Editing Robinson projection

{{Short description|Pseudocylindrical compromise map projection}}
[[File:Robinson projection SW.jpg|thumb|350px|right|Robinson projection of the world]]
[[Image:Robinson with Tissot's Indicatrices of Distortion.svg|thumb|350px|The Robinson projection with [[Tissot's indicatrix]] of deformation]]
[[File:CIA World Factbook 2016 physical world map.svg|thumb|right|350px|Map of the world created by the [[Central Intelligence Agency]], with [[Map projection#Notable lines|standard parallels]] 38°N and 38°S]]
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.<ref name="impossible">{{cite news |title=The Impossible Quest for the Perfect Map |url=https://www.nytimes.com/1988/10/25/science/the-impossible-quest-for-the-perfect-map.html?pagewanted=all&src=pm |newspaper=The New York Times |access-date=1 May 2012 |author=John Noble Wilford |date=October 25, 1988}}</ref>

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]].<ref name="Snyder">
{{cite book
|title = Flattening the Earth: 2000 Years of Map Projections
|first = John P.
|last = Snyder
|year = 1993
|publisher = University of Chicago Press
|page = 214
|isbn = 0226767469
}}</ref> In 1998, the 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".<ref>{{cite web |title=National Geographic Maps – Wall Maps – World Classic (Enlarged) |url=https://www.natgeomaps.com/re-world-classic-enlarged |publisher=National Geographic Society |access-date=2019-02-17 |quote=This map features the Winkel Tripel projection to reduce distortion of land masses as they near the poles.}}</ref><ref>{{cite web |title=Selecting a Map Projection |url=https://www.nationalgeographic.org/media/selecting-map-projection/ |publisher=National Geographic Society |access-date=2019-02-17}}</ref>

==Strengths and weaknesses==
The Robinson projection is neither [[Equal-area projection|equal-area]] nor [[conformal map projection|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 [[Meridian (geography)|meridian]]s curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points.<ref name="impossible"/>

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.<ref>{{cite news |title=Arthur H. Robinson, 89; Cartographer Hailed for Map's Elliptical Design |url=https://www.latimes.com/archives/la-xpm-2004-nov-17-me-robinson17-story.html |newspaper=Los Angeles Times |access-date=1 May 2012 |author=Myrna Oliver |date=November 17, 2004}}</ref><ref>{{cite news |title=Arthur H. Robinson, 89 Geographer improved world map |url=https://www.chicagotribune.com/2004/11/16/arthur-h-robinson-89/ |newspaper=Chicago Tribune |access-date=1 May 2012 |author=New York Times News Service |date=November 16, 2004}}</ref>

{{quote|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<ref name="impossible"/>}}

==Formulation==
The projection is defined by the table:<ref name=Ipbuker>{{cite journal |url=https://vdocuments.site/a-computational-approach-to-the-robinson-projection.html |first=C. |last=Ipbuker |title=A Computational Approach to the Robinson Projection |journal=Survey Review |date=July 2005 |volume=38 |issue=297 |pages=204–217 |doi= 10.1179/sre.2005.38.297.204|s2cid=123437786 |access-date=2019-02-17|url-access=subscription }}</ref><ref>{{cite web |url=http://www.radicalcartography.net/projections/robinsontable.html |title=Table for Constructing the Robinson Projection |publisher=RadicalCartography.net |access-date=2019-02-17}}</ref><ref name=USGS>{{cite book |last1=Snyder |first1=John P. |author-link1=John P. Snyder |last2=Voxland |first2=Philip M. |title=An Album of Map Projections |series=U.S. Geological Survey Professional Paper 1453 |publisher=U.S. Government Printing Office |location=Washington, D.C. |url=http://pubs.usgs.gov/pp/1453/report.pdf |year=1989 |pages=82–83, 222–223 |access-date=2022-02-04 |doi=10.3133/pp1453}}</ref>

{| class="wikitable"
! 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 spline]]s while analyzing area deformation on the Robinson projection.<ref>{{cite journal |last=Richardson |first=Robert T. |title=Area deformation on the Robinson projection |journal=The American Cartographer |date=1989 |volume=16 |issue=4 |pages=294–296 |doi=10.1559/152304089783813936 |url=https://fdocuments.net/document/area-deformation-on-the-robinson-projection.html|url-access=subscription }}</ref> 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<ref>From the formulas below, this can be calculated as <math>\frac{1.3523}{0.8487 \cdot 2\pi} \approx 0.2536</math>.</ref> to obtain the ratio of the distance of that parallel from the equator to the length of the equator.<ref name=Ipbuker/><ref name=USGS/>

Coordinates of points on a map are computed as follows:<ref name=Ipbuker/><ref name=USGS/>

<math display="block">
\begin{align}
 x &= 0.8487 \, R X (\lambda - \lambda_0), \\
 y &= 1.3523 \, R Y,
\end{align}
</math>
where ''R'' is the radius of the globe at the scale of the map, ''λ'' is the longitude of the point to plot, and ''λ''<sub>0</sub> is the central meridian chosen for the map (both ''λ'' and ''λ''<sub>0</sub> are expressed in [[radian]]s).

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]] [[The World Factbook|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.<ref>{{Cite book|last=European Centre for Disease Prevention and Control.|url=https://data.europa.eu/doi/10.2900/452488|title=Guidelines for presentation of surveillance data: tables graphs maps.|date=2018|publisher=Publications Office|location=LU|doi=10.2900/452488}}</ref>

==See also==

* [[List of map projections]]
* [[Cartography]]
* [[Kavrayskiy VII projection|Kavrayskiy VII]]

==References==
{{reflist}}

== Further reading ==
*[[Arthur H. Robinson]] (1974). "A New Map Projection: Its Development and Characteristics". In: ''International Yearbook of Cartography''. Vol 14, 1974, pp.&nbsp;145–155.
*John B. Garver Jr. (1988). "New Perspective on the World". In: ''National Geographic'', December 1988, pp.&nbsp;911–913.
*John P. Snyder (1993). ''Flattening The Earth—2000 Years of Map Projections'', The University of Chicago Press. pp.&nbsp;214–216.

==External links==
{{Commons category|Maps with Robinson projection}}
* [http://www.radicalcartography.net/?projectionref Table of examples and properties of all common projections], from radicalcartography.net
* [http://findarticles.com/p/articles/mi_hb3006/is_2_31/ai_n29118548/?tag=content;col1 Numerical evaluation of the Robinson projection], from Cartography and Geographic Information Science, April, 2004 by Cengizhan Ipbuker

{{Map projections}}

[[Category:Map projections]]