[Proj] Objections to some projections

[Michael Ossipoff]

I don't know why my previous post posted in such an awkward fashion, with lines wider than the screen. Maybe because I wrote it "plain text". I'll try the "rich text" option this time. My previous post, about linearity definitions, relates in a way to this list's usual discussion topic--co-ordinate transformations--because linearity greatly eases the transformation between lat/lon and X/Y co-ordinates. I hope that, because this is also a general map projections mailing list, it's alright to post this message too: It seems to me that all of the map projections that are used at all have each their own justification, advantages and appeal. But, as we all know, some of them are inappropriately used. I'd like to mention a few: 1. Nonlinear data maps: I won't say much about this, because that would be repeating what I said last year. It's just that data maps (by which I mean maps intended to show the geographical distribution of something such as temperature, climate zones, or species habitat ranges, etc.) have the primary purpose of telling where something is. The positions on the boundaries of the zones are the important thing. Most map users won't be able to accurately find or determine lat/lon positions on such a map unless it's linear. Of course another thing that someone might want from a data maps is the _areas_ of the zones. Biologists might be interested in the areas of habitat ranges. Geography instructors might want to show to their students the areas of climate or vegetation zones, etc. When linearity and equal area are both desired, the sinusoidal projection is the best choice, it being the only projection that is both linear and equal area. In general, of course, it would be good to accomodate those who want position and those who want area, and so the sinusoidal may be the best data map projection, when the user's particular need isn't known.
 It's customary to try to minimize scale variation, by using locally centered maps such as conic, azimuthal equal area, etc. But, for data maps, distance measurement is not the purpose. Position determination and maybe area depiction are the purpose. For instance, a user of a bird-book or other nature-guide asks just one question of its range-maps: Is that species found here? 2. Robinson "projection": The Robinson projection isn't a projection. Projections have a definition, and the Robinson projection doesn't have a definition. It's only defined as a family of unspecified projections. As I've read, Robinson specified numbers for the map's width at certain latitudes, and for the Y position of certain parallels. From those number lists, anyone can make their own Robinson projection by interpolating the numbers as they choose.  Correct me if I'm wrong, and if Robinson's projection has been standardized as one projection. It seems to me that Robinson's "projection" does an excellent job of achieving its intended purpose--an attractive world map with continents upright enough to not bother someone who wants uprightness, and with good shapes and reasonable areas. If only it had a definition.  Hopefully, if it hasn't happened already, publishers will agree on a standard Robinson's projection, and its definition will be disclosed somewhere. 3. Equal area maps of countries and states: Of course one often might be interested in the relative areas of data-map zones, and of countries in maps of continents and multi-country regions. But why use equal area for non-data-map maps of countries and states, unless the map's purpose is specifically to show resources, land-use, etc., for quantitative purposes? For a given type of map, equal area roughly doubles the percentage scale variation. There's no reason to do that unless equal area is genuinely important, as described in the previous paragraph.
On general-purpose maps, distance is probably the most often measured quantity, and so the scale variation shouldn't be unnecessarily doubled.
 4. Peters projection: The Peters fiasco is too well-known to justify posting about it, but I just want to mention a few things. As you know, Lambert introduced the cylindrical equal area map in the 18th century, and so there isn't really justification to name it after anyone else. Cylindrical equal area maps of course differ in their aspect ratio. That of Peters is nearly the same as that of Gall, so it's questionable to name the aspect ratio after Peters. But that's debatable, because Peters' aspect ratio isn't _exactly_ the same as Gall's. The worst thing about the Peters projection is its promotion as the only equal area projection, or the first equal area projection. Of course equal area goes back at least to sinusoidal and Stabius-Werner, in the 16th century. Arguably it goes back to Ptolemy, in Alexandria, Egypt, in Roman times. It's claimed, and I agree, that it can be reasonably assumed that one of Ptolemy's projections was intended as an approximation to what is now called the Bonne projection, an equal-area projection. Ptolemy used circles to approximate the Bonne's meridians. But, in those days, when longitudes weren't known with accuracy, there was no need for more longitude accuracy than that of his approximation. So Ptolemy's circle approximation of the meridians is perfectly justified. It must have been obvious, at the time, that one could truly divide the parallels, and that that would ideally be better, though unnecessary, given the lack of good longitude information in those days. Ptolemy invented the Bonne projection.
 Another worst thing about the Peters projection is the fact that its promoters have claimed that it should be used for all purposes. It's common knowledge that different projections are better for different purposes. Mike Ossipoff 
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