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I have a Mercator projection map as a JPEG and I would like to know how to relate a given x, y coordinate to its latitude and longitude. I've looked at the Gudermannian function but I honestly don't understand how to take that function and apply it. Namely, what input is it expecting? The implementation I found (JavaScript) seems to take a range between -PI and PI, but what's the correlation between my y-value in pixels and that range? Also, I found this function which takes a latitude and returns the tile for Google Maps, which also uses Mercator. It would seem that if I knew how to inverse this function, I'd be pretty close to having my answer. /*<summary>Get the vertical tile number from a latitude using Mercator projection formula</summary>*/ private int getMercatorLatitude(double lati) { double maxlat = Math.PI; double lat = lati; if (lat > 90) lat = lat - 180; if (lat < -90) lat = lat + 180; // conversion degre=>radians double phi = Math.PI * lat / 180; double res; //double temp = Math.Tan(Math.PI / 4 - phi / 2); //res = Math.Log(temp); res = 0.5 * Math.Log((1 + Math.Sin(phi)) / (1 - Math.Sin(phi))); double maxTileY = Math.Pow(2, zoom); int result = (int)(((1 - res / maxlat) / 2) * (maxTileY)); return (result); }

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