List of map projections

Last updated

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.

Contents

Table of projections

YearProjectionImageTypePropertiesCreatorNotes
c.120 Equirectangular
= equidistant cylindrical
= rectangular
= la carte parallélogrammatique
Equirectangular projection SW.jpg CylindricalEquidistant 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 CylindricalEquidistant César-François Cassini de Thury Transverse of equirectangular projection; distances along central meridian are conserved.
Distances perpendicular to central meridian are preserved.
1569 Mercator
= Wright
Mercator projection Square.JPG CylindricalConformal 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 CylindricalCompromise 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 CylindricalConformal 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 Roussilhe oblique stereographic projection.svg Henri Roussilhe
1903Hotine oblique Mercator Hotine Mercator projection SW.jpg CylindricalConformalM. Rosenmund, J. Laborde, Martin Hotine
1855 Gall stereographic
Gall Stereographic projection SW centered.jpg CylindricalCompromise 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 CylindricalCompromise 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 CylindricalEqual-area Johann Heinrich Lambert Cylindrical equal-area projection with standard parallel at the equator and an aspect ratio of π (3.14).
1910 Behrmann Behrmann projection SW.jpg CylindricalEqual-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 Hobo-Dyer projection SW.jpg CylindricalEqual-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
Gall-Peters projection SW.jpg CylindricalEqual-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.
c.1850 Central cylindrical Central cylindric projection square.JPG CylindricalPerspective(unknown)Practically unused in cartography because of severe polar distortion, but popular in panoramic photography, especially for architectural scenes.
c.1600 Sinusoidal
= Sanson–Flamsteed
= Mercator equal-area
Sinusoidal projection SW.jpg PseudocylindricalEqual-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 PseudocylindricalEqual-area Karl Brandan Mollweide Meridians are ellipses.
1953 Sinu-Mollweide Sinu-Mollweide (Philbrick) projection.jpg PseudocylindricalEqual-area Allen K. Philbrick An oblique combination of the sinusoidal and Mollweide projections.
1906 Eckert II Eckert II projection SW.JPG PseudocylindricalEqual-area Max Eckert-Greifendorff
1906 Eckert IV Ecker IV projection SW.jpg PseudocylindricalEqual-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 PseudocylindricalEqual-area Max Eckert-Greifendorff Parallels are unequal in spacing and scale; meridians are half-period sinusoids.
1540 Ortelius oval Ortelius oval projection SW.JPG PseudocylindricalCompromise Battista Agnese

Meridians are circular. [2]

1923 Goode homolosine Goode homolosine projection SW.jpg PseudocylindricalEqual-area John Paul Goode Hybrid of Sinusoidal and Mollweide projections.
Usually used in interrupted form.
1939 Kavrayskiy VII Kavraiskiy VII projection SW.jpg PseudocylindricalCompromise Vladimir V. Kavrayskiy Evenly spaced parallels. Equivalent to Wagner VI horizontally compressed by a factor of .
1963 Robinson Robinson projection SW.jpg PseudocylindricalCompromise 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 PseudocylindricalEqual-areaBojan Šavrič, Tom Patterson, Bernhard JennyInspired by the Robinson projection, but retains the relative size of areas.
2011 Natural Earth Natural Earth projection SW.JPG PseudocylindricalCompromise Tom Patterson Originally by interpolation of tabulated values. Now has a polynomial.
1973 Tobler hyperelliptical Tobler hyperelliptical projection SW.jpg PseudocylindricalEqual-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 PseudocylindricalCompromise K. H. Wagner Equivalent to Kavrayskiy VII vertically compressed by a factor of .
c.1865 Collignon Collignon projection SW.jpg PseudocylindricalEqual-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 PseudocylindricalEqual-area Krzysztof M. Górski Hybrid of Collignon + Lambert cylindrical equal-area.
1929 Boggs eumorphic Boggs eumorphic projection SW.JPG PseudocylindricalEqual-areaSamuel Whittemore BoggsThe equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate.
1929Craster parabolic
=Putniņš P4
Craster parabolic projection SW.jpg PseudocylindricalEqual-areaJohn CrasterMeridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 aspect.
1949McBryde–Thomas flat-pole quartic
= McBryde–Thomas #4
McBryde-Thomas flat-pole quartic projection SW.jpg PseudocylindricalEqual-areaFelix W. McBryde, Paul ThomasStandard 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 PseudocylindricalEqual-areaKarl Siemon

Oscar S. Adams

Parallels are unequal in spacing and scale. No distortion along the equator. Meridians are fourth-order curves.
1965The Times The Times projection SW.jpg PseudocylindricalCompromiseJohn MuirStandard 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 PseudocylindricalCompromiseKarl 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 PseudoazimuthalCompromise 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 PseudoazimuthalEqual-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 PseudoazimuthalEqual-areaDaniel "daan" StrebeFormulated by using other equal-area map projections as transformations.
1921 Winkel tripel Winkel triple projection SW.jpg PseudoazimuthalCompromise 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 OtherCompromise 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.
c.150 Equidistant conic
= simple conic
Equidistant conic projection SW.JPG ConicEquidistantBased on Ptolemy's 1st ProjectionDistances along meridians are conserved, as is distance along one or two standard parallels. [3]
1772 Lambert conformal conic Lambert conformal conic projection SW.jpg ConicConformal Johann Heinrich Lambert Used in aviation charts.
1805 Albers conic Albers projection SW.jpg ConicEqual-area Heinrich C. Albers Two standard parallels with low distortion between them.
c.1500 Werner Werner projection SW.jpg PseudoconicalEqual-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, cordiformEqual-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 PseudoconicalEqual-area Henry Bottomley Alternative to the Bonne projection with simpler overall shape

Parallels are elliptical arcs
Appearance depends on reference parallel.

c.1820 American polyconic American Polyconic projection.jpg PseudoconicalCompromise Ferdinand Rudolph Hassler Distances along the parallels are preserved as are distances along the central meridian.
c.1853 Rectangular polyconic Rectangular polyconic projection SW.jpg PseudoconicalCompromise United States Coast Survey Latitude along which scale is correct can be chosen. Parallels meet meridians at right angles.
1963 Latitudinally equal-differential polyconic PseudoconicalCompromiseChina State Bureau of Surveying and MappingPolyconic: parallels are non-concentric arcs of circles.
c.1000 Nicolosi globular Nicolosi globular projections SW.jpg Pseudoconical [4] Compromise Abū Rayḥān al-Bīrūnī; reinvented by Giovanni Battista Nicolosi, 1660. [1] :14
c.1000 Azimuthal equidistant
=Postel
=zenithal equidistant
Azimuthal equidistant projection SW.jpg AzimuthalEquidistant 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 AzimuthalGnomonic 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 AzimuthalEqual-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.150 BC Stereographic Stereographic projection SW.JPG AzimuthalConformal 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.150 BC Orthographic Orthographic projection SW.jpg AzimuthalPerspective Hipparchos*View from an infinite distance.
1740 Vertical perspective Vertical perspective SW.jpg AzimuthalPerspectiveMatthias Seutter*View from a finite distance. Can only display less than a hemisphere.
1919 Two-point equidistant Two-point equidistant projection SW.jpg AzimuthalEquidistantHans MaurerTwo "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.
2021Gott, Goldberg and Vanderbei’s
Gott-Goldberg-Vanderbei Projection.png
AzimuthalEquidistant 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 Peirce quincuncial projection SW.jpg OtherConformal 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 OtherConformal Émile Guyou Tessellates.
1925 Adams hemisphere-in-a-square projection Adams hemisphere in a square.JPG OtherConformal Oscar S. Adams
1965 Lee conformal world on a tetrahedron Lee Conformal World in a Tetrahedron projection.png PolyhedralConformal Laurence Patrick Lee Projects the globe onto a regular tetrahedron. Tessellates.
1514 Octant projection Leonardo da Vinci's Mappamundi.jpg PolyhedralCompromise 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 PolyhedralCompromise 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 PolyhedralCompromise 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 PolyhedralCompromise 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 PolyhedralEqual-areaF. Kenneth Chan, E. M. O'Neill
1943 Dymaxion map Dymaxion projection.png PolyhedralCompromise Buckminster Fuller Also known as a Fuller Projection.
1999 AuthaGraph projection Projection AuthaGraph.png PolyhedralCompromise Hajime Narukawa Approximately equal-area. Tessellates.
2008 Myriahedral projections PolyhedralEqual-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
Craig projection SW.jpg RetroazimuthalCompromiseJames 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 RetroazimuthalConformal Joseph Johann Littrow On equatorial aspect it shows a hemisphere except for poles.
1943 Armadillo Armadillo projection SW.JPG OtherCompromise Erwin Raisz
1982 GS50 GS50 projection.png OtherConformal John P. Snyder Designed specifically to minimize distortion when used to display all 50 U.S. states.
1941Wagner VII
= Hammer-Wagner
Wagner-VII world map projection.jpg PseudoazimuthalEqual-areaK. H. Wagner
1947? Chamberlin trimetric projection Chamberlin trimetric projection SW.jpg OtherCompromiseWellman ChamberlinMany National Geographic Society maps of single continents use this projection.
1948Atlantis
= Transverse Mollweide
Atlantis-landscape.jpg PseudocylindricalEqual-areaJohn BartholomewOblique version of Mollweide
1953Bertin
= Bertin-Rivière
= Bertin 1953
Bertin-map.jpg OtherCompromiseJacques BertinProjection 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]
2002Hao projection Hao projection (north).png PseudoconicalCompromiseHao XiaoguangKnown 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]
1879 Wiechel projection Wiechel Projection Earth.svg PseudoazimuthalEqual-areaWilliam H. WiechelIn its polar version, meridians form a pinwheel

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

Key

Type of projection surface

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

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.
Perspective
Can be constructed by light shining through a globe onto a developable surface.

See also

Notes

  1. 1 2 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

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