survey 1853 c. 1853 Latitude along which scale is correct can be chosen. Parallels meet meridians at right angles.
Latitudinally equal-differential polyconic Pseudoconical Compromise China State Bureau of Surveying and Mapping 1963 Polyconic: parallels are non-concentric arcs of circles.
Nicolosi globular   Pseudoconical[4] Compromise Abū Rayḥān al-Bīrūnī; reinvented by Giovanni Battista Nicolosi, 1660.[1]:14 1000 c. 1000
Azimuthal equidistant
=Postel
=zenithal equidistant
  Azimuthal Equidistant Abū Rayḥān al-Bīrūnī 1000 c. 1000 Distances from center are conserved.

Used as the emblem of the United Nations, extending to 60° S.

Gnomonic   Azimuthal Gnomonic Thales (possibly) c. 580 BC All great circles map to straight lines. Extreme distortion far from the center. Shows less than one hemisphere.
Lambert azimuthal equal-area   Azimuthal Equal-area Johann Heinrich Lambert 1772 The straight-line distance between the central point on the map to any other point is the same as the straight-line 3D distance through the globe between the two points.
Stereographic   Azimuthal Conformal Hipparchos* c. 200 BC Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres. Maps all small circles to circles, which is useful for planetary mapping to preserve the shapes of craters.
Orthographic   Azimuthal Perspective Hipparchos* c. 200 BC View from an infinite distance.
Vertical perspective   Azimuthal Perspective Matthias Seutter* 1740 View from a finite distance. Can only display less than a hemisphere.
Two-point equidistant   Azimuthal Equidistant Hans Maurer 1919 Two "control points" can be almost arbitrarily chosen. The two straight-line distances from any point on the map to the two control points are correct.
Peirce quincuncial   Other Conformal Charles Sanders Peirce 1879 Tessellates. Can be tiled continuously on a plane, with edge-crossings matching except for four singular points per tile.
Guyou hemisphere-in-a-square projection   Other Conformal Émile Guyou 1887 Tessellates.
Adams hemisphere-in-a-square projection   Other Conformal Oscar Sherman Adams 1925
Lee conformal world on a tetrahedron   Polyhedral Conformal L. P. Lee 1965 Projects the globe onto a regular tetrahedron. Tessellates.
AuthaGraph projection Link to file Polyhedral Compromise Hajime Narukawa 1999 Approximately equal-area. Tessellates.
Octant projection   Polyhedral Compromise Leonardo da Vinci 1514 Projects the globe onto eight octants (Reuleaux triangles) with no meridians and no parallels.
Cahill's butterfly map   Polyhedral Compromise Bernard Joseph Stanislaus Cahill 1909 Projects the globe onto an octahedron with symmetrical components and contiguous landmasses that may be displayed in various arrangements.
Cahill–Keyes projection   Polyhedral Compromise Gene Keyes 1975 Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses that may be displayed in various arrangements.
Waterman butterfly projection   Polyhedral Compromise Steve Waterman 1996 Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses that may be displayed in various arrangements.
Quadrilateralized spherical cube Polyhedral Equal-area F. Kenneth Chan, E. M. O'Neill 1973
Dymaxion map   Polyhedral Compromise Buckminster Fuller 1943 Also known as a Fuller Projection.
Myriahedral projections Polyhedral Equal-area Jarke J. van Wijk 2008 Projects the globe onto a myriahedron: a polyhedron with a very large number of faces.[5][6]
Craig retroazimuthal
= Mecca
  Retroazimuthal Compromise James Ireland Craig 1909
Hammer retroazimuthal, front hemisphere   Retroazimuthal Ernst Hammer 1910
Hammer retroazimuthal, back hemisphere   Retroazimuthal Ernst Hammer 1910
Littrow   Retroazimuthal Conformal Joseph Johann Littrow 1833 on equatorial aspect it shows a hemisphere except for poles.
Armadillo   Other Compromise Erwin Raisz 1943
GS50   Other Conformal John P. Snyder 1982 Designed specifically to minimize distortion when used to display all 50 U.S. states.
Wagner VII
= Hammer-Wagner
  Pseudoazimuthal Equal-area K. H. Wagner 1941
Atlantis
= Transverse Mollweide
  Pseudocylindrical Equal-area John Bartholomew 1948 Oblique version of Mollweide
Bertin
= Bertin-Rivière
= Bertin 1953
  Other Compromise Jacques Bertin 1953 Projection in which the compromise is no longer homogeneous but instead is modified for a larger deformation of the oceans, to achieve lesser deformation of the continents. Commonly used for French geopolitical maps.[7]

*The first known popularizer/user and not necessarily the creator.

KeyEdit

Type of projectionEdit

Cylindrical
In standard presentation, these map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines.
Pseudocylindrical
In standard presentation, these map the central meridian and parallels as straight lines. Other meridians are curves (or possibly straight from pole to equator), regularly spaced along parallels.
Conic
In standard presentation, conic (or conical) projections map meridians as straight lines, and parallels as arcs of circles.
Pseudoconical
In standard presentation, pseudoconical projections represent the central meridian as a straight line, other meridians as complex curves, and parallels as circular arcs.
Azimuthal
In standard presentation, azimuthal projections map meridians as straight lines and parallels as complete, concentric circles. They are radially symmetrical. In any presentation (or aspect), they preserve directions from the center point. This means great circles through the central point are represented by straight lines on the map.
Pseudoazimuthal
In standard presentation, pseudoazimuthal projections map the equator and central meridian to perpendicular, intersecting straight lines. They map parallels to complex curves bowing away from the equator, and meridians to complex curves bowing in toward the central meridian. Listed here after pseudocylindrical as generally similar to them in shape and purpose.
Other
Typically calculated from formula, and not based on a particular projection
Polyhedral maps
Polyhedral maps can be folded up into a polyhedral approximation to the sphere, using particular projection to map each face with low distortion.

PropertiesEdit

Conformal
Preserves angles locally, implying that local shapes are not distorted and that local scale is constant in all directions from any chosen point.
Equal-area
Area measure is conserved everywhere.
Compromise
Neither conformal nor equal-area, but a balance intended to reduce overall distortion.
Equidistant
All distances from one (or two) points are correct. Other equidistant properties are mentioned in the notes.
Gnomonic
All great circles are straight lines.
Retroazimuthal
Direction to a fixed location B (by the shortest route) corresponds to the direction on the map from A to B.

NotesEdit

  1. ^ a b Snyder, John P. (1993). Flattening the earth: two thousand years of map projections. University of Chicago Press. p. 1. ISBN 0-226-76746-9.
  2. ^ Donald Fenna (2006). Cartographic Science: A Compendium of Map Projections, with Derivations. CRC Press. p. 249. ISBN 978-0-8493-8169-0.
  3. ^ Furuti, Carlos A. "Conic Projections: Equidistant Conic Projections". Archived from the original on December 20, 2013. Retrieved February 11, 2020.CS1 maint: unfit url (link)
  4. ^ "Nicolosi Globular projection"
  5. ^ Jarke J. van Wijk. "Unfolding the Earth: Myriahedral Projections".
  6. ^ Carlos A. Furuti. "Interrupted Maps: Myriahedral Maps".
  7. ^ Rivière, Philippe (October 1, 2017). "Bertin Projection (1953)". visionscarto. Retrieved January 27, 2020.

Further readingEdit