Simple Guide on Geospatial Coordinates Transformation with Mathematica

A few questions on geospatial coordinates transformation have shown up in Mathematica.Stackexchange. Here is a very brief summary.

In US, you probably likely deal with two projection systems: State Plane Coordinates System and UTM.

1. State Plane Coordinates System
In the U.S. State Plane Coordinate System (SPCS), the transverse Mercator projection is used for states that are long in the north-south direction, a Lambert conformal conic projection is used for states that extend in the east-west direction, and the oblique Mercator projection is used for Alaska.

In GeoProjectionData, SPCS83IN01 and SPCS83IN02 represent Indiana Steate Plane east zone and west zone. SPCS83TX01 ~ SPCS83TX05 represent 5 zones from north to south in Texas. Tennessee has only one zone: SPCS83TN00. Here is an online interactive map on SPCS.

There are also SPCS27 series, which are based on NAD27 datum, however, it is quite rare to get the data in the old coordinate system.

One common mistakes is usually caused by the unit: meters vs feet. In Mathematica, the coordinate is calculated in meters, the data you get is probably in feet.

Related posts on stack exchange convert spcs to (lat, lon), convert (lat, lon) to spcs

2. UTM
Universal Transverse Mercator (UTM) coordinate system divides the Earth into sixty zones: UTMZone01 ~ UTMZone60.

In Mathematica 9, there is a problem with UTMZone data:

GeoProjectionData["UTMZone16"]
{"TransverseMercator", {"Centering" -> {0, -87},  "CentralScaleFactor" -> 1, "GridOrigin" -> {0, 0}, "ReferenceModel" -> "WGS84"}}

The scale factor: 0.9996 and the grid origin: {500000,0} shall be specified for coordinate transformation: 

GeoGridPosition[
 GeoPosition[{39.162147, -86.529045}, "WGS84"], {"UTMZone33",
  "CentralScaleFactor" -> 0.9996, "GridOrigin" -> {500000, 0}}]

Related posts on stack exchange convert between (lat, lon) and UTM

This problem is fixed in next version of Mathematica.