List of map projections

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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
Equirectangular projection SW.jpg 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
Cassini projection SW.jpg 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
Mercator projection Square.JPG 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 Web maps Mercator projection SW.jpg 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
Ellipsoidal transverse Mercator projection SW.jpg 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 Hotine Mercator projection SW.jpg Cylindrical Conformal M. Rosenmund, J. Laborde, Martin Hotine
1855 Gall stereographic
Gall Stereographic projection SW centered.jpg Cylindrical Compromise James Gall Intended to resemble the Mercator while also displaying the poles. Standard parallels at 45°N/S.
1942 Miller
= Miller cylindrical
Miller projection SW.jpg Cylindrical Compromise Osborn Maitland Miller Intended to resemble the Mercator while also displaying the poles.
1772 Lambert cylindrical equal-area Lambert cylindrical equal-area projection SW.jpg Cylindrical Equal-area Johann Heinrich Lambert Standard parallel at the equator. Aspect ratio of π (3.14). Base projection of the cylindrical equal-area family.
1910 Behrmann Behrmann projection SW.jpg Cylindrical Equal-area Walter Behrmann Horizontally compressed version of the Lambert equal-area. Has standard parallels at 30°N/S and an aspect ratio of 2.36.
2002 Hobo–Dyer Hobo–Dyer projection SW.jpg Cylindrical Equal-area Mick Dyer 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.
1855 Gall–Peters
= Gall orthographic
= Peters
Gall–Peters projection SW.jpg Cylindrical Equal-area James Gall

(Arno Peters)

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.
1850 c. 1850 Central cylindrical Central cylindric projection square.JPG 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
Sinusoidal projection SW.jpg 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
Mollweide projection SW.jpg Pseudocylindrical Equal-area Karl Brandan Mollweide Meridians are ellipses.
1906 Eckert II Eckert II projection SW.JPG Pseudocylindrical Equal-area Max Eckert-Greifendorff
1906 Eckert IV Ecker IV projection SW.jpg Pseudocylindrical Equal-area Max Eckert-Greifendorff Parallels are unequal in spacing and scale; outer meridians are semicircles; other meridians are semiellipses.
1906 Eckert VI Ecker VI projection SW.jpg Pseudocylindrical Equal-area Max Eckert-Greifendorff Parallels are unequal in spacing and scale; meridians are half-period sinusoids.
1540 Ortelius oval Ortelius oval projection SW.JPG Pseudocylindrical Compromise Battista Agnese

Meridians are circular.[2]

1923 Goode homolosine Goode homolosine projection SW.jpg Pseudocylindrical Equal-area John Paul Goode Hybrid of Sinusoidal and Mollweide projections.
Usually used in interrupted form.
1939 Kavrayskiy VII Kavraiskiy VII projection SW.jpg Pseudocylindrical Compromise Vladimir V. Kavrayskiy Evenly spaced parallels. Equivalent to Wagner VI horizontally compressed by a factor of .
1963 Robinson Robinson projection SW.jpg 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 Equal Earth projection SW.jpg Pseudocylindrical Equal-area Bojan Šavrič, Tom Patterson, Bernhard Jenny Inspired by the Robinson projection, but retains the relative size of areas.
2011 Natural Earth Natural Earth projection SW.JPG Pseudocylindrical Compromise Tom Patterson Originally by interpolation of tabulated values. Now has a polynomial.
1973 Tobler hyperelliptical Tobler hyperelliptical projection SW.jpg 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 Wagner VI projection SW.jpg Pseudocylindrical Compromise K. H. Wagner Equivalent to Kavrayskiy VII vertically compressed by a factor of .
1865 c. 1865 Collignon Collignon projection SW.jpg 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 HEALPix projection SW.svg Pseudocylindrical Equal-area Krzysztof M. Górski Hybrid of Collignon + Lambert cylindrical equal-area.
1929 Boggs eumorphic Boggs eumorphic projection SW.JPG 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
Craster parabolic projection SW.jpg 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
McBryde-Thomas flat-pole quartic projection SW.jpg 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 Quartic authalic projection SW.jpg 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 The Times projection SW.jpg 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 Loximuthal projection SW.JPG 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 Aitoff projection SW.jpg 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
Hammer projection SW.jpg 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 Strebe 1995 11E SW.jpg Pseudoazimuthal Equal-area Daniel "daan" Strebe Formulated by using other equal-area map projections as transformations.
1921 Winkel tripel Winkel triple projection SW.jpg 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 Van der Grinten projection SW.jpg 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
Equidistant conic projection SW.JPG 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 Lambert conformal conic projection SW.jpg Conic Conformal Johann Heinrich Lambert Used in aviation charts.
1805 Albers conic Albers projection SW.jpg Conic Equal-area Heinrich C. Albers Two standard parallels with low distortion between them.
1500 c. 1500 Werner Werner projection SW.jpg 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 Bonne projection SW.jpg 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 Bottomley projection SW.JPG 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 American Polyconic projection.jpg Pseudoconical Compromise Ferdinand Rudolph Hassler Distances along the parallels are preserved as are distances along the central meridian.
1853 c. 1853 Rectangular polyconic Rectangular polyconic projection SW.jpg Pseudoconical Compromise U.S. 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 Nicolosi globular projections SW.jpg 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 projection SW.jpg 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 Gnomonic projection SW.jpg 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 Lambert azimuthal equal-area projection SW.jpg 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 Stereographic projection SW.JPG 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 Orthographic projection SW.jpg Azimuthal Perspective Hipparchos* View from an infinite distance.
1740 Vertical perspective Vertical perspective SW.jpg Azimuthal Perspective Matthias Seutter* View from a finite distance. Can only display less than a hemisphere.
1919 Two-point equidistant Two-point equidistant projection SW.jpg 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.
1879 Peirce quincuncial Peirce quincuncial projection SW.jpg 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 Guyou doubly periodic projection SW.JPG Other Conformal Émile Guyou Tessellates.
1925 Adams hemisphere-in-a-square projection Adams hemisphere in a square.JPG Other Conformal Oscar Sherman Adams
1965 Lee conformal world on a tetrahedron Lee Conformal World in a Tetrahedron projection.png Polyhedral Conformal L. P. Lee Projects the globe onto a regular tetrahedron. Tessellates.
1514 Octant projection Leonardo da Vinci’s Mappamundi.jpg Polyhedral Compromise Leonardo da Vinci Projects the globe onto eight octants (Reuleaux triangles) with no meridians and no parallels.
1909 Cahill's butterfly map Cahill Butterfly Map.jpg 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 Cahill-Keyes projection.png 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 Waterman projection.png 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 Dymaxion projection.png Polyhedral Compromise Buckminster Fuller Also known as a Fuller Projection.
1999 AuthaGraph projection Link to file 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.[5][6]
1909 Craig retroazimuthal
= Mecca
Craig projection SW.jpg Retroazimuthal Compromise James Ireland Craig
1910 Hammer retroazimuthal, front hemisphere Hammer retroazimuthal projection front SW.JPG Retroazimuthal Ernst Hammer
1910 Hammer retroazimuthal, back hemisphere Hammer retroazimuthal projection back SW.JPG Retroazimuthal Ernst Hammer
1833 Littrow Littrow projection SW.JPG Retroazimuthal Conformal Joseph Johann Littrow on equatorial aspect it shows a hemisphere except for poles.
1943 Armadillo Armadillo projection SW.JPG Other Compromise Erwin Raisz
1982 GS50 GS50 projection.png Other Conformal John P. Snyder Designed specifically to minimize distortion when used to display all 50 U.S. states.
1941 Wagner VII
= Hammer-Wagner
Wagner-VII world map projection.jpg Pseudoazimuthal Equal-area K. H. Wagner
1948 Atlantis
= Transverse Mollweide
Atlantis-landscape.jpg Pseudocylindrical Equal-area John Bartholomew Oblique version of Mollweide
1953 Bertin
= Bertin-Rivière
= Bertin 1953
Bertin-map.jpg 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.[7]

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

Key[edit]

Type of projection[edit]

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.

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.

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"
  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 reading[edit]