# {Latitude, Longitude} to Transverse Mercator projection

I have a shapefile with the following "CoordinateSystemInformation":

"PROJCS" -> {"NAD_1983_StatePlane_Illinois_East_FIPS_1201_Feet",
"GEOGCS" -> {
"GCS_North_American_1983",
"DATUM" -> {
"North_American_Datum_1983",
"SPHEROID" -> {"GRS_1980", 6.37814*10^6, 298.257}},
"PRIMEM" -> {"Greenwich", 0.},
"UNIT" -> {"Degree", 0.0174533}},
"PROJECTION" -> {"Transverse_Mercator"},
"PARAMETER" -> {"False_Easting", 984250.},
"PARAMETER" -> {"False_Northing", 0.},
"PARAMETER" -> {"Central_Meridian", -88.3333},
"PARAMETER" -> {"Scale_Factor", 0.999975},
"PARAMETER" -> {"Latitude_Of_Origin", 36.6667},
"UNIT" -> {"Foot_US", 0.304801}}


I would like to plot {Latitude, Longitude} points and overlay these images, but I am having trouble converting coordinates. The shapefile data contains coordinates in the vicinity of {1.16328*10^6, 1.89271*10^6}. (This is Chicago.)

One point I would like to plot is {41.8713, -87.6737}.

GeoGridPosition[GeoPosition[{41.8713, -87.6737}], "TransverseMercator"]


gives the wrong coordinates:

GeoGridPosition[{-0.164851, 0.743066}, "TransverseMercator"]


As does

GeoGridPosition[GeoPosition[{41.8713, -87.6737}], "Mercator"]


which yields:

GeoGridPosition[{1.6114, 0.806147}, "Mercator"]


What am I doing wrong? It's not a question of reversed coordinates as in this thread.

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Could you please specify what would be the correct result in your example? –  belisarius Feb 19 at 4:11
@belisarius I'm not certain what the numbers should be but the coordinates should be quite close to {1.16328*10^6, 1.89271*10^6} –  mfvonh Feb 19 at 4:14
Try GeoPositionXYZ[GeoPosition[{41.8713, -87.6737}], "NAD83CORS96"] –  belisarius Feb 19 at 4:33
@belisarius That doesn't seem to do it. It gives me 3D coords (seeking 2d). And converting the 3D coords using GeoGridPosition does not yield answers in the right range. –  mfvonh Feb 19 at 4:52
Ok, it was just a try :(. Anyway, I fail to see what kind of 2D projection could give coordinates in that range (I don't know anything about Georeference!) –  belisarius Feb 19 at 5:02

it is "SPCS83IL01" in GeoProjection Data

GeoGridPosition[GeoPosition[{41.8713, -87.6737}], "SPCS83IL01"]


This gives the coordinates in state plan system in meters, convert them into feet shall produce the right number you are looking for.

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I modified the formatting of your answer so that the code is in a code block. I shouldn't have changed the actual code, but please check just to make sure. –  bobthechemist Feb 19 at 15:05
@Tuku Perfect, thanks! Meters should have been obvious but was throwing me off. –  mfvonh Feb 19 at 17:50