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I've drawn a cylindrical world map for a fictional planet. Exported it as png and scaled it, so one pixel corresponds to one km at the equator and from north to south pole.

I tried several cylindrical crs on it but it does never work out as I want and I can't find out why.
My goal: When I use the measure tool it should give me the following outputs:

  • Horizontal length of equator (width of my png) = 38,211km
  • Vertical distance from north to south pole (height of my png) = 19,105.5km
  • When I measure the horizontal distance where the poles are (top and bottom rim of my png) it should show 0 km because of the cylindrical projection.

How can I georeference my png to get these results?

  • You would need a world projection that maps the pole as a point, not a line. That would be sinusoidal. Most world projections map pole as line somewhat shorter than equator--various Eckerts for example. – mkennedy Dec 19 '17 at 0:01
  • Check out Furuti's pages or the Esri ArcGIS pages. Some projections may not be supported in QGIS/PROJ.4. – mkennedy Dec 19 '17 at 0:03
  • @mkennedy thanks for your comment! Is there any list as the "Esri ArcGis pages" for QGIS? Would help quite a lot to know what crs to use in what occasion. Furuti's page is quite helpful. But it isn't that easy to convert a raster map into another projection using gimp or photoshop, or is there any easier method? – DonMeles Dec 19 '17 at 10:02
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You could define a custom CRS adapting EPSG:4088 - World Equidistant Cylindrical (Sphere) to your planet, because the length of equator (width of your png) is just the double of the vertical distance from north to south pole (height of your png). Changing only the semi-maior and semi-minor axis parameters, the proj4 string should be:

+proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +a=6081469.53 +b=6081469.53 +units=m +no_defs 

where +a and +b are equal to equator_km / 2PI * 1000 (meters).

Note that the third condition - "When I measure the horizontal distance where the poles are (top and bottom rim of my png) it should show 0 km because of the cylindrical projection." - can't be never satisfied in a cylindrical projection. In such case you would need a polar stereographic one, in which the poles are projected as points.

  • Thanks for your answer! Sadly it didn't work, the measurement tool still gives me the same distance when measuring a horizontal line on the poles as when measuring on the equator... And why is the length of the equator the vertical distance from north to south pole? The Equator equals the total perimeter while the vertival distance from pole to pole only represents half of the perimeter... – DonMeles Dec 18 '17 at 22:26
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    Ops... There were some typos in the answer that I've just corrected. However, there's not a unique projection able to satisfy your goal. That's the reason why we usually use UTM and UPS here on Earth. – Antonio Falciano Dec 19 '17 at 11:33
  • I loaded a google satellite map from the open layers plugin. It shows the same false results when measuring east-west distances in polar regions, which surprises me... So conic projections are the only ones which allow correct measurements? – DonMeles Dec 19 '17 at 13:37

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