Talk:Robinson projection

Untitled
WHAT IS THE SIZE OF THE ROBINSON PROJECTION? - User:69.215.246.57 ; 23:37, 26 September 2005


 * As big as the piece of paper it is printed on. (If you want a better answer, please clarify your question.) - Liberty 03:09, 13 October 2005 (UTC)

The Robinson Projection
How did Robinson come up with the idea about this amazing projection?

What kind of interpolation?
Did Robinson ever specify what interpolation formula should be used? The article doesn't seem to address the question. The obvious linear interpolation is tempting, but it would cause the edge of the map to be polygonal.... – Smjg 15:48, 23 January 2006 (UTC)
 * Robinson didn't use an interpolation formula. There's an article in the April 2004 issue of the Cartography and Geographic Information Science journal with further explanation and a numerical approximation of the interpolation. bennylope (talk) 15:29, 17 July 2009 (UTC)

---

Correction: Robinson did use an interpolation formula.

Robinson specified a table of y-coordinates for 19 parallels of latitude, from 0 to 90, in increments of 5 degrees.

He also specified a table of lengths of those same parallels. (90 degrees is represented as another parallel of finite length, because this is an extended-pole map).

Robinson intended for the Y-coordinate for latitudes between the tabular values to be interpolated, by some interpolation formula. He didn't specify any particular interpolation formula, leaving that choice up to publishers.

It has been said that he used Aitkens interpolation. That's an implementation of polynomial interpolation. For any set of N data-points, there's only one N-1 degree polynomial that can go through all of those data points. Aitkens is just one way of finding that polynomial. Some methods are preferred to others, due to various convenience considerations.

But that kind of polynomial interpolation, the kind that passes an N-1 degree polynomial through N data-points can vary, in terms of how many points are interpolated at a time. Does one pass a single high-degree polynomial through all of the points, or does one do piecewise linear, quadratic or cubic interpolation?

The artcles that say that Robinson passed an N-1 degree polynomial through N data points don't specify whether Robinson used piecewise linear, piecewise quadratic, or piecewise cubic interpolation.

But passing an N-1 degree polynomial through N data points isn't the only way to do polynomial interpolation (though it's the way that it's said that Robinson used for his projection).

There are other methods that create a polynomial that not only matches the Y value of the data points, but also matches the derivative (rate of change) of Y at the data points. Some of those methods also match the second derivative (rate of change of the rate of change) of Y at the data points.

Spline interpolation does the latter. It matches Y, the derivative of Y, and the 2nd derivative of Y. Thereby, it gives a particularly smooth polynomial representation. Usually used in the form of the cubic spline, where it passes a cubic polynomial through each pair of points, matching the derivative and the 2nd derivative at those points too.

A "shape-preserving" Cubic Hermite polynomial is sometimes used, when it's desired to avoid the "overshoot" that spline interpolation can be subject to--when the polynomial loops up or down, when the data points are all rising or falling steadily. That method doesn't require that second derivatives be matched, allowing 2nd derivatives to change abruptly at data points, avoiding the undesired overshoots.

But overshoot is unlikely for the monotonically varying Y-coordinate of the Robinson parallels, and so spline interpolation seems the most desirable choice for interpolating Robinson.

It should be mentioned also that, for equally-spaced data points (like those of Robinson), high-degree polynomials can depart wildly from the data points' Y values, in regions between the data points--especially toward the ends of the interpolated region.

For that reason, high-degree polynomial interpolation probably wouldn't be a good idea, for Robinson's 19 data points.

So, presumably Robinson would have used piecewise linear, quadratic or cubic interpolation. I haven't found any source that says which.

Which of the above-described interpolation methods do publishers use for the Robinson projection. I don't know. If you find out, will you please post the answer here?

--MichaelOssipoff (talk) 13:47, 22 June 2015 (UTC)MichaelOssipoff

- I should add that, if you want to find the latitude of a point on the map, or if you want to find a place on the map that has a certain latitude, then that's when you'd have use for interpolation of Robinson's table.

Spline interpolatioin and Hermite interpolation are probably more involved than you'll want to get into, unless you're a mathematician or programmer. So my suggestions will be about the kind of interpolation that looks only at Y values, not at derivatives. That's the kind that I mentioned above, that puts an N-1 degree polynomial through N points.

As I suggested, you'll probably want the polynomial to be linear, quadratic, or maybe cubic. Lower degree polynomials have less of a tendency to have inappropriate excursions between data points. I'd suggest using only linear or quadratic interpolation.

For sufficient accuracy, it doesn't really matter whether your interpolation is linear, quadratic or cubic. At most latitudes, up to and including interpolation between 70 and 75 degrees latitude, linear interplation is good enough. Any error, any difference from a result gotten by more elaborate interpolation, will be negligible. ...smaller than the fraction of a millimeter that you'd expect to be able to reliably accurately measure with a ruler. ...and amounting to only a few miles, smaller than the uncertainty of the mapped data. Additionally, it has been suggested that changes in the paper's dimensions due to temperature and humidity could mask any interpolation errors.

From 75 on up, quadratic interpolation might be preferable.

But what if you want to find the latitude that corresponds to a place on the map?:

You could write the linear or quadratic polynomial, and then solve for the latitude.

Of course linear interpolation doesn't require any additional instructions. For a latitude P percent through the latitude interval, you find the distance that's P percent of the way from one latitude's distance to the next.

For quadratic interpolation, you could use the formula of Newton, Gauss, Bessel, Stirling, or Lagrange. You can find those by a web-search, or you could just search for "Polynomial Interpolation".

Of course I couldn't have said any of this in the article, without citations.

Of course, because Robinson is "pseudocylindrical", interpolating longitude isn't a problem. The relation between longitude and horizontal distance is perfectly linear, along any parallel of latitude.

--MichaelOssipoff (talk) 23:54, 22 June 2015 (UTC)Michael Ossipoff --

I should clarify that my suggestions above were intended mostly for Robinson maps in atlases--where maps are smaller than wall-maps.

But the main case where you need to find or determine the relation between latitude/longitude and map-position is when you're using a data-map, also called a thematic map.

They're usually found in atlases rather than wall-maps. For position-finding on a general-purpose map, of course it's best to use a large-scale (small region) map, such as a map of a country or state. Of course every atlas has such maps.

Interpolating Robinson could be necessary when thematic information is only shown on Robinson world maps. Though my suggestions were for a full-size atlas world map, of course data maps, thematic maps, are often even smaller than that, and so the small errors with linear interpolation would be even less measurable.

--108.132.201.105 (talk) 01:56, 23 June 2015 (UTC)MichaelOssipoff

From the article and its quoted sources it appears that Robinson himself didn't specify a particular interpolation method. It's not clear if he himself has even used any interpolation method, as he only designed the projection in rather crude terms (a grid with 5-degree steps), and not necessarily ever implemented it for any practical purpose. The only place where Aitken interpolation is mentioned as having been used, is in analyzing area deformation: it's mentioned by Robert T. Richardson in his 1989 technical note (see Refs in the article) that Beckwith and Tobler originally did some analysis for Robinson using Aitken interpolation, while Richardson himself re-did this analysis using cubic splines. So it doesn't sound right that currently the article mentions Aitken interpolation as having been used by Richardson. We should probably fix it to say that the choice of interpolation is left to implementers. cherkash (talk) 03:58, 2 May 2022 (UTC)

Math
Does anyone know the math that is involved in making a Robinson projection map? I'm looking to use it for a map, but I can't find any explanations... 87.196.55.187 13:18, 20 June 2006 (UTC)
 * Here is some C code. I have no clue if it is good. --vossman 18:18, 31 May 2007 (UTC)

Let me just add this: If you're going to make a Robinson map, then be nice and specify (next to where you name the projection) how you did the interpolation of Robinson's Y values for the latitudes.

But it would be negligent to not add that there are other projections that are easier to make, and just as good.

Michael Ossipoff

Replace low-contrast images
I will be replacing images on the various map projection pages. Presently many are on a satellite composite image from NASA that, while realistic, poorly demonstrates the projections because of dark color and low contrast. I have created a stylization of the same data with much brighter water areas and a light graticule to contrast. See the thumbnail of the example from another article. Some images on some pages are acceptable but differ stylistically from most articles; I will replace these also.

The images will be high resolution and antialiased, with 15° graticules for world projections, red, translucent equator, red tropics, and blue polar circles.

Please discuss agreement or objections over here (not this page). I intend to start these replacements on 13 August. Thank you. Strebe (talk) 22:47, 6 August 2011 (UTC)

File:Robinson projection SW.jpg to appear as POTD soon
Hello! This is a note to let the editors of this article know that File:Robinson projection SW.jpg will be appearing as picture of the day on November 2, 2016. You can view and edit the POTD blurb at Template:POTD/2016-11-02. If this article needs any attention or maintenance, it would be preferable if that could be done before its appearance on the Main Page. — Chris Woodrich (talk) 06:39, 19 October 2016 (UTC)


 * Looks good, Chris Woodrich! Many thanks, as always. Strebe (talk) 18:26, 24 October 2016 (UTC)

File:Map of the world by the US Gov as of 2016 no legend.svg scheduled for POTD
Hello! This is to let editors know that the featured picture File:Map of the world by the US Gov as of 2016 no legend.svg, which is used in this article, has been selected as the English Wikipedia's picture of the day (POTD) for February 1, 2021. A preview of the POTD is displayed below and can be edited at Template:POTD/2021-02-01. For the greater benefit of readers, any potential improvements or maintenance that could benefit the quality of this article should be done before its scheduled appearance on the Main Page. If you have any concerns, please place a message at Wikipedia talk:Picture of the day. Thank you! Cwmhiraeth (talk) 14:20, 19 January 2021 (UTC)

April 2023
that's not an outdated map, in fact it's the one that is always kept up to date. The other is a bad copy of it by a disruptive editor who was reported at the time to the Commons admin's board for using my map and lying about it. Besides, this article is about the Robinson projection and not the latest political pov of a country. M.Bitton (talk) 18:30, 18 April 2023 (UTC)


 * Looking at the two images, I'm not so sure about that. It seems to me that Physical_Map_of_the_World_(2021) matches the most recent version of the source (The CIA World Factbook), while I understand that Physical_World_Map is a synthesis of the current source and a version of the source from 2016.  I agree that this article shouldn’t be concerned with the latest political POV of a country, but it also shouldn't be concerned with the previous political POV of a country.  And if we set political POVs aside, I don't see any reason to use elements from the old CIA map when we can just use the current one. Justin Kunimune (talk) 19:22, 18 April 2023 (UTC)
 * I already explained the reason: the editor copied the map that I spent ages making (within days) and lied about it (they just couldn't optimize it, hence the 17mb file). It's not the previous political pov of any country as it's the closest you can get to the UN's map. It's not old either, it's kept up to date (cities, capitals, etc) as I have the original one together with the required fonts, etc. If you spot anything that needs updating, let me know on my Commons talk page or start a request on WP:GL/M and ping me from there. M.Bitton (talk) 19:28, 18 April 2023 (UTC)


 * I don’t really follow this business about “my map” and “bad copy” and “disruptive editor” and “reported to Commons admin board”. What’s shown in the article should not be an editor’s interpretation when avoidable. What’s in the article should be something from a credible source. In this case, it’s the US State Department’s map that was the intent, as is. If someone wants to assert that their own version is better or preferable and starts reverting WP:RELIABLE content, that’s concerning and inappropriate. Strebe (talk) 23:00, 18 April 2023 (UTC)
 * It's really simple: the map that you reverted to is a plagiarized copy of the one that I made, and a bad copy at that. I know for a fact that it's not an exact copy of any map that has been published by the US department (because I corrected the errors that are found in their official map). M.Bitton (talk) 23:30, 18 April 2023 (UTC)
 * I agree that the Physical_Map_of_the_World_(2021) appears to be a derivative of Physical_World_Map. I don’t think the right answer here is to prefer the latter over the former; I think the right answer is to use either the original PDF from the CIA or to use an SVG file that has had no other processing than the format conversion, such as World_map_2011_CIA_World_Factbook or something newly converted. Strebe (talk) 06:57, 19 April 2023 (UTC)


 * I agree with Strebe. Here's a version I took directly from cia.gov; the only edits I made were to convert from PDF to SVG and shrink the margins: CIA_World_Factbook_2021_physical_world_map Justin Kunimune (talk) 17:16, 19 April 2023 (UTC)
 * I'm not exactly sure which part you're agreeing with or why. In any case, some points need clarification:
 * 1) If the map is about the Robinson projection, accuracy and the chance to offer something extra to the readers, then the stable one that was removed does that reasonably well. Its a derivative of the 2016 CIA map that has had all the names of places updated.
 * 2) If the issue is about using a map that hasn't been updated, and frankly, I don't see why this would be case given that we use derivatives all the time and the article itself has a couple that are technically unsourced, then I guess the 216 CIA map (highlighted in the section above) can be used.
 * 3) If on the other hand, this is about imposing the latest US political POV as this edit seems to suggest, then we have a problem because the map that is being suggested clearly violates our NPOV policy.
 * I have removed the recent map from article until we decide which one (if any) is the most appropriate. M.Bitton (talk) 18:46, 21 April 2023 (UTC)


 * The way I see it, there are two issues. The first is that the map should be as up-to-date as possible. The version I uploaded is more up-to-date than the one previously on this page, as it matches the current version of the source in several places where the previous one did not (the depiction of Western Sahara as part of Morocco and Jerusalem as the capital of Israel).  The second is that the notion of synthesizing two copies of a CIA map in order to alter the POV being expressed from the US’s to the UN’s seems to me an infraction of NPOV – a minor one to be sure, but still nonideal.  Let’s remember that neither the UN nor the US is unbiased, so given that the map’s source is the US government, the NPOV thing to do is neutrally present the US’s view of the borders.
 * It’s true that neither of these issues is very important for a purely illustrative map such as this one. However, I see no counterissues that would cause us to favor the previous map over the newly uploaded one, other than personal disagreement with the specific POVs being expressed (which should not factor into the article). Justin Kunimune (talk) 19:24, 21 April 2023 (UTC)
 * You're missing the point: the new map clearly violates the NPOV policy by giving UNDUE weight to the latest US political POV that erases a territory and a member of the African Union from existence. That is simply not acceptable.
 * Let’s remember that neither the UN nor the US is unbiased Let's not compare apples and oranges. The UN is an intergovernmental organization, while the the US is a single country that has had decades of its diplomacy turned on their head by a passing president. M.Bitton (talk) 19:34, 21 April 2023 (UTC)
 * Please avoid arrogant statements such as, “You're missing the point,“ and “clearly” this and clearly that. You’re not a WP:RELIABLE source. Official US documents are. Whether they are correct or biased by your estimation is not relevant to following Wikipedia policies. One purpose of those policies is, specifically, to avoid wasting editors’ time on these kinds of debates. Strebe (talk) 22:29, 21 April 2023 (UTC)
 * Please avoid casting aspersions. The official documents are only reliable for stating the country's position and nothing else. When that position is at odds with every RS out there, then our NPOV policy comes into play, and since you think that you can impose your will through edit warring, I'll ping some editors who are familiar with the subjects (WS as well as Jerusalem).
 * could you please share your thoughts on this? Thanks. M.Bitton (talk) 22:39, 21 April 2023 (UTC)
 * Unfortunately, CIA maps that represent Western Sahara as integrated into Morocco are virtually the definition of WP:FRINGE. They are not NPOV and cannot be used as typical maps. ―Justin ( koavf ) ❤T☮C☺M☯ 04:21, 22 April 2023 (UTC)

What's being stated here is nothing more than the CIA's position. The map is there to provide a real-world example of the Robinson projection, not an accurate description of the political situation, and the caption makes that clear. If we wanted to provide an accurate political description, we would need to state both sides of the argument (as the Western Sahara article does) for every disputed border. But for a simple illustrative example that’s not necessary. Justin Kunimune (talk) 23:19, 21 April 2023 (UTC)


 * Why do we need to state the CIA's position if not to push its POV through the backdoor? Its 2016 map is also a real-world example of the Robinson projection, so why not use it to avoid violating the NPOV policy? M.Bitton (talk) 23:25, 21 April 2023 (UTC)
 * I don’t agree with the POV comments. The UN isn’t NPOV; it’s a collection of positions that plenty of members disagree with. There is no such thing as NPOV in this circumstance, which is why those who make maps have to abide by the perspective of the country they dispense their products into. Meanwhile the Robinson projection was developed by an American and its use is dominated by American mapmakers. Demonstrating a real Robinson map using the official American position is reasonable, and it’s one of the few freely usable Robinson maps from a reliable source. Strebe (talk) 02:05, 22 April 2023 (UTC)
 * The claim that since the Robinson projection was developed by an American we therefore have to use the American position is simply ludicrous. By that standard, we should all follow the American position since Wikipedia was developed by two Americans. M.Bitton (talk) 13:18, 22 April 2023 (UTC)
 * I don't know much about this but since I was pinged, using a CIA map that reflects a US centric view of global politics strikes me as being a bad idea on first principles. Selfstudier (talk) 07:19, 22 April 2023 (UTC)
 * Thanks for the reply. Basically, following the US recognition of Israel's sovereignty over the Golan and Morocco's sovereignty over Western Sahara, the CIA started rolling out new maps that reflect the changes of the US position; and now, we have a couple of editors who seem to think that we have to follow suit. The explanations given so far as to why we should violate our NPOV policy by giving UNDUE weight to such a minority view have been anything but convincing, with the latest being frankly laughable: according to Strebe, since the Robinson projection was developed by an American we have to use the American position. M.Bitton (talk) 13:18, 22 April 2023 (UTC)
 * There could be appropriate times to include them with commentary about the issue of mapping, but they are fringe perspectives that should not be used for general purpose maps. ―Justin ( koavf ) ❤T☮C☺M☯ 03:19, 23 April 2023 (UTC)
 * I wouldn’t describe this as a general purpose map; it’s purely illustrative. The goal is to show an example of the Robinson projection in use outside of Wikipedia, ideally by an organization the readers have heard of. I think we’re unlikely to find such an example that doesn’t include inaccurate and/or fringe viewpoints (e.g. both versions of the CIA map and all UN maps call Taiwan part of China). Therefore, I don’t think it makes sense to hold its contents to the standards of WP:UNDUE and WP:FRINGE. A different example made by a different organization would work just as well, but I didn’t see any other good examples when I did a cursory search. The 2016 version of the CIA map would also be fine; I just think it’s better to use an updated one. To be clear, the map previously on this page was not the 2016 version, but a modification of it, which thus did not reflect the caption or the source; that’s the main issue I take with it. Justin Kunimune (talk) 12:03, 23 April 2023 (UTC)
 * The UNDUE policy applies here since the prominence of placement and the use of imagery to give UNDUE weight are mentioned in it. Giving UNDUE weight to a FRINGE view is frankly beyond the pale. If the goal is to show an example of the Robinson projection by an organization the readers have heard of and nothing else, then the 2016 version would do that without violating our policies. M.Bitton (talk) 13:53, 23 April 2023 (UTC)
 * Yes I agree that the 2016 version is fine; I’ve uploaded it here and will add it to the article if everyone agrees. I disagree with the implication that this fixes the issues you raise. It still marks Taiwan as part of China, Somaliland as part of Somalia, etc., so it’s still UNDUE and FRINGE by the same arguments. Frankly, the main reason I argue for 2021 is because the only reason I see to prefer 2016 is a desire to push a Western Sahara POV. I maintain that the NPOV course of action is to take the most recent version without regard for its contents. But I mostly want an accurately sourced example, so 2016 is a fine compromise. Justin Kunimune (talk) 15:58, 23 April 2023 (UTC)
 * The only issue it will fix is the blatant violation of UNDUE and FRINGE. Taiwan is also shown as part of China in the UN map (please don't you dare compare the UN to a single country that contradicts itself by condemning one occupation and condoning another). Since you are being frank, let me return the favour: the only reason anyone would want to deliberately violate our policies by adding the 2021 version is to push a Moroccan and Israeli POV. M.Bitton (talk) 16:16, 23 April 2023 (UTC)


 * There is a difference between "this is a map of the world using the Robinson projection" and "this is a map of the world created by the USA Central Intelligence Agency using the Robinson projection". By definition, all political maps are going to be political.  There are many borders around the world that are disputed.  So either do not use any political maps for examples of the Robinson projection, or make sure that any political biases from the map authors are clearly stated.  Citing authorship to the CIA (as required for map attribution) should make it clear that the map represents the USA political view of the world, which may not be in agreement with other nation-states or even the United Nations.  But if you are using a map from the CIA, then you should use the most up-to-date map available.  Reverting to an older map because the CIA has taken a controversial position on Western Sahara is not an accurate portrayal of how the Robinson projection is currently used by the CIA.  Nicole Sharp (talk) 15:56, 26 April 2023 (UTC)
 * The point of the article should be to show how the Robinson projection is actually used. As such, the article citation for the outdated map should be changed from "Map of the world created by the Central Intelligence Agency" to "Former (2016) map of the world by the Central Intelligence Agency", perhaps with a footnote as to why Wikipedia is not willing to show the most up-to-date map from the CIA.  Whether you show the old map or the new map, you are presenting a certain political viewpoint since it is a political map, and you probably still need to link to the article on Western Sahara in order for readers to understand the CIA's map changes.  Or just display both maps, which helps to show how the CIA has continued to use the Robinson projection even as their recognition of international borders has changed over the years.  Nicole Sharp (talk) 16:31, 26 April 2023 (UTC)
 * Since the idea is to show an example of the Robinson projection, then the 2016 map does that perfectly (it fits the description and the attribution). There is no reason whatsoever (other than what you stated in your edit summary) to give UNDUE weight to a controversial FRINGE view. We don't need to explain why a FRINGE view is ignored, we just ignore it, that's the whole point of the UNDUE policy. M.Bitton (talk) 16:34, 26 April 2023 (UTC)