List of map projections

From Wikipedia, the free encyclopedia

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 projections[edit]

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

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

1745 Cassini
= Cassini–Soldner
Cylindrical Equidistant César-François Cassini de Thury Transverse of equidistant projection; distances along central meridian are conserved.
Distances perpendicular to central meridian are preserved.
1569 Mercator
= Wright
Cylindrical Conformal Gerardus Mercator Lines of constant bearing (rhumb lines) are straight, aiding navigation. Areas inflate with latitude, becoming so extreme that the map cannot show the poles.
2005 Web Mercator Cylindrical Compromise Google 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.
1822 Gauss–Krüger
= Gauss conformal
= (ellipsoidal) transverse Mercator
Cylindrical Conformal Carl Friedrich Gauss

Johann Heinrich Louis Krüger

This transverse, ellipsoidal form of the Mercator is finite, unlike the equatorial Mercator. Forms the basis of the Universal Transverse Mercator coordinate system.
1922 Roussilhe oblique stereographic Henri Roussilhe
1903 Hotine oblique Mercator Cylindrical Conformal M. Rosenmund, J. Laborde, Martin Hotine
1855 Gall stereographic
Cylindrical Compromise James Gall Intended to resemble the Mercator while also displaying the poles. Standard parallels at 45°N/S.
1942 Miller
= Miller cylindrical
Cylindrical Compromise Osborn Maitland Miller Intended to resemble the Mercator while also displaying the poles.
1772 Lambert cylindrical equal-area Cylindrical Equal-area Johann Heinrich Lambert Cylindrical equal-area projection with standard parallel at the equator and an aspect ratio of π (3.14).
1910 Behrmann Cylindrical Equal-area Walter Behrmann Cylindrical equal-area projection with standard parallels at 30°N/S and an aspect ratio of (3/4)π ≈ 2.356.
2002 Hobo–Dyer Cylindrical Equal-area Mick Dyer Cylindrical equal-area projection with standard parallels at 37.5°N/S and an aspect ratio of 1.977. Similar are Trystan Edwards with standard parallels at 37.4° and Smyth equal surface (=Craster rectangular) with standard parallels around 37.07°.
1855 Gall–Peters
= Gall orthographic
= Peters
Cylindrical Equal-area James Gall

(Arno Peters)

Cylindrical equal-area projection with standard parallels at 45°N/S and an aspect ratio of π/2 ≈ 1.571. Similar is Balthasart with standard parallels at 50°N/S and Tobler’s world in a square with standard parallels around 55.66°N/S.
1850 c. 1850 Central cylindrical Cylindrical Perspective (unknown) Practically unused in cartography because of severe polar distortion, but popular in panoramic photography, especially for architectural scenes.
1600 c. 1600 Sinusoidal
= Sanson–Flamsteed
= Mercator equal-area
Pseudocylindrical Equal-area, equidistant (Several; first is unknown) Meridians are sinusoids; parallels are equally spaced. Aspect ratio of 2:1. Distances along parallels are conserved.
1805 Mollweide
= elliptical
= Babinet
= homolographic
Pseudocylindrical Equal-area Karl Brandan Mollweide Meridians are ellipses.
1906 Eckert II Pseudocylindrical Equal-area Max Eckert-Greifendorff
1906 Eckert IV Pseudocylindrical Equal-area Max Eckert-Greifendorff Parallels are unequal in spacing and scale; outer meridians are semicircles; other meridians are semiellipses.
1906 Eckert VI Pseudocylindrical Equal-area Max Eckert-Greifendorff Parallels are unequal in spacing and scale; meridians are half-period sinusoids.
1540 Ortelius oval Pseudocylindrical Compromise Battista Agnese

Meridians are circular.[2]

1923 Goode homolosine Pseudocylindrical Equal-area John Paul Goode Hybrid of Sinusoidal and Mollweide projections.
Usually used in interrupted form.
1939 Kavrayskiy VII Pseudocylindrical Compromise Vladimir V. Kavrayskiy Evenly spaced parallels. Equivalent to Wagner VI horizontally compressed by a factor of .
1963 Robinson Pseudocylindrical Compromise Arthur H. Robinson Computed by interpolation of tabulated values. Used by Rand McNally since inception and used by NGS in 1988–1998.
2018 Equal Earth Pseudocylindrical Equal-area Bojan Šavrič, Tom Patterson, Bernhard Jenny Inspired by the Robinson projection, but retains the relative size of areas.
2011 Natural Earth Pseudocylindrical Compromise Tom Patterson Originally by interpolation of tabulated values. Now has a polynomial.
1973 Tobler hyperelliptical Pseudocylindrical Equal-area Waldo R. Tobler A family of map projections that includes as special cases Mollweide projection, Collignon projection, and the various cylindrical equal-area projections.
1932 Wagner VI Pseudocylindrical Compromise K. H. Wagner Equivalent to Kavrayskiy VII vertically compressed by a factor of .
1865 c. 1865 Collignon Pseudocylindrical Equal-area Édouard Collignon Depending on configuration, the projection also may map the sphere to a single diamond or a pair of squares.
1997 HEALPix Pseudocylindrical Equal-area Krzysztof M. Górski Hybrid of Collignon + Lambert cylindrical equal-area.
1929 Boggs eumorphic Pseudocylindrical Equal-area Samuel Whittemore Boggs The equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate.
1929 Craster parabolic
=Putniņš P4
Pseudocylindrical Equal-area John Craster Meridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 aspect.
1949 McBryde–Thomas flat-pole quartic
= McBryde–Thomas #4
Pseudocylindrical Equal-area Felix W. McBryde, Paul Thomas 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.
1937

1944

Quartic authalic Pseudocylindrical Equal-area Karl Siemon

Oscar Adams

Parallels are unequal in spacing and scale. No distortion along the equator. Meridians are fourth-order curves.
1965 The Times Pseudocylindrical Compromise John Muir Standard parallels 45°N/S. Parallels based on Gall stereographic, but with curved meridians. Developed for Bartholomew Ltd., The Times Atlas.
1935

1966

Loximuthal Pseudocylindrical Compromise Karl Siemon

Waldo R. Tobler

From the designated centre, lines of constant bearing (rhumb lines/loxodromes) are straight and have the correct length. Generally asymmetric about the equator.
1889 Aitoff Pseudoazimuthal Compromise David A. Aitoff Stretching of modified equatorial azimuthal equidistant map. Boundary is 2:1 ellipse. Largely superseded by Hammer.
1892 Hammer
= Hammer–Aitoff
variations: Briesemeister; Nordic
Pseudoazimuthal Equal-area Ernst Hammer Modified from azimuthal equal-area equatorial map. Boundary is 2:1 ellipse. Variants are oblique versions, centred on 45°N.
1994 Strebe 1995 Pseudoazimuthal Equal-area Daniel "daan" Strebe Formulated by using other equal-area map projections as transformations.
1921 Winkel tripel Pseudoazimuthal Compromise Oswald Winkel Arithmetic mean of the equirectangular projection and the Aitoff projection. Standard world projection for the NGS since 1998.
1904 Van der Grinten Other Compromise Alphons J. van der Grinten 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.
0150 c. 150 Equidistant conic
= simple conic
Conic Equidistant Based on Ptolemy's 1st Projection Distances along meridians are conserved, as is distance along one or two standard parallels.[3]
1772 Lambert conformal conic Conic Conformal Johann Heinrich Lambert Used in aviation charts.
1805 Albers conic Conic Equal-area Heinrich C. Albers Two standard parallels with low distortion between them.
1500 c. 1500 Werner Pseudoconical Equal-area, equidistant Johannes Stabius 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.
1511 Bonne Pseudoconical, cordiform Equal-area, equidistant Bernardus Sylvanus Parallels are equally spaced concentric circular arcs and standard lines. Appearance depends on reference parallel. General case of both Werner and sinusoidal.
2003 Bottomley Pseudoconical Equal-area Henry Bottomley Alternative to the Bonne projection with simpler overall shape

Parallels are elliptical arcs
Appearance depends on reference parallel.

1820 c. 1820 American polyconic Pseudoconical Compromise Ferdinand Rudolph Hassler Distances along the parallels are preserved as are distances along the central meridian.
1853 c. 1853 Rectangular polyconic Pseudoconical Compromise United States Coast Survey Latitude along which scale is correct can be chosen. Parallels meet meridians at right angles.
1963 Latitudinally equal-differential polyconic Pseudoconical Compromise China State Bureau of Surveying and Mapping Polyconic: parallels are non-concentric arcs of circles.
1000 c. 1000 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 Distances from center are conserved.

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

c. 580 BC Gnomonic Azimuthal Gnomonic Thales (possibly) All great circles map to straight lines. Extreme distortion far from the center. Shows less than one hemisphere.
1772 Lambert azimuthal equal-area Azimuthal Equal-area Johann Heinrich Lambert 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.
c. 200 BC Stereographic Azimuthal Conformal Hipparchos* 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.
c. 200 BC Orthographic Azimuthal Perspective Hipparchos* View from an infinite distance.
1740 Vertical perspective Azimuthal Perspective Matthias Seutter* View from a finite distance. Can only display less than a hemisphere.
1919 Two-point equidistant Azimuthal Equidistant Hans Maurer 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.
2021 Gott, Goldberg and Vanderbei’s
Azimuthal Equidistant J. Richard Gott, Goldberg and Robert J. Vanderbei Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions. Not properly "a" map projection because it is on two surfaces instead of one, it consists of two hemispheric equidistant azimuthal projections back-to-back.[5][6][7]
1879 Peirce quincuncial Other Conformal Charles Sanders Peirce Tessellates. Can be tiled continuously on a plane, with edge-crossings matching except for four singular points per tile.
1887 Guyou hemisphere-in-a-square projection Other Conformal Émile Guyou Tessellates.
1925 Adams hemisphere-in-a-square projection Other Conformal Oscar Sherman Adams
1965 Lee conformal world on a tetrahedron Polyhedral Conformal L. P. Lee Projects the globe onto a regular tetrahedron. Tessellates.
1514 Octant projection Polyhedral Compromise Leonardo da Vinci Projects the globe onto eight octants (Reuleaux triangles) with no meridians and no parallels.
1909 Cahill's butterfly map Polyhedral Compromise Bernard Joseph Stanislaus Cahill Projects the globe onto an octahedron with symmetrical components and contiguous landmasses that may be displayed in various arrangements.
1975 Cahill–Keyes projection Polyhedral Compromise Gene Keyes Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses that may be displayed in various arrangements.
1996 Waterman butterfly projection Polyhedral Compromise Steve Waterman Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses that may be displayed in various arrangements.
1973 Quadrilateralized spherical cube Polyhedral Equal-area F. Kenneth Chan, E. M. O'Neill
1943 Dymaxion map Polyhedral Compromise Buckminster Fuller Also known as a Fuller Projection.
1999 AuthaGraph projection Polyhedral Compromise Hajime Narukawa Approximately equal-area. Tessellates.
2008 Myriahedral projections Polyhedral Equal-area Jarke J. van Wijk Projects the globe onto a myriahedron: a polyhedron with a very large number of faces.[8][9]
1909 Craig retroazimuthal
= Mecca
Retroazimuthal Compromise James Ireland Craig
1910 Hammer retroazimuthal, front hemisphere Retroazimuthal Ernst Hammer
1910 Hammer retroazimuthal, back hemisphere Retroazimuthal Ernst Hammer
1833 Littrow Retroazimuthal Conformal Joseph Johann Littrow on equatorial aspect it shows a hemisphere except for poles.
1943 Armadillo Other Compromise Erwin Raisz
1982 GS50 Other Conformal John P. Snyder Designed specifically to minimize distortion when used to display all 50 U.S. states.
1941 Wagner VII
= Hammer-Wagner
Pseudoazimuthal Equal-area K. H. Wagner
1947? Chamberlin trimetric projection Other Compromise Wellman Chamberlin Many National Geographic Society maps of single continents use this projection.
1948 Atlantis
= Transverse Mollweide
Pseudocylindrical Equal-area John Bartholomew Oblique version of Mollweide
1953 Bertin
= Bertin-Rivière
= Bertin 1953
Other Compromise Jacques Bertin 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.[10]
2002 Hao projection Pseudoconical Compromise Hao Xiaoguang Known as "plane terrestrial globe",[11] it was adopted by the People's Liberation Army for the official military maps and China’s State Oceanic Administration for polar expeditions.[12][13]

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

Key[edit]

Type of projection surface[edit]

Cylindrical
In normal aspect, these map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines.
Pseudocylindrical
In normal aspect, 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 normal aspect, conic (or conical) projections map meridians as straight lines, and parallels as arcs of circles.
Pseudoconical
In normal aspect, 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 normal aspect, 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.

Properties[edit]

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.

See also[edit]

Notes[edit]

  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 November 30, 2012. Retrieved February 11, 2020.{{cite web}}: CS1 maint: unfit URL (link)
  4. ^ ""Nicolosi Globular projection"" (PDF). Archived (PDF) from the original on 2016-04-29. Retrieved 2016-09-18.
  5. ^ "New Earth Map Projection". vanderbei.princeton.edu. Retrieved 2023-04-27.
  6. ^ Fuller-Wright, Liz. "Princeton astrophysicists re-imagine world map, designing a less distorted, 'radically different' way to see the world". Princeton University. Archived from the original on 2022-07-13. Retrieved 2022-07-13.
  7. ^ Gott III, J. Richard; Goldberg, David M.; Vanderbei, Robert J. (2021-02-15). "Flat Maps that improve on the Winkel Tripel". arXiv:2102.08176 [astro-ph.IM].
  8. ^ Jarke J. van Wijk. "Unfolding the Earth: Myriahedral Projections". Archived from the original on 2020-06-20. Retrieved 2011-03-08.
  9. ^ Carlos A. Furuti. "Interrupted Maps: Myriahedral Maps". Archived from the original on 2020-01-17. Retrieved 2011-11-03.
  10. ^ Rivière, Philippe (October 1, 2017). "Bertin Projection (1953)". visionscarto. Archived from the original on January 27, 2020. Retrieved January 27, 2020.
  11. ^ Hao, Xiaoguang; Xue, Huaiping. "Generalized Equip-Difference Parallel Polyconical Projection Method for the Global Map" (PDF). Archived (PDF) from the original on February 9, 2023. Retrieved February 14, 2023.
  12. ^ Alexeeva, Olga; Lasserre, Frédéric (October 20, 2022). "Le concept de troisième pôle: cartes et représentations polaires de la Chine". Géoconfluences (in French). Archived from the original on February 14, 2023. Retrieved February 14, 2023.
  13. ^ Vriesema, Jochem (April 7, 2021). "Arctic geopolitics: China's remapping of the world". Clingendael Spectator. The Hague: Clingendael. Archived from the original on February 14, 2023. Retrieved February 14, 2023.

Further reading[edit]