[GIS] How to represent an imaginary flat world in QGIS without using a round-world CRS

cartographycoordinate systemqgis

Like one or two other users, I'm interested in using QGIS to map an imaginary flat world. A previous answer suggested simply refraining from defining a CRS for such a world, but I cannot seem to make that work well with QGIS 1.7 on Mac OS X. Pretty much every time I interact with a layer, the software warns me that no CRS is defined, and if I ever inadvertently open the CRS dialog for any reason, QGIS appears to apply the default CRS to my map. That happens quite often when I'm fumbling around looking for a way to find a setting that will establish the appropriate scale for distances on the map.

The fictional world is a flat plane of unknown (and possibly infinite) extent. The map is centered on a location that is locally taken to be the center of the world. Although the world is of unknown extent, the mapped area is about ten thousand kilometers north-to-south, and the same east-to-west.

I can map the world adequately using tools like Photoshop and Illustrator, but obviously they aren't GIS systems. I'd like to use QGIS for the myriad additional data-handling features it would provide, but I'm pretty well stumped by my inability so far to find or create a CRS –or to get QGIS to accept working without one.

I'm close to concluding that I'll have to write my own quasi-GIS system for this purpose that obeys the (admittedly idiosyncratic) rules of the fictional world.

Best Answer

Simply tell the GIS that your coordinates are for an equidistant azimuthal projection, polar aspect (either pole will do). Employ a spherical datum (such as an authalic sphere. Just make sure never to ask the GIS to do "spherically correct" calculations or to "unproject" the coordinates, so that it sticks to Euclidean distance, area, and angle calculations.

One advantage of this projection is that the usual latitude-longitude graticule maps to a polar coordinate graticule. (Otherwise, you might just as well use any extensive projection, such as the world Mercator.)

GISes have a proclivity to clip this projection to a hemisphere. Thus, if you map parts of a world that are greater than 10,000 Km from the origin, you will likely need a workaround. One way would be to change your unit of measurement. E.g., interpret one meter (as reported by the GIS) as a "disc kilometer" and adjust all your coordinates accordingly: that will allow the GIS to handle distances out to 20,000,000 km, which will be enough room for a while :-).

Related Solutions

[GIS] How to specify a CRS for a fictional game map in QGIS

There are a couple of things to note about the map. First, the lines of latitude are the same distance apart, which means it is in an equirectangular projection. The upshot of this is that neither distances or angles are preserved making it not so useful for navigation. The second point is that it has a scale bar in linear units. Because distances on the ground vary according to their latitude when viewed on this map, the scale is mostly meaningless.

However, as this is a game world, you are at liberty to play around with it to your heart's content. The first thing you can do is decide how big a world it is by assuming the scalebar represents horizontal distances at the equator. It looks to be about 32 degrees over 1000km, giving you an equatorial circumference of 11,250,000m and a radius of 1790493.11m, making it about the size of the moon. The next thing is that the earth is approximately an ellipsoid, being flatter at the poles. For the earth, the inverse ratio of pole-to-pole radius and equatorial is about 298.25, the moon is almost spherical at 800.

Armed with that information, you are able to create your proj4 definition:

+proj=eqc +a=1790493.11 +lat_ts=0 +lon_0=0 +rf=800 +units=m +no_defs

+lat_ts isn't strictly necessary, but is useful for reference. It is the "latitude of true scale", which is what we based our equatorial circumference from. +lon_0 represents the longitude of the centre of the map, which in this case is the prime meridian.

Opening up QGIS and selecting Custom CRS..., I've put in our parameters into the test box, and entered north 0, east 32, which gives me 1,000,000m which is our 1,000km we were expecting for that many degrees at the equator. So go ahead and create your own CRS with a memorable name.

Now you just need to georeference the map by using the georeferencer plugin, and choosing three known points. When I did it, I put one at the equator/prime meridian, one 32 degrees (ish) east on the equator, one 32 degrees (ish) north on the prime meridian. Both these latter points have x and y values of 1000000 respectively.

And that's it! As I said before however, in this projection your east-west distances will be increasingly inaccurate away from the equator, so it might be worth creating a few more "local" projections for different countries, as well as a lat/long CRS, but that is getting a bit deep at this stage. You may find it helpful to read up on map projections (just Google it), and read the Wikipedia entry for map projections, which should give you a better idea of how it all works.

Incidentally, a long/lat CRS for your world will simply be:

+proj=lonlat +a=1790493.11 +rf=800 +no_defs

[GIS] How to create an Azimuthal Equidistant map for long-distance radio

You have to specify the radius of a sphere, because proj seems to only support the spherical formulas of this projection:

+proj=aeqd  +R=6371000 +lat_0=51 +lon_0=7

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[GIS] How to specify a CRS for a fictional game map in QGIS

[GIS] How to create an Azimuthal Equidistant map for long-distance radio

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