How to map a latitude/longitude to a distorted map? | I have a bunch of latitude/longitude pairs that map to known x/y coordinates on a (geographically distorted) map.


Then I have one more latitude/longitude pair. I want to plot it on the map as best is possible. How do I go about doing this?


At first I decided to create a system of linear equations for the three nearest lat/long points and compute a transformation from these, but this doesn't work well at all. Since that's a linear system, I can't use more nearby points either.


You can't assume North is up: all you have is the existing lat/long->x/y mappings.


EDIT: it's not a Mercator projection, or anything like that. It's arbitrarily distorted for readability (think subway map). I want to use only the nearest 5 to 10 mappings so that distortion on other parts of the map doesn't affect the mapping I'm trying to compute.


Further, the entire map is in a very small geographical area so there's no need to worry about the globe--flat-earth assumptions are good enough.