# Converting from unknown coordinate system into common one using fiducial points?

I have a thousand of points that I want to project in a different coordinate system. These points were generated using an old and odd coordinate system (let's call it CS) so it's not possible to use some library to convert them. Luckily for each 50 points I have 1 point in both coordinate systems (the old and odd CS system and the WGS84). So how can I convert the remaining 49 points to WGS84. I think it is matter of interpolation but I don't know the math to use. I have the WGS84 and the CS coordinates of the red points, I need the WGS84 coordinates of the black points.

I know how to do this in QGIS using a custom CRS string with 1 point but here I need at least 3 points because 1 point will only move the layer. I also need to scale or deform.

Is it possible to have a custom CRS string based on 3 points?

I am also interested by the math to use (I will eventually do the math in Python).

• You can create a custom coordinate system for most Projection engines. What software do you prefer? – klewis Apr 12 '16 at 21:37
• I'm starting with QGIS, is there some plugin? – isar Apr 12 '16 at 21:38
• Take 3 known points at the 'corners', calculate affine transformation parameters and recalculate all geometries – FelixIP Apr 12 '16 at 22:53
• Here is the qgis plugin explained, gis.stackexchange.com/questions/25193/… – klewis Apr 12 '16 at 23:15
• GIS libraries can reproject almost every "old and odd" coordinate system. Mercator invented his system in 1569, surely older than your data. You just have to calculate the parameters. With a few points in both systems, it is easy to calculate the origin of the projection, and define a custom projection on it. – AndreJ Apr 13 '16 at 5:50