Why Mercator for the Web?(mapthematics.com)
mapthematics.com
Why Mercator for the Web?
https://www.mapthematics.com/forums/viewtopic.php?f=8&t=251
8 comments
I'd love to see a mapping service with dynamic projection functionality based on zoom and window view. The concept of one fixed projection doesn't account for the nature of digital mapping today.
Yes, I'd love a major mapping service to consider something like http://cartography.oregonstate.edu/demos/AdaptiveCompositeMa...
We now have maps that resemble nothing like any paper map before. There's no reason at all they have to be like zooming closer to the biggest paper map ever made.
(Web) Mercator is almost certainly the right choice for the things most people use maps for: local directions, routing etc. Minimal distortion on that scale. If you look at the "Projection Diagram" on that page, Mercator is only used for the highest zoom levels, however. Above that it's adaptive based on both zoom and latitude.
We now have maps that resemble nothing like any paper map before. There's no reason at all they have to be like zooming closer to the biggest paper map ever made.
(Web) Mercator is almost certainly the right choice for the things most people use maps for: local directions, routing etc. Minimal distortion on that scale. If you look at the "Projection Diagram" on that page, Mercator is only used for the highest zoom levels, however. Above that it's adaptive based on both zoom and latitude.
By the way, a comparison between Google Maps in satellite view and in map view: http://imgur.com/a/GXczm
(satellite view uses a projection on a sphere, and then renders the sphere from the users current viewpoint)
(satellite view uses a projection on a sphere, and then renders the sphere from the users current viewpoint)
The transition into Mercator is pretty jarring at high latitudes (try zooming into Greenland). I wonder if there's a good way to smoothly interpolate between projections as you zoom.
I like the idea to just show the globe (i.e. orthographic projection); it is familiar, interactive, distortions are not deceiving and naturally disappear with zoom.
i built an interactive virtual globe using open gl (like nasa worldwind/google earth, but with real time satellite imagery). it's super fun.
when you're dealing with things like constellations of satellites, it's often useful to have a map alternative, since you can only (continuously) see half the earth at once with a globe.
when you're dealing with things like constellations of satellites, it's often useful to have a map alternative, since you can only (continuously) see half the earth at once with a globe.
There’s been some work along these lines recently:
http://cartography.oregonstate.edu/pdf/2012_Jenny_AdaptiveCo...
http://web.stanford.edu/~sukolsak/projects/cs448b_final_pape...
http://cartography.oregonstate.edu/pdf/2012_Jenny_AdaptiveCo...
http://web.stanford.edu/~sukolsak/projects/cs448b_final_pape...
The Mercator distortion automatically decreases as you increase zoom levels. Street level zoom is only noticeable really close to the poles so even micmerdo staion looks fine.
"Yet when you look objectively at the impact a map projection has on the beliefs and world view of the general populace, you really don’t come up with much. Maps are only a tiny part of most people’s lives. They’re exposed to many projections anyway—as they should be. They take cues from a map in many ways, not just relative sizes. And mostly, they really don’t care."
Well, personally, I've never been exposed to other projections until 28 years of age and that was only because I happened upon an article about how wrong mercator projection is on Hacker News.
While it really is a tiny part of my life and I don't really care, the realization that Africa is huge and almost three times bigger then Europe and that Greenland is tiny is something I consider an important thing to know - and probably changes some of my views on things (for instance I never quite understood how Africa has so many countries - which if you triple it's size, it becomes much clearer).
Well, personally, I've never been exposed to other projections until 28 years of age and that was only because I happened upon an article about how wrong mercator projection is on Hacker News.
While it really is a tiny part of my life and I don't really care, the realization that Africa is huge and almost three times bigger then Europe and that Greenland is tiny is something I consider an important thing to know - and probably changes some of my views on things (for instance I never quite understood how Africa has so many countries - which if you triple it's size, it becomes much clearer).
"Well, personally, I've never been exposed to other projections until 28 years…"
That is vanishingly unlikely. These are projections you have practically certainly seen: https://www.mapthematics.com/ProjectionsList.php?Projection=... https://www.mapthematics.com/ProjectionsList.php?Projection=... https://www.mapthematics.com/ProjectionsList.php?Projection=... https://www.mapthematics.com/ProjectionsList.php?Projection=...
And many others. Also, people often mistake any rectangular projection for Mercator. I have even seen this happen in academic literature.
That is vanishingly unlikely. These are projections you have practically certainly seen: https://www.mapthematics.com/ProjectionsList.php?Projection=... https://www.mapthematics.com/ProjectionsList.php?Projection=... https://www.mapthematics.com/ProjectionsList.php?Projection=... https://www.mapthematics.com/ProjectionsList.php?Projection=...
And many others. Also, people often mistake any rectangular projection for Mercator. I have even seen this happen in academic literature.
The thing is, all projections are wrong in some sense. That's an unavoidable fact when transposing between flat surfaces where the angles in triangles always add up to 180 degrees, and triangles on curved surfaces where they don't.
For instance, on a flat plane, given a straight line with two lines perpendicular (i.e. both at 90 degrees), those two lines will be parallel, and will not form a triangle with the base. But on a globe, two lines of longitude that are both at 90 degrees to the equatorial line will nevertheless converge at the pole. Depending on how far apart they are, the sum of the angles in a triangle on a curved surface can approach 360 degrees.
What this means is that it's mathematically impossible to express triangles that work on a curved surface using triangles that work on a flat plane, because the latter is limited in ways that the former is not. In other words, in going from curved figures to flat ones, you're going to have to distort something.
Your three choices are shape, distance, and direction. The more a projection preserves one, the more it's going to have to distort another. Some projections try to strike a balance, others focus on one aspect at the expense of another.
The Mercator - which was originally designed for mariners - opted to preserve direction, and did so at the expense of shape, and, to a lesser degree, distance. So instead of a map where the distance between degrees varies at different points on the map, Mercator provides uniform measures of degree at every point. That means you can pick a location on the map, draw a straight line to your desired destination, note the angle formed by that line and magnetic and / or polar north, then set a course along that bearing with full confidence that you'll arrive where you want to. As far as direction goes, Mercator is absolutely correct.
To visualize how this works, see this Wikipedia article showing Tissot's Indicatrix on a sphere, then see this Esri writeup and note that on a Mercator, all the indices are perfect circles.
http://en.wikipedia.org/wiki/Tissot%27s_indicatrix
http://blogs.esri.com/esri/arcgis/2011/03/24/tissot-s-indica...
For instance, on a flat plane, given a straight line with two lines perpendicular (i.e. both at 90 degrees), those two lines will be parallel, and will not form a triangle with the base. But on a globe, two lines of longitude that are both at 90 degrees to the equatorial line will nevertheless converge at the pole. Depending on how far apart they are, the sum of the angles in a triangle on a curved surface can approach 360 degrees.
What this means is that it's mathematically impossible to express triangles that work on a curved surface using triangles that work on a flat plane, because the latter is limited in ways that the former is not. In other words, in going from curved figures to flat ones, you're going to have to distort something.
Your three choices are shape, distance, and direction. The more a projection preserves one, the more it's going to have to distort another. Some projections try to strike a balance, others focus on one aspect at the expense of another.
The Mercator - which was originally designed for mariners - opted to preserve direction, and did so at the expense of shape, and, to a lesser degree, distance. So instead of a map where the distance between degrees varies at different points on the map, Mercator provides uniform measures of degree at every point. That means you can pick a location on the map, draw a straight line to your desired destination, note the angle formed by that line and magnetic and / or polar north, then set a course along that bearing with full confidence that you'll arrive where you want to. As far as direction goes, Mercator is absolutely correct.
To visualize how this works, see this Wikipedia article showing Tissot's Indicatrix on a sphere, then see this Esri writeup and note that on a Mercator, all the indices are perfect circles.
http://en.wikipedia.org/wiki/Tissot%27s_indicatrix
http://blogs.esri.com/esri/arcgis/2011/03/24/tissot-s-indica...
conformality and area are preserved on globes, both physical and virtual (like in google earth). as a kid, i remember thinking africa was huge from the globes that teachers had in classrooms.
in ~2007 or so, i actually tried to buy a physical globe for my desk. i went into a couple office supply stores and the high school age employees had never even heard of a globe. it was the strangest thing trying to explain what a globe was: "it's like a ball with a map on it".
in ~2007 or so, i actually tried to buy a physical globe for my desk. i went into a couple office supply stores and the high school age employees had never even heard of a globe. it was the strangest thing trying to explain what a globe was: "it's like a ball with a map on it".
Hey, some of us like the extreme distortion of the Mercator projection!
http://mrgris.com/projects/merc-extreme/
It is interesting how WebGL is enabling the use of dynamic re-projection and making the old web Mercator tile pyramid obsolete. Also kind of sad, though; the 'slippy map' heralded a new age of map openness, interoperability, and opportunities for remixing. I will be very sad to see that go...
http://mrgris.com/projects/merc-extreme/
It is interesting how WebGL is enabling the use of dynamic re-projection and making the old web Mercator tile pyramid obsolete. Also kind of sad, though; the 'slippy map' heralded a new age of map openness, interoperability, and opportunities for remixing. I will be very sad to see that go...
How good are you at identifying country shapes with the mercator distortion?
http://bramus.github.io/mercator-puzzle-redux/
Might need to zoom in a little. The original was a little easier, but didn't randomise the country set - the redux version picks lots of tiny globs that are hard to identify at scale
https://gmaps-samples.googlecode.com/svn/trunk/poly/puzzledr...
http://bramus.github.io/mercator-puzzle-redux/
Might need to zoom in a little. The original was a little easier, but didn't randomise the country set - the redux version picks lots of tiny globs that are hard to identify at scale
https://gmaps-samples.googlecode.com/svn/trunk/poly/puzzledr...
Do people really complain because google maps uses Mercator (or a similar) projection? My understanding was that the complaint was when Mercator is used for wall maps like in the classroom. When you show the whole world using it, the sizes of the continents are way off proportion.
On a zoomed in scale like when showing streets or smaller areas, it doesn't matter.
On a zoomed in scale like when showing streets or smaller areas, it doesn't matter.
The problem is that Google Maps has become a very convenient always available source for maps, and the brand is highly trusted. Moreover, many other online mapping services have adopted the same projection.
Students (or whoever else) who might have previously gone to look up a region of the world on a globe, large paper map, or atlas are now turning to sites like Google Maps instead. The market for high quality paper maps has fallen quite a bit as more convenient online maps become the go-to source for answering all sorts of geographic questions.
Moreover, Mercator maps are turning up as the basis for many other tools. For instance, several online map collections have started georeferencing and reprojecting historical maps onto a Mercator projection, saving them as raster tiles, and allowing visitors to pan and zoom around on those reprojected maps, Google-Maps style. Instead of looking at various original maps with region-specific projections, now the viewer is getting more and more exposure to just Mercator maps.
If you look around the web, there are many examples of good maps with reasonable projections, but there are also many many examples of people using the Mercator projection in wholly inappropriate contexts. For example, I see Mercator choropleths of US statistical data quite frequently, which should be using something like an Albers equal-area conic projection instead. (http://bl.ocks.org/mbostock/3734308)
On the bright side, work like the D3 guys (Mike Bostock & Jason Davies) and others have been doing has made it easier than ever to construct nice web maps in all sorts of projections, without shelling out big bucks for fancy GIS software.
http://www.jasondavies.com/maps/
https://github.com/d3/d3-geo-projection/
Students (or whoever else) who might have previously gone to look up a region of the world on a globe, large paper map, or atlas are now turning to sites like Google Maps instead. The market for high quality paper maps has fallen quite a bit as more convenient online maps become the go-to source for answering all sorts of geographic questions.
Moreover, Mercator maps are turning up as the basis for many other tools. For instance, several online map collections have started georeferencing and reprojecting historical maps onto a Mercator projection, saving them as raster tiles, and allowing visitors to pan and zoom around on those reprojected maps, Google-Maps style. Instead of looking at various original maps with region-specific projections, now the viewer is getting more and more exposure to just Mercator maps.
If you look around the web, there are many examples of good maps with reasonable projections, but there are also many many examples of people using the Mercator projection in wholly inappropriate contexts. For example, I see Mercator choropleths of US statistical data quite frequently, which should be using something like an Albers equal-area conic projection instead. (http://bl.ocks.org/mbostock/3734308)
On the bright side, work like the D3 guys (Mike Bostock & Jason Davies) and others have been doing has made it easier than ever to construct nice web maps in all sorts of projections, without shelling out big bucks for fancy GIS software.
http://www.jasondavies.com/maps/
https://github.com/d3/d3-geo-projection/
> Students (or whoever else) who might have previously gone to look up a region of the world on a globe, large paper map, or atlas are now turning to sites like Google Maps instead.
If they're looking for a globe replacement, they should use Google Earth instead. (Or click the "Earth" view in Google Maps, which returns satellite footage on a globe.)
If they're looking for a globe replacement, they should use Google Earth instead. (Or click the "Earth" view in Google Maps, which returns satellite footage on a globe.)
There are orders of magnitude more users of services like Google Maps, Bing Maps, and OpenStreetMap than separate apps like Google Earth. If a non-savvy map user has a simple question, they’re unlikely to turn to Google Earth.
Anyhow, I think the “earth” view of Google Maps is a “let’s make something that looks cool in a 2 minute demo” gimmick, not a serious tool. When zoomed out, it adds fake atmosphere, arbitrary static clouds which entirely cover some countries, and silly reflection effects. Its user interface is laggy and glitchy as heck, even on top-of-the-line current hardware. It’s impossible to look at either the arctic or antarctic head-on, as the rotation of the globe is strictly constrained.
More generally, orthographic projections have a place as a reference to compare maps to a view on a 3D globe, but they make it impossible to answer many kinds of questions because they involve severe distortions in any particular view, and it’s impossible to see more than about 40% of the globe at a time. Even a draggable orthographic projection makes it difficult to make inferences about distances, directions, and areas that are easy on a physical globe or on the appropriate flat map. Furthermore, satellite pictures are a wonderful tool sometimes, and a nearly useless tool other times.
Anyhow, I think the “earth” view of Google Maps is a “let’s make something that looks cool in a 2 minute demo” gimmick, not a serious tool. When zoomed out, it adds fake atmosphere, arbitrary static clouds which entirely cover some countries, and silly reflection effects. Its user interface is laggy and glitchy as heck, even on top-of-the-line current hardware. It’s impossible to look at either the arctic or antarctic head-on, as the rotation of the globe is strictly constrained.
More generally, orthographic projections have a place as a reference to compare maps to a view on a 3D globe, but they make it impossible to answer many kinds of questions because they involve severe distortions in any particular view, and it’s impossible to see more than about 40% of the globe at a time. Even a draggable orthographic projection makes it difficult to make inferences about distances, directions, and areas that are easy on a physical globe or on the appropriate flat map. Furthermore, satellite pictures are a wonderful tool sometimes, and a nearly useless tool other times.
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What's the problem with a mercator choropeth? Assuming scaling by area (if necessary) is done on the true area (not the distorted area visible), I can't see any obvious issues - am I missing something?
It depends on the extent of the map. For local areas, what you suggest is just fine. At the scale of a continent, it’s problematic, and gets more and more problematic as you zoom out.
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Summary: It's about the only conformal map out there where "north" is always up. (Conformal: when you zoom in on it, the map that you see has the right shapes and so makes sense locally, and is not terribly distorted.) So you can pan and zoom to your heart's content.
That is the first over-two-thirds of the article, which is an argument for Mercator. Web Mercator is not conformal, which is admitted in the last part of the document. I personally find the final argument for Web Mercator to be a bunch of hand waving that seems to use "complexity" in inconsistent ways, ignoring that having data that is actually accurate and based on a consistent formula is "less complex" even if it requires a small amount of extra trigonometry (and I'm not even certain that that is really true, though I have not had a chance to finish all of the reading I have on my todo list for map projections, Web Mercator in particular; see URL).
http://cegis.usgs.gov/projection/pdf/Battersby_Implications%...
http://cegis.usgs.gov/projection/pdf/Battersby_Implications%...
It’s kind of stupid to use “Google Mercator” instead of a conformal cylindrical projection of an ellipsoid http://en.wikipedia.org/wiki/Mercator_projection#Generalizat...
However, the difference between that and Google Mercator is in practice pretty slight, since the flattening of the WGS84 ellipsoid is only about 1 part in 300. It’s not really that big a deal for most uses, IMO. Anyone with a use case where it matters can pick a different projection and either source data elsewhere or reproject the data from Google Maps or whatever similar source. If people are using Google Maps (or similar) data in inappropriate contexts, they should stop doing that.
The bigger problem is using a Mercator projection at all for small-scale (zoomed out) views of the map in contexts like a convenient online map viewer where less savvy viewers are likely to be mislead by the scale distortion, and get little benefit from having straight rhumb lines.
However, the difference between that and Google Mercator is in practice pretty slight, since the flattening of the WGS84 ellipsoid is only about 1 part in 300. It’s not really that big a deal for most uses, IMO. Anyone with a use case where it matters can pick a different projection and either source data elsewhere or reproject the data from Google Maps or whatever similar source. If people are using Google Maps (or similar) data in inappropriate contexts, they should stop doing that.
The bigger problem is using a Mercator projection at all for small-scale (zoomed out) views of the map in contexts like a convenient online map viewer where less savvy viewers are likely to be mislead by the scale distortion, and get little benefit from having straight rhumb lines.
Couple of points.
* It’s not trigonometry. The inverse of a proper ellipsoidal Mercator has no closed-form solution.
* Data generally are in geographic coordinates, not map coordinates. If your data are in map coordinates, then definitely do not use Web Mercator unless your map coordinates are also Web Mercator. The same is true for any projection: You need to know what coordinates your source data are in (Geographic? Than what datum? Or map? Then what projection?). If there is a mismatch between your data coordinates and the projection you’re using, you have to convert between them. Web Mercator adds nothing new to that problem.
* There is nothing “inconsistent” about Web Mercator formulas.
The simpler calculation was probably chosen because it would be a bad idea to store or analyze data in Web Mercator (so the projection is done each time a tile is rendered).
I wouldn't be terribly surprised if the person who set it all up chose the "wrong" radius (from your link) in order to make the projection even less useful for analysis.
I wouldn't be terribly surprised if the person who set it all up chose the "wrong" radius (from your link) in order to make the projection even less useful for analysis.
That's pretty long post about nothing. It starts with a lie ("As you may know, Google Maps uses the Mercator projection."), which is admitted in the very end of the post, making previous musings somewhat misdirected.
The most obvious reason to use web-mercator is it is easily computed. Probably the real reason to use it now is that people are used to it. Most google maps (or even OSM) users probably don't even suspect there's something wrong with that map, and don't imagine there are other projections. The only people who complain is a bunch of cartographers, and who cares about them, right?
So I don't expect something is gonna change and don't really know if it is easy enough to provide alternative projections for OSM. For google maps at least there's google earth.
For me, as a user, it is inconvenient. I almost never care for north to be exactly on top. I use maps on large scale to answer questions like "hm, so where is that Sahara desert? How large is 9,400,000 square kilometres? How far is the distance between these two airports? What is Cambodia?" To answer these questions web-mercator is nearly the worst projection possible.
On small scale I don't even expect the map to be precise, I just need it to tell me where should I turn to get where I need. So on small scale web-mercator isn't harmful for me, but most other projections wouldn't be either.
Personally I like Kavrayskiy VII projection¹. The only thing I dislike about it is the fact it make Antarctica to look huge. I wonder why it isn't more popular, really.
[1] - http://en.wikipedia.org/wiki/Kavrayskiy_VII_projection
The most obvious reason to use web-mercator is it is easily computed. Probably the real reason to use it now is that people are used to it. Most google maps (or even OSM) users probably don't even suspect there's something wrong with that map, and don't imagine there are other projections. The only people who complain is a bunch of cartographers, and who cares about them, right?
So I don't expect something is gonna change and don't really know if it is easy enough to provide alternative projections for OSM. For google maps at least there's google earth.
For me, as a user, it is inconvenient. I almost never care for north to be exactly on top. I use maps on large scale to answer questions like "hm, so where is that Sahara desert? How large is 9,400,000 square kilometres? How far is the distance between these two airports? What is Cambodia?" To answer these questions web-mercator is nearly the worst projection possible.
On small scale I don't even expect the map to be precise, I just need it to tell me where should I turn to get where I need. So on small scale web-mercator isn't harmful for me, but most other projections wouldn't be either.
Personally I like Kavrayskiy VII projection¹. The only thing I dislike about it is the fact it make Antarctica to look huge. I wonder why it isn't more popular, really.
[1] - http://en.wikipedia.org/wiki/Kavrayskiy_VII_projection
"It starts with a lie"
Web Mercator is a Mercator projection, so it's not a lie, just slightly imprecise.
"which is admitted in the very end of the post"
The post discusses Web Mercator in the second sentence.
"The most obvious reason to use web-mercator is it is easily computed."
Which the article discusses.
"For me, as a user, it is inconvenient. I almost never care for north to be exactly on top."
Google maps has a lot of users with various use cases. For uses involving directions, conformal maps are better, and the maps are heavily used for that. All engineering decisions are compromises, Google's compromises apparently were the best for their expected use cases.
Web Mercator is a Mercator projection, so it's not a lie, just slightly imprecise.
"which is admitted in the very end of the post"
The post discusses Web Mercator in the second sentence.
"The most obvious reason to use web-mercator is it is easily computed."
Which the article discusses.
"For me, as a user, it is inconvenient. I almost never care for north to be exactly on top."
Google maps has a lot of users with various use cases. For uses involving directions, conformal maps are better, and the maps are heavily used for that. All engineering decisions are compromises, Google's compromises apparently were the best for their expected use cases.
Friendly note: you’re using “large scale” and “small scale” precisely the opposite of the way geographers/cartographers use those terms. A “large scale” map is one that is zoomed in on one tiny area, while a “small scale” map is one showing a large region or the whole world. https://en.wikipedia.org/wiki/Scale_(map)#Large_scale.2C_med...
Those of us with experiments in Antarctica really dislike Google's Mercator projection.
« laugh » No kidding…
The West Wing did a really good clip on what's wrong with the Mercator Projection.
https://www.youtube.com/watch?v=vVX-PrBRtTY
https://www.youtube.com/watch?v=vVX-PrBRtTY