Talk:Web Mercator projection

Reworking

This article needs a lot of work.

• “Web Mercator is a mathematically flawed version”: WP:POV violation, no source, no reasonable theory by which this could be meaningful.
• “It drops a term from the ellipsoidal Mercator equations…”: That’s not at all what it does. Down in Web Mercator#Formulas section, some partial derivatives for the ellipsoidal Mercator are given (instead of the actual formulas), and states that Google Maps drops the e term. It doesn’t “drop” it; it uses 0 for the projection. Meanwhile the derivatives are irrelevant, and what are alleged to be the formulas for the projection are not.
• “Web Mercator uses the formulæ for the spherical Mercator, but it uses the semi-major axis of the WGS 84 datum as the radius of the sphere. The difference between this sphere and the WGS 84 ellipsoid causes the resultant projection not to be precisely conformal.” This is flat-out wrong. The radius of the sphere has nothing to do with conformality. The only reason the projection is “not conformal” is because geodetic coordinates are treated as spherical coordinates. Meanwhile all whole-world projections do this because spherical coordinates are not available because there is no such thing as surveys based on spherical coordinates. People could convert geodetic coordinates to spherical coordinates for use in small-scale projections, but no one bothers to because the discrepancies are too tiny to matter at those scales.
• “Compared to the standard Mercator, Web Mercator is not conformal due to use of spherical coordinates”: Without more precise phrasing, this is wrong, too. What does “standard Mercator” here refer to? Ellipsoidal or spherical?
• The article claims, …spherical Mercator which uses a sphere with an average Earth radius, but that is wrong. Mercator is a projection, not a projection+datum. You can use any sphere you want with it.

I have made extensive corrections. Comments welcome. Thanks. Strebe (talk) 08:47, 15 February 2015 (UTC)

Hi Strebe. Thanks for doing this! I don't really have a GIS or cartography background so I did the best I could to try to understand the topic better. I'm still confused about a few things:

• Are 3857 and 3785 the same thing or not?
• What does the "spherical development of ellipsoidal coordinates" bit actually mean? I added these quotes but I don't actually understand them. Any chance of another sentence or two explaining exactly what that means and why it matters? Stevage 05:51, 3 March 2015 (UTC)

Sorry; I thought I answered this long ago but apparently I did not save my response properly. No, 3857 and 3785 differ as described. “Spherical development of ellipsoidal coordinates” means that the coordinates of locations on the earth assume an ellipsoidal model, since surveys are always against the ellipsoid. But if you project the earth as a sphere, then you introduce error due to the mismatch between the datum of the coordinates and the datum of the projection. If you want to use the sphere as your projection datum then you can convert the ellipsoidal coordinates to spherical coordinates. That’s pointless if the projection is small scale. If it’s large scale, though, then the discrepancy is noticeable. That’s a big reason why the Web Mercator receives so much flack. While historically it’s completely normal to use spherical projections for small scale maps even though the geographical data are given in geodetic (instead of spherical) coordinates, the Web Mercator retains this practice all the way down to large scale maps. That is an aberration. Technically the practice amounts to a different projection than standard Mercator usage. If you understood this explanation, and have ideas about how to convey it cleanly and concisely in the text, feel free. Strebe (talk) 22:50, 29 March 2015 (UTC)

Formulas

One small question/comment under "Formulas": Shouldn't the expression for maximum φ be determined from "φ given y = 0" rather than the current "φ given y = π"? Pbogdude (talk) 19:50, 14 March 2015 (UTC)

No. y = 0 is the equator, where φ = 0. Strebe (talk) 02:01, 15 March 2015 (UTC)

While y = 0 is the equator for Mercator, that's not the case for Web Mercator. As stated earlier in this section: 'the "world coordinates" are adjusted such that the upper left corner is (0, 0)'. In this case, y=0 corresponds to the upper left corner, where φ reaches its maximum value. The expression for φ_max (third equation in this section) follows from y = 0 in the previous equation. Pbogdude (talk) 01:47, 17 March 2015 (UTC)

I see where the misunderstanding lies. The "φ given y = π" was intended to mean from the normal Mercator formulas, not the Web Mercator formulas, but that intent was not clear from the text. Since the Web Mercator formula can be used instead, I went ahead and made that change. Strebe (talk) 04:07, 17 March 2015 (UTC)

Why is $\varphi$ not in radian in ${\begin{aligned}\varphi _{\text{max}}^{\circ }={\frac {180}{\pi }}[2\arctan(e^{\pi })-{\frac {\pi }{2}}]\end{aligned}}$ of the current article ? Kkddkkdd (talk) 15:09, 29 March 2015 (UTC)

Because coordinates people use are given in degrees. Strebe (talk) 22:39, 29 March 2015 (UTC)

It seems inconsistent with $y={\frac {128}{\pi }}2^{\text{zoom level}}(\pi -\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {\varphi }{2}}\right)\right]){\text{ pixels}}$in the current article. Kkddkkdd (talk) 16:10, 30 March 2015 (UTC)

Hence the ° symbol for it. Notice that the article talks about 85.051129°. The formula describes how to arrive at that. Meanwhile in general projection formulas are given using radians; otherwise the whole thing just becomes unwieldy. I agree: It’s not ideal, but I’m not sure how to improve it. Do you have suggestions? Strebe (talk) 04:23, 31 March 2015 (UTC)

$\varphi _{\text{max}}^{\circ }$ doesn't use a good technical notation. My suggestions are as follows:

$\varphi _{\text{max}}=2\arctan(e^{\pi })-{\frac {\pi }{2}}$, with the additional description of "If the quantity is required not in radian but degree, multiply the right side by ${\frac {128}{\pi }}$". Kkddkkdd (talk) 14:21, 1 April 2015 (UTC)

Citation needed

I think this claim "General lack of understanding that the Web Mercator differs from standard Mercator usage has caused considerable confusion and misuse." needs a citation. The next citation doesn't justify this statement. If one of the other references does, then please add it here as well - it's ok to use a reference many times. Stevage 23:03, 18 March 2015 (UTC)

NGA issued the advisory notice because people were confused, using Web Mercator for situations where the governmental agencies required true Mercator maps. That’s why NGA issued the advisory. I have cited Battersby et al, who directly describe the situation as “confusion”. Strebe (talk) 23:44, 18 March 2015 (UTC)

Ah, thank you. Stevage 23:12, 22 March 2015 (UTC)

"First Google Maps"

I'm pretty sure the very first public version of Google Maps actually used a plate carrée projection (maybe with some rescaling to get shapes approximately right at contiguous US latitudes), not a Mercator variant. At that point it only covered North America, and the shape distortion got pretty severe in northern Canada. They switched to the Web Mercator before long, though; I'm not sure exactly when. --50.177.151.55 (talk) 14:41, 18 April 2015 (UTC)