# Finding points on an odd map projection using interpolation between known points

I have an image of a somewhat idiosyncratic projection that is a frame from a film:

A geographer friend of mine said it was probably some kind of Gnomic projection, but that from the resolution it wasn't possible to know for sure. I wouldn't know.

You can see North America at top left, and the Soviet Union and China (!) in red with a black border around it in the middle-right of the frame. The dark vertical and lighter horizontal lines visible seem to go through the North Pole. As you can guess this is a declassified target map from the Cold War; those branched lines are bomber routes (some from bases, some from refueling points).

I am interested in finding the rough lat/lngs of the ends of the branched lines (the "targets"), knowing, of course, there is going to be a large margin of error because of the resolution,. I could hunt and peck these by hand, working first to identify targets that ought to be on there (e.g. Moscow), but it seems like there ought to be an easier way.

There are plenty of identifiable geographical locations on there, such as James Bay in Canada, the tip of Gujarat in India, the Caspian Sea, and so on.

My first thought was to try line between a number of these by hand in Adobe Illustrator, then draw similar lines in Google Earth, and use them as a rough grid to triangulate the missing points by hand. This is of course difficult. I then thought maybe there was some way to do this algorithmically.

If I know the lat/lng of fixed pixel locations, can I move from there to figuring out the missing lat/lngs of other pixel locations?

I suspect this might be harder than it sounds, given that I don't really know the projection that produced those pixel locations.

I think the easiest approach would be to geo-rectify your image, then you could get the approximate coordinates directly.

Geo-rectifying is the process of projecting a dataset that is not projected (or unknown projection in your case) using known points in the dataset such as boundary lines and well known landmarks.

You specify the pixel position or original coordinates of a few known points in your dataset and the corresponding projected coordinates and the software will do the rest. Generally the more known reference points the better.

Most popular GIS software has geo-rectifying capabilities. I've personally used ArcGIS and GRASS for the task many times.

• Thanks! Knowing the name for something goes a long way (geo-rectifying). I have access to ArcGIS, so I'll see if I can figure out how to do it there. Googling around, it doesn't seem too hard to do it (but I know enough about ArcGIS to be suspicious of this). Will report back on my success or lack thereof. Dec 15, 2013 at 13:40
• “georeferencing” is a slightly more common term for this. QGIS has a decent georeferencing module, and it's free. Dec 15, 2013 at 13:56
• @scruss You are correct in that georectifying is a process for georeferencing a dataset. The difference is that georeferencing is a broader term which doesn't always include georectifying. Dec 15, 2013 at 14:12
• So it turns out that georeferencing/georectifying a gnomonic projection is not easy to do. ArcMap can't seem to handle it at all (it produces crraaaazzy results because it doesn't scale linearly at all) and ArcGlobe doesn't seem to have as robust georeferencing (?). Hmm. Dec 16, 2013 at 19:15
• What projection were you trying to georectify to? Ideally, you should get better results when using a projection that is similar to your image. I'm ignorant to gnomonic projections, but your image looks like it's a polar/conical projection. ESRI has a projection called 'North Pole Gnomonic' that looks similar to your image, you may have better results if you georectify to that. Dec 16, 2013 at 19:26