Editing Robinson projection (section)

==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.