Talk:Equirectangular projection

Questions

Who invented it ? When was it first used? What advantages does it give over other projections?

Lumos3 09:24, 31 October 2006 (UTC)

left and right side

The context of the subject – "map projection" – is that the left side are linear measures on the circle (aka "angles") and the right side are linear measures on the plane. Do we really need to spell this out explicitly? There are hundreds of published map projections, and if even 10% of them get documented here, things like this will get tedious real fast. mdf 21:42, 31 October 2006 (UTC)

The use of "180" and "360" is also questionable. The left hand arguments are radians, not degrees. mdf 21:53, 31 October 2006 (UTC)

image size

I feel the new image size is too small. I carefully picked 512px, since it works about best without being obnoxiously large, and, frankly, there is going to be minimal text for an article on (most) map projections, but maximal image – the subject matter is intrinsically graphical. I "have" (such as it can be with a wiki) six other projections in, with more on the way, and a standard size is extremely important as it facilitates very easy comparison, particularly between projections of the same class. (Example: load up hammer projection and mollweide projection in separate tabs and you can "blink" them.) mdf 21:48, 31 October 2006 (UTC)

Mercator

Isn't this just the Mercator projection? Steinbach (fka Caesarion) 22:31, 31 October 2006 (UTC)

No, in a mercator projection, lines of latitude are closer together at the equator than at the poles. In an equirectangular projection, they are all equidistant. On a mercator projection, land masses near the poles, like Greenland, have their shape fairly accurately represented, but on an equirectangular projection, they are squished. Compare Image:Normal Mercator map 85deg.jpg with Image:Equirectangular-projection.jpg to see the difference.

On the other hand, sizes are more distorted in a Mercator projection, as you can see by comparing Greenland with Africa—the latter is fourteen times the size, but appears smaller. However, accurate representation of sizes is not the goal of either projection.

Foobaz·o< 15:52, 1 November 2006 (UTC)

Distorted earth?

the plate carrée has become a de-facto standard for computer applications that process global maps, such as (...) Google Earth,

Is this really true? This would mean that map fragments at high latitudes are relatively compressed in north-south direction, but this seems not to be the case. 88.211.131.57 17:40, 19 July 2007 (UTC)

You're right, Google Earth uses a orthographic projection. I don't know about the other two. Foobaz·o< 18:32, 19 July 2007 (UTC)

Definition question

what a hell is cosine doing in there? It is said, and can be seen, that the projection has "equally spaced meridians". This is simply impossible with cosine in it. If noone replies to this, I will remove it in a week. 82.207.15.147

oh wait, I take it back. Just noticed cosine is a constant :) 82.207.15.147

I agree that the cosine term is confusing. I recommend changing the variable name. — Preceding unsigned comment added by 192.0.232.239 (talk) 05:11, 16 October 2013 (UTC)

It’s not a variable, so there’s no variable name to change. The formulæ are given in standard form. Just read the description. Strebe (talk) 07:08, 16 October 2013 (UTC)

description of projection

The Platte Carre projection is a cylindrical projection but should not be referred to as an equidistant cylindrical projection.

A cylindrical equidistant projection is equidistant along the equator AND along all meridians, making a map of the world slightly more than twice as wide as it is high due to the equatorial bulge.

The Platte Carre projection is only equidistant along the equator, and can never be equidistant along any meridians because distances between lines of latitude on earth are not constant. Refering to it as equidistant is like refering to the cylindrical equal-area projection(which is of course only equidistant along the equator) or pretty much any projection there is, as equidistant.Mr Picky (talk) 20:56, 27 August 2008 (UTC)

Huh?

1. Is there some other projection that would be more appropriate for the name "equidistant cylindrical projection"? Please tell us any other synonyms you know, or give us a reference that describes this other projection.

That projection *should* be listed on the category: equidistant projections -- is it already listed there (perhaps under a synonym), or should it be added?

2. I honestly can't tell the difference between the projection Mr Picky describes as the "equidistant cylindrical projection" vs. the "plate carrée projection".

If they are not the same thing, please tell me -- what is the difference?

I agree that "distances between lines of latitude on earth are not constant" in cylindrical equal-area projections and most other cylindrical projections.

However, equirectangular projections (and, if I understand Mr Picky correctly, a cylindrical equidistant projection) are some of the few cylindrical projections that do, in fact, have a constant distance on paper between any two consecutive lines of latitude. --DavidCary (talk) 19:31, 17 July 2014 (UTC)

User:Mr Picky isn’t distinguishing between spherical and ellipsoidal models of the earth. On a spherical model, the plate carée has equally spaced parallels. On an ellipsoidal model, it doesn’t. Strebe (talk) 03:51, 19 July 2014 (UTC)

panorama software

Why is this article in panorama software category? While it is related, it's not a software. esby (talk) 12:00, 8 January 2009 (UTC)

Equirectangular projection is a common choice in 360x180 panorama making i believe. --TiagoTiago (talk) 17:56, 18 December 2009 (UTC)

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) 22:38, 6 August 2011 (UTC)

Map image is incorrectly downsampled, missing paralleles and meridians

The image map, as it appears in the main page, is incorrectly downsampled, missing parallels and meridians.

This is very confusing, considering that the scope of the image is to represent how the coordinates are projected.

See here https://www.evernote.com/shard/s2/sh/7254fce9-94fd-4f4b-b337-c8380d1d3671/e3f0a8cf4dd88a722ec1ba1d281bcc01

— Preceding unsigned comment added by Gabriel Radic (talk • contribs) 14:12, 13 September 2013 (UTC) 

I see the same problem on my desktop computer. Ironically it looks fine on my Android cellphone. Such problems are a hazard of SVG rendering. Strebe (talk) 01:05, 14 September 2013 (UTC)

File:Equirectangular projection SW.jpg to appear as POTD soon

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Picture of the day

The equirectangular projection is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing, and circles of latitude to horizontal straight lines of constant spacing. The projection is neither equal area nor conformal. Because of the distortions introduced by this projection, it has few applications beyond base imagery to be reprojected to some more useful projection.Map: Strebe, using Geocart

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Adding indicatrices on the poles and International Dateline

Plate Carrée with Tissot's Indicatrices of Distortion

I can't help but notice that the Tissot's indicatrix image on this page lacks indicatrices on the International Dateline and poles - the poles being where the majority of the distortion occurs for this projection. Would anyone be averse to me inserting my own image, which both spaces out the indicatrices at high latitudes and adds indicatrices in these regions? I know technically the ellipses are supposed to be calculated at infinitesimal scale and then sized up, so it doesn't technically make sense to put them on the poles, but I feel that it's important to illustrate just how distorted the poles are.

Justin Kunimune (talk) 03:58, 16 February 2018 (UTC)

Radius not taken into account in formula?

Source: https://frew.eri.ucsb.edu/private/ESM263/week/2/An_Album_of_Map_Projections.pdf (on-page number 219)

As seen in the linked source, both projections have the radius term R in front of both the x and y formulas. This is absent from the current formulas. It might also be good to explicitly state the Plato Carrée projection formulas, as it is different.

Aaronshenhao (talk) 01:48, 23 August 2019 (UTC)

I think you're right. Most other map projection pages include R. I went ahead and changed it; the current formulations don't have citations so I think it's fine to just make a simple change like that without messing with references?

I don't think the Plate Carree equation needs to be explicitly stated; the page describes what Plate Carree means, and it's simple enough to see in the current formulation what happens when \phi_1 and \lambda_0 go to zero.

Justin Kunimune (talk) 11:45, 23 August 2019 (UTC)

Why would the radius have to be taken into account? You could just define a map height and a map width and scale $\lambda$ and $\varphi$ appropriately to make them span the desired width and height, respectively. As it is written in the article currently, the height of the map is 20,000 km, and presumably the "default width" of the map would be 40,000 km. That's a ridiculously large map, if you ask me. It would be difficult to put on your wall. —Kri (talk) 19:35, 4 November 2022 (UTC)

Conventionally, map projection equations are given for an actual-size map (or at least one that is true-scale at some particular point, such as at the equator). If you were making a real map to print out, you would then decide on a scale factor (1/10million or something), multiply that number by the final coordinates, and write it under the legend on the resulting map. But you're right that most digital maps and many decorative maps don't care about scale and thus don't need that factor; it's more a convention than a necessity. —Justin Kunimune (talk) 19:56, 4 November 2022 (UTC)

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Transformation

Would the transformation for the plate carée version not be simply

(x,y) = (long, lat)

?

I don't see this mentioned. Butterfly or Chuang Tzu? (talk) 02:12, 21 September 2023 (UTC)

The equations for transforming globe coordinates to plane coordinates are mentioned in Definition § Forward. The text notes that for Plate Carée specifically you have to set ф1 to zero, so the cosine term disappears. Since these articles make no assumption about scale or centering there are also some R, ф0, and λ0 included. Justin Kunimune (talk) 11:29, 21 September 2023 (UTC)