Projective.

The blog of map-projections.net

Tue Feb 21, 2023 13 Projections for 2023 (Part 2)

A collection of projections for political world maps
(see Intro for further explanations)

February: Robinson Projection

Robinson
Creator Arthur H. Robinson (1963)
Group Pseudocylindric
Property Compromise
Other Names
Remarks Not based upon mathematical formulas but tabular coordinates providing positions of the parallels in order to produce a »right-looking« map.

Sorry for the delay, but various things kept me from writing the February blogpost. In order to get it online before March hits, I’ll make it really short:

As said in the table above, the Mr. Robinson created this projection in order to produce a “right-looking” map. And I think he really achieved that goal!
Granted, distortion metrics like the Airy-Kavraiskiy criterion will usually show that projections with equally spaced parallels (along the central meridian) – like Kavraiskiy VII, Frančula XI, Györffy B or Winkel Tripel – come up with better overall distortion values. But since (as I’ve said in the January part and probably lots of times before) I always like a bit less areal inflation near the poles, the Robinson indeed looks or rather feels “more right” to me.

Moreover, I have seen it used as political map in atlases and on wall maps more than once (for example, in the current edition of Meyers Universalatlas and since years in the CIA World Factbook). When I decided on the leitmotif for the calendar, it was clear to me that the Robinson projection could not be missing.

It also looks very fine in the OGABO version and the plagal aspect:

Remember that I was going to talk about Pacific-centered maps again in the January part of the calendar, but then postponed it to the February part? Well, that will be postponed to the March part…

My 2023 Map Projection Calendar

To read another part of my 2023 map projection calendar series, select the desired month.

Comments

2 comments

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Peter Denne

Personally, I've never been a big fan of the Robinson projection, partly because it's overused, partly because I'm not a big fan of pseudocylindricals in general, and partly because it's very similar to Wagner V but with the disadvantage that it has no equations and has to be interpolated from values in a table:

https://www.map-projections.ne…

This raises the question: how closely could a variant of Wagner V approximate the Robinson?

I also think there are plenty of other projections that are more "right-looking". Admittedly, the Robinson does a good job over the populated part of the globe, but high latitudes are severely stretched. Alaska is particularly bad, suffering both from this stretching and from the stubborn refusal of the parallels to bend as they approach the boundary.
Wed Feb 22, 2023 9:27 am CET   –    5 replies

Tobias Jung

> and partly because it's very similar to Wagner V

Yeah, their similarities are basically the reason that this website even exists, see
https://map-projections.net/wh…


> how closely could a variant of Wagner V approximate the Robinson?

Probably very close, but see for yourself – here’s a quick & dirty implementation of a customizable Wagner V (and others) layered over a Robinson image:
https://map-projections.net/d3…
Select "Mollweide [Var.Id 2]" as Modified Projection.


"right-looking" is of course a very subjective term – that’s why I wrote above that it "feels" more right to me. And I couldn’t even exactly say WHAT it is that makes a projection "look right" to me…
Wed Feb 22, 2023 4:53 pm CET

Peter Denner

It's taken me nearly a week to get round to it, but it was fun playing with this - thanks!

I settled on 68-60-60-29-197 with a scale of 156. You have to increase the graticule spacing to 15 to get it to line up.
Tue Feb 28, 2023 2:01 pm CET

Peter Denner

Speaking of pseudocylindricals with polewardly decreasing parallel spacing, and speaking of projections that I find more "right-looking" than the Robinson, I recently came across the Winkel-Snyder, which is the average of the Mollweide and the equirectangular projection with standard parallel phi0 = arccos(2/pi):

https://www.giss.nasa.gov/tool…

If you did a Bartholomew on it and reduced the standard parallel of the parent equirectangular projection to 40° or so, or if you took the Bromley instead of the Mollweide, I bet it would look really good - for a pseudocylindrical, that is.
Tue Feb 28, 2023 2:40 pm CET

Tobias Jung

> I settled on 68-60-60-29-197 with a scale of 156.

Looks like a very good approximation to me (considering that these two projection will always differ to a certain degree)!


> I recently came across the Winkel-Snyder (…) If you did a Bartholomew on it
> and reduced the standard parallel of the parent equirectangular projection to 40°

A while ago, I wrote a Winkel-Snyder implementation for d3.
Here’s the result of your proposed modification:
https://map-projections.net/im…

However, with phi0 = arccos(2/pi) my implementation didn’t match with G.Projector’s image so I’m not certain if it’s a real Winkel-Snyder at all.
I always wanted to explore this further, but … well, I never did.
Tue Feb 28, 2023 3:25 pm CET

Peter Denner

Real or not, I still like it better than the Robinson.

If you send me the code for your implementation, I'd be more than happy to check it.
Tue Feb 28, 2023 5:43 pm CET
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Peter Denner

I'd like to add that for non-cylindrical projections, the unweighted Airy-Kavrayskiy criterion actually gives the lowest distortion values to projections like Györffy E and F where the parallel spacing increases towards the poles. By adjusting the weighting, you can change the preferred parallel spacing. My preferred weighting is currently 64:36 (or 16:9 in lowest terms, like TVs) in favour of minimizing areal distortions, which does indeed give lowest distortion values to projections with equally (or nearly equally) spaced parallels. (The optimum parallel spacing also depends on pole line length, with long pole lines favouring polewardly decreasing parallel spacing and vice versa.)

By adjusting the ratio a bit further, you can easily get a lower distortion value for the Robinson than for Kavrayskiy VII, Francula XI or Györffy B, but you have to go really far for the Robinson to have a lower distortion value than the Winkel tripel, which has the benefit of curved parallels.
Wed Feb 22, 2023 9:52 am CET   –    One Reply

Tobias Jung

Thanks for the explanations! :-)
Wed Feb 22, 2023 4:54 pm CET
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