Which projections you favor?

General discussion of map projections.
RogerOwens
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Re: Which projections you favor?

Post by RogerOwens »

daan wrote: I encourage you to acquire and study, for example, Bertin’s Semiology of Graphics, any or several of the Atlas of Design volumes put out by the North American Cartographic Information Society.
Probably a good idea before I make a map, but making a map is a project for later.
A good map is far more than the minor matter of projection. It is rich in information and design
Of course, and, as I was saying in my reply to Tobias, most information for which we refer to a map can be gotten just as well from a map that is conformal, equal-area, or neither.

But there are times when we want information about relative areas, or about information that is closely-related to area. And there are times when we want the good local shapes or directions, or distances that are available only from a conformal map (because of its having, at every point, the same scale in every direction).

But yes, admittedly, usually the information for which we refer to a map doesn't require conformality or equal-area.
The information dribbled out by projection alone—and made even worse by inevitable distortion—is paltry in comparison to the wealth of information a general purpose map gives. The comparisons you make are completely overwhelmed by other concerns of a map, and since you are only rarely going to get a superb map on two different projections, forget the projection and pick the map that is, overall, a better map.
Well, I don't notice much, if any, difference in the information-richness of the wall maps (Mercator (but not anymore), Miller-Cylindrical, Gall-Stereographic, Robinson, or Peters) sold in stores. They're all uniformly sparse of information. Only a few cities shown, practically no physical geographical information. Mostly stark blank empty space.

Michael Ossipoff
Last edited by RogerOwens on Thu Mar 01, 2018 8:23 pm, edited 1 time in total.
RogerOwens
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Re: Which projections you favor?

Post by RogerOwens »

Though stores don't have equal-area maps other than Peters, and though, for that reason, I don't have an equal-area world map on the wall...

...I should add that, of course, like everyone who likes maps, I have a collection of atlases, and many or most of them have equal-area world maps.

Michael Ossipoff
Atarimaster
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Re: Which projections you favor?

Post by Atarimaster »

RogerOwens wrote: Well, I don't notice much, if any, difference in the information-richness of the wall maps (Mercator (but not anymore), Miller-Cylindrical, Gall-Stereographic, Robinson, or Peters) sold in stores. They're all uniformly sparse of information. Only a few cities shown, practically no physical geographical information. Mostly stark blank empty space.
Well, if you’d prefer a more detailed map, find a good printing service.
At shadedrelief.com, there’s a great Physical Map of the World – available in Natural Earth 1 projection, at two sizes, for a smaller and a larger wall map, with LOTS of detailed information. And Political World Map (Natural Earth 1 and 2 as well as Patterson projection).

Okay, all of them are compromise projections, but as I said, very detailed, and…
RogerOwens wrote: stores don't have equal-area maps other than Peters, and though, for that reason, I don't have an equal-area world map on the wall...
With Geocart’s raster reprojection, you can reproject them to any projection you want. Yes, that will distort the labels, but most of them will still be legible, as long as you choose a projection (for the new map) that’s not too different from the input map. Since NE1 is currently the only one of the three projections mentioned above that can be reprojected by Geocart, you’d probably get the best result using another pseudocylindrical like e.g. Eckert IV.
daan
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Re: Which projections you favor?

Post by daan »

Atarimaster wrote:With Geocart’s raster reprojection, you can reproject them to any projection you want. Yes, that will distort the labels, but most of them will still be legible, as long as you choose a projection (for the new map) that’s not too different from the input map. Since NE1 is currently the only one of the three projections mentioned above that can be reprojected by Geocart, you’d probably get the best result using another pseudocylindrical like e.g. Eckert IV.
Coincidentally, just a few days ago I put together a version of Patterson’s map using the labels from the less detailed map but the raster from the more detailed map on Natural Earth projection. I reprojected that to my 1995 equal-area projection, and printed it at 24" x 33" using archival inks on glossy photographic paper. Quite pretty, and the labels survive the reprojection abuse surprisingly well—it’s even more interesting that way because the text warping directly shows the difference in distortion between the source and target projection. You also get a bit of a 3-D effect for the text out toward the map’s limbs.

I went with the lower detail on labeling because 24" height is too small for the more detailed labeling. I can reproject it to whatever projection, of course. My wife thinks she might start putting stuff like this up on Etsy.com. I have plenty of material.

— daan
RogerOwens
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Re: Which projections you favor?

Post by RogerOwens »

Tobias--

Thanks for the info about the more detailed maps. Even most political maps have room for a lot more city, town and physical information than they have.

It will just be a matter of when I can, on my own, work with the graphic files to re-project a map.

Until that time, I could hand-draw a map, copying from a printed map, into whatever projection-graticule I've drawn.

A lot of copying work, but that's how they used to always make maps. If I make a map in that way, obviously I should take the time to optimize the choice of projection and parameters as well as I can, before I commit that all that copying labor to it.

Michael Ossipoff
Last edited by RogerOwens on Thu Mar 01, 2018 7:52 pm, edited 1 time in total.
Atarimaster
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Re: Which projections you favor?

Post by Atarimaster »

daan wrote: Coincidentally, just a few days ago I put together a version of Patterson’s map using the labels from the less detailed map but the raster from the more detailed map on Natural Earth projection.
Oh.
Stupid me, I didn’t think of that!

I thought about reprojecting that map to print it and put it on my wall a while ago – but the less detailed map is a bit too small, while the more detailed map is a bit too large.
Of course, I could’ve used to large map and reproject it to the smaller size that I want, but in that case I think some labels would become too small to be readable.

But combining the labels from the smaller version with the raster from the larger map should work for me, too!
I think I’ve got a new project coming up. :-)
The hardest part, I guess, will be to decide which new projection I’m going to use. There are so many that I like…

By the way, when you combined labels and raster, did you
a) combine them in AI (or whatever application you’re using), import the combined result in Geocart to reproject it, or
b) reproject labels and raster separately, export them from Geocart to put the two reprojected maps together again in AI?

I think I’d prefer b, because that’d enable me to choose a different graticule (with 15° or 10° spacing) but still put the labels layer on top of it. Although on the other hand, I like that in the original map, the graticule lines are interrupted sometimes in order not to strike through labels.
I’ll have to experiment a bit on that.
daan
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Re: Which projections you favor?

Post by daan »

Atarimaster wrote:But combining the labels from the smaller version with the raster from the larger map should work for me, too!
I think I’ve got a new project coming up. :-)
Be aware that the text placement might be a lot more work than you anticipate. In the less detailed labeling file, a problem is that any place name for a feature at significant elevation or depression is shifted, including the “bullseye” mark for it. I spent many hours adjusting the placement of these marks and text by superposing its layer against the detailed label set (which has no such problem), toggling visibility for the layer off and on, and then manually moving anything that failed the “blink test”. It was tedious and error-prone. Patterson says this is a natural consequence of the shaded relief rendering used for the less-detailed file, and that it looks right there. I didn’t check that claim, but I can certainly confirm that it’s not right for the high-detail raster.

I can just give you what I have.
By the way, when you combined labels and raster, did you
a) combine them in AI (or whatever application you’re using), import the combined result in Geocart to reproject it, or
b) reproject labels and raster separately, export them from Geocart to put the two reprojected maps together again in AI?

I think I’d prefer b, because that’d enable me to choose a different graticule (with 15° or 10° spacing) but still put the labels layer on top of it. Although on the other hand, I like that in the original map, the graticule lines are interrupted sometimes in order not to strike through labels.
I’ll have to experiment a bit on that.
I like the gaps in the graticule to avoid running through test, but ultimately I opted to use the graticule from Geocart because then I have control over it. So, with regrets, I eliminated the graticule layer from the labels file. Patterson recently cleaned up the text layer a lot, by the way, after I reported that what he had posted was messed up. The text-converted-to-outlines did not, in fact, preserve the special diacriticals. Kudos to Tom for responsiveness, and especially for making all this available.

— daan
Piotr
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Re: Which projections you favor?

Post by Piotr »

RogerOwens is more sensitive to vertical stretch/horizontal squish (or just "vertical"), while I'm more sensitive to horizontal stretch/vertical squish (or just horizontal). This is why I think 45° equirectangular looks much better than 30° or 0° equirectangular. Or maybe it's the bias of me living in Poland. This, that or both. To me, there are boring projections (like Robinson; this one seems to mirror the RogerOwens' dislike of Winkel Tripel) that I have no reason to like or use, but I don't really hate any map projection (well, except for a theoretical projection that distorted the map to the shape of "Piotr *s dumb" or something).

Why do I think Robinson is boring? Because it just is to me. It's pseudocylindrical, so there is extreme shearing, and makes the map more biased (less compromise). It's not simple, compared to Apian II. It has way too much flattening on higher latitudes (and I seriously don't just mean Arctic or Antarctic). Winkel Tripel is just better and more "compromise" to me.

It seems that I'm completely different than RogerOwens.
RogerOwens
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Re: Which projections you favor?

Post by RogerOwens »

Piotr wrote:RogerOwens is more sensitive to vertical stretch/horizontal squish (or just "vertical"), while I'm more sensitive to horizontal stretch/vertical squish (or just horizontal).
I consider both to be equally undesirable. The measure consisting of min/max scale counts both directions of compression equally.

But yes, it's true that the shape-distortion of Africa stands out particularly much, because of Africa's size and location.
This is why I think 45° equirectangular looks much better than 30° or 0° equirectangular. Or maybe it's the bias of me living in Poland. This, that or both.
Sure, and likewise Equirectangular with standard parallel at lat 45 likewise portrays the U.S. more accurately than does the one with standard parallel at lat 30.

One thing I like about Behrmann equal-area is that its shape-compromise is between the equator and lat 41.4 ...resulting in the U.S. being about as accurately-portrayed as Africa.

With Cylindrical Equal-Area, lat 35. 4 has cos^2(lat) that's equal to the average cos^2(lat), averaged over the entire surface of the Earth.

Half of the Earth's surface is farther from the equator than lat 30, and half of the Earth's surface is closer to the equator than lat 30.


To me, there are boring projections (like Robinson; this one seems to mirror the RogerOwens' dislike of Winkel Tripel) that I have no reason to like or use, but I don't really hate any map projection.
I feel that Robinson achieves its design purpose of overall good appearance. I like it because it's pseudocylindrical. I understand and respect the preference that many people have for maps that minimize the worst magnification and shape-distortion, without being conformal or equal area.

I just personally prefer a map that gives the exact information of a conformal or equal-area map.

I, too, like all map-projections (...but prefer ones with useful properties and without appearance-spoiling distortion that doesn't bring any usefulness).
Why do I think Robinson is boring? Because it just is to me. It's pseudocylindrical, so there is extreme shearing
It's just a matter of what a person wants from a map. To me, usefulness is important. Pseudocylindrical maps have some useful properties. For pseudocylindrrical maps, a latitude-ruler can be marked with scales that tell latitude, horizontal scale, and area-magnification at any particular Y-value on the map. They more meaningfully portray latitude-related information. Longitudes can be easily judged or measured too, on a pseudocylindrical.
, and makes the map more biased (less compromise).
Well, it's a subjective individual matter, what kind of compromise one prefers.

Yes, Robinson must have valued reducing Arctic magnification more than accurate Arctic shape-portrayal. Well, which is more important: The area of the Arctic, or island-shapes in the Arctic Ocean?

Relatively good shapes, and areas not so bad, in the non-polar Arctic, instead of more accurate shapes very near to the pole.

It's impossible to say which kind of compromise is better.

As I said, I personally prefer maps that are exactly equal-area or conformal, but I consider Robinson to be a good compromise, if a compromise is desired--and many people like a compromise map whose area and shape errors aren't so bad, over most of the map.
It's not simple, compared to Apian II.
I like the simplicity of Apianus II. I've suggested it as an early map to display in school-rooms for the early school-years.
It [Robinson] has way too much flattening on higher latitudes (and I seriously don't just mean Arctic or Antarctic).


I don't find it so. The U.S. is portrayed with shape that I don't notice anything wrong with*. Canada isn't seriously magnified, in comparison to the U.S., compared to their relative sizes on a globe. Greenland is, of course, flattened, in comparison to a globe, but not as badly as it is in cylindrical projections.

*Sure, Robinson's U.S. is barely east-west compressed, compared to its shape in Mercator. But that's barely noticeable, and certainly not problematic. It doesn't stand out as an error. Poland is farther north, and farther from Robinson's standard parallel, and I can understand that residents of Northern Europe might prefer Winkel's North-European shapes to those of Robinson. Winkel probably has a more northern standard parallel than Robinson does.

But i want to repeat here that half of the Earth's surface is within 30 degrees of the equator, and that about 75% of the Earth's surface is within 49 degrees of the equator.

Sure, there's great flattening in the high arctic, but not so outrageously bad in northern land-masses, other than arctic islands.
Winkel Tripel is just better and more "compromise" to me.
Africa is unrealistically skinny in Winkel-Tripel. That could be justified in an equal-area map, but there's no excuse for it in a map that has no exact useful properties. The U.S., too, is greatly horizontally-compressed in Winkel.

Half of the Earth's surface is in the +30 to -30 latitude band, a region of outrageous horizontal compression in Winkel.

About 75% of the Earth's surface is in the +49 to -49 latitude band (a parallel that coincides with the northern U.S. border), which, as I said, is highly horizontally compressed.

There's just no excuse for that in a "compromise" map that has no exact useful properties.
It seems that I'm completely different than RogerOwens.
Undeniably different people often prefer different advantages for maps. That doesn't mean that anyone is wrong.

Michael Ossipoff
quadibloc
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Re: Which projections you favor?

Post by quadibloc »

I certainly agree with Daniel Strebe that different projections serve different purposes, and so you can't just use one favorite projection for everything.
But that doesnt mean one can't have a "favorite projection" or two - I've seen a few projections I liked, often because they were particularly low in shape distortion.
I think my all-time favorite is Bartholomew's Regional Projection, specifically the modified version that was conical to the poles that appeared in the Times World Atlas.
That's despite the fact that there is a kink in the projection where the conical part joins the Bonne's part (actually, in the Times version, but not the earlier ones, they fudged the projection slightly to get rid of the kink) which is an attribute that turned me against Goode's Homolosine projection.
As for my own projections, I've played with an interrupted Bonne's, and with putting the world on two hemispheres (the conventional Eastern and Western ones, divided at 20 degrees West) each displayed on a (transverse) conic conformal.
Also, I prefer the Hammer-Aitoff to the Mollweide, and the Miller Cylindrical to the Gall Stereographic; I'd rather not have too much equatorial stretching in a projection.
I am enraptured also by the beauty of some exotic projections, even though I admit they're not practical for every-use; the conformal projection on an octahedron using Dixon elliptic functions, and Guyou's Doubly-Periodic projection using ordinary elliptic integrals, and August's conformal.
And the Van der Grinten IV is a nice compromise projection that's easy to draw. Not only that, but the scale is uniform all the way across the Equator. So, although nobody else, to my knowledge, has ever tried it, you can interrupt it just the same way you can interrupt a Sinusoidal or a Mollweide.
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