Robinson projection

Last updated November 05, 2024

The Robinson projection is a map projection of a world map that shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image.^[1]

The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, which has used the projection in general-purpose world maps since that time. Robinson published details of the projection's construction in 1974. The National Geographic Society (NGS) began using the Robinson projection for general-purpose world maps in 1988, replacing the Van der Grinten projection.^[2] In 1998, NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, as the latter "reduces the distortion of land masses as they near the poles".^[3]^[4]

Strengths and weaknesses

The Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt that this produced a better overall view than could be achieved by adhering to either. The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points.^[1]

Hence, distortion close to the poles is severe, but quickly declines to moderate levels moving away from them. The straight parallels imply severe angular distortion at the high latitudes toward the outer edges of the map – a fault inherent in any pseudocylindrical projection. However, at the time it was developed, the projection effectively met Rand McNally's goal to produce appealing depictions of the entire world.^[5]^[6]

I decided to go about it backwards. … I started with a kind of artistic approach. I visualized the best-looking shapes and sizes. I worked with the variables until it got to the point where, if I changed one of them, it didn't get any better. Then I figured out the mathematical formula to produce that effect. Most mapmakers start with the mathematics.
— 1988 New York Times article^[1]

Formulation

The projection is defined by the table:^[7]^[8]^[9]

Latitude	X	Y
0°	1.0000	0.0000
5°	0.9986	0.0620
10°	0.9954	0.1240
15°	0.9900	0.1860
20°	0.9822	0.2480
25°	0.9730	0.3100
30°	0.9600	0.3720
35°	0.9427	0.4340
40°	0.9216	0.4958
45°	0.8962	0.5571
50°	0.8679	0.6176
55°	0.8350	0.6769
60°	0.7986	0.7346
65°	0.7597	0.7903
70°	0.7186	0.8435
75°	0.6732	0.8936
80°	0.6213	0.9394
85°	0.5722	0.9761
90°	0.5322	1.0000

The table is indexed by latitude at 5-degree intervals; intermediate values are calculated using interpolation. Robinson did not specify any particular interpolation method, but it is reported that others used either Aitken interpolation (with polynomials of unknown degrees) or cubic splines while analyzing area deformation on the Robinson projection.^[10] The X column is the ratio of the length of the parallel to the length of the equator; the Y column can be multiplied by 0.2536^[11] to obtain the ratio of the distance of that parallel from the equator to the length of the equator.^[7]^[9]

Coordinates of points on a map are computed as follows:^[7]^[9]

${\begin{aligned}x&=0.8487\,RX(\lambda -\lambda _{0}),\\y&=1.3523\,RY,\end{aligned}}$ where R is the radius of the globe at the scale of the map, λ is the longitude of the point to plot, and λ₀ is the central meridian chosen for the map (both λ and λ₀ are expressed in radians).

Simple consequences of these formulas are:

With x computed as a constant multiplier to the meridian across the entire parallel, meridians of longitude are thus equally spaced along the parallel.
With y having no dependency on longitude, parallels are straight horizontal lines.

Applications

The Central Intelligence Agency World Factbook uses the Robinson projection in its political and physical world maps.

The European Centre for Disease Prevention and Control recommends using the Robinson projection for mapping the whole world.^[12]

Related Research Articles

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The Eckert II projection is an equal-area pseudocylindrical map projection. In the equatorial aspect the network of longitude and latitude lines consists solely of straight lines, and the outer boundary has the distinctive shape of an elongated hexagon. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert II is the Eckert I projection.

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In the cartography of the United States, the American polyconic projection is a map projection used for maps of the United States and its regions beginning early in the 19th century. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Often the American polyconic is simply called the polyconic projection.

The rectangular polyconic projection is a map projection was first mentioned in 1853 by the United States Coast Survey, where it was developed and used for portions of the U.S. exceeding about one square degree. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Sometimes the rectangular polyconic is called the War Office projection due to its use by the British War Office for topographic maps. It is not used much these days, with practically all military grid systems having moved onto conformal projection systems, typically modeled on the transverse Mercator projection.

References

1 2 3 John Noble Wilford (October 25, 1988). "The Impossible Quest for the Perfect Map". The New York Times. Retrieved 1 May 2012.
↑ Snyder, John P. (1993). Flattening the Earth: 2000 Years of Map Projections. University of Chicago Press. p. 214. ISBN 0226767469.
↑ "National Geographic Maps – Wall Maps – World Classic (Enlarged)". National Geographic Society. Retrieved 2019-02-17. This map features the Winkel Tripel projection to reduce distortion of land masses as they near the poles.
↑ "Selecting a Map Projection". National Geographic Society. Retrieved 2019-02-17.
↑ Myrna Oliver (November 17, 2004). "Arthur H. Robinson, 89; Cartographer Hailed for Map's Elliptical Design". Los Angeles Times. Retrieved 1 May 2012.
↑ New York Times News Service (November 16, 2004). "Arthur H. Robinson, 89 Geographer improved world map". Chicago Tribune. Retrieved 1 May 2012.
1 2 3 Ipbuker, C. (July 2005). "A Computational Approach to the Robinson Projection". Survey Review. 38 (297): 204–217. doi:10.1179/sre.2005.38.297.204. S2CID 123437786 . Retrieved 2019-02-17.
↑ "Table for Constructing the Robinson Projection". RadicalCartography.net. Retrieved 2019-02-17.
1 2 3 Snyder, John P.; Voxland, Philip M. (1989). An Album of Map Projections (PDF). U.S. Geological Survey Professional Paper 1453. Washington, D.C.: U.S. Government Printing Office. pp. 82–83, 222–223. doi:10.3133/pp1453 . Retrieved 2022-02-04.
↑ Richardson, Robert T. (1989). "Area deformation on the Robinson projection". The American Cartographer. 16 (4): 294–296. doi:10.1559/152304089783813936.
↑ From the formulas below, this can be calculated as ${\frac {1.3523}{0.8487\cdot 2\pi }}\approx 0.2536$ .
↑ European Centre for Disease Prevention and Control. (2018). Guidelines for presentation of surveillance data: tables graphs maps. LU: Publications Office. doi:10.2900/452488.

External links

Table of examples and properties of all common projections, from radicalcartography.net
Numerical evaluation of the Robinson projection, from Cartography and Geographic Information Science, April, 2004 by Cengizhan Ipbuker

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[impossible-1] 1 2 3 John Noble Wilford (October 25, 1988). "The Impossible Quest for the Perfect Map". The New York Times. Retrieved 1 May 2012.

[Snyder-2] Snyder, John P. (1993). Flattening the Earth: 2000 Years of Map Projections. University of Chicago Press. p. 214. ISBN 0226767469.

[3] "National Geographic Maps – Wall Maps – World Classic (Enlarged)". National Geographic Society. Retrieved 2019-02-17. This map features the Winkel Tripel projection to reduce distortion of land masses as they near the poles.

[4] "Selecting a Map Projection". National Geographic Society. Retrieved 2019-02-17.

[5] Myrna Oliver (November 17, 2004). "Arthur H. Robinson, 89; Cartographer Hailed for Map's Elliptical Design". Los Angeles Times. Retrieved 1 May 2012.

[6] New York Times News Service (November 16, 2004). "Arthur H. Robinson, 89 Geographer improved world map". Chicago Tribune. Retrieved 1 May 2012.

[Ipbuker-7] 1 2 3 Ipbuker, C. (July 2005). "A Computational Approach to the Robinson Projection". Survey Review. 38 (297): 204–217. doi:10.1179/sre.2005.38.297.204. S2CID 123437786 . Retrieved 2019-02-17.

[8] "Table for Constructing the Robinson Projection". RadicalCartography.net. Retrieved 2019-02-17.

[USGS-9] 1 2 3 Snyder, John P.; Voxland, Philip M. (1989). An Album of Map Projections (PDF). U.S. Geological Survey Professional Paper 1453. Washington, D.C.: U.S. Government Printing Office. pp. 82–83, 222–223. doi:10.3133/pp1453 . Retrieved 2022-02-04.

[10] Richardson, Robert T. (1989). "Area deformation on the Robinson projection". The American Cartographer. 16 (4): 294–296. doi:10.1559/152304089783813936.

[11] From the formulas below, this can be calculated as ${\frac {1.3523}{0.8487\cdot 2\pi }}\approx 0.2536$ .

[12] European Centre for Disease Prevention and Control. (2018). Guidelines for presentation of surveillance data: tables graphs maps. LU: Publications Office. doi:10.2900/452488.

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