# Projected Coordinate System

A projected coordinate system (PCS) is a method of transforming the surface (or a portion of the surface) of the earth into a flat plane.  VSP uses a flat, planar system of coordinates for its sample plans.

The projected coordinates system begins with an idealized model of the earth (a geographic coordinate system) and then uses a projection to convert a portion of the curved surface of the earth into a plane.  VSP currently supports two projection types:

### Transverse Mercator Projection

The transverse mercator projection is often used for sections of the earth that are taller (south to north) than they are wide (west to east).  The Universal Transverse Mercator (UTM) coordinate systems use this projection.  Many state plane coordinates systems (SPCS) in the U.S. also use this projection.  The transverse mercator projection uses the following parameters for its projection equations:

Central Meridian

False Easting

False Northing

Latitude of Origin

Scale Factor

### Lambert Conformal Conic Projection

The Lambert conformal conic projection is often used for sections of the earth that are wider (west to east) than they are tall (south to north).  The majority of state plane coordinate systems in the U.S. use this projection.  The Lambert conformal conic projection uses the following parameters for its projection equations:

Central Meridian

False Easting

False Northing

Latitude of Origin

Standard Parallel 1

Standard Parallel 2

These two projections represent a majority (but not all) of the coordinate systems in use today.  VSP may support more projections in the future as demand and resources warrant.

Using the projection equations, geodetic locations on the surface of the earth (usually designated as degrees longitude and latitude) can be converted to coordinates (usually designated as eastings and northings, or x and y) in the planar system.  Using the reverse projection equations, the coordinates on the planar system can be converted to locations on the surface of the earth.

Important Notes:

1.  The coordinates in one planar system (PCS) do not usually align with the coordinates in a different planar system.  To translate a coordinate from one PCS to another requires you to convert the coordinate from the first PCS to a geodetic location (longitude, latitude) on the surface of the earth and then project that location to a coordinate in the second PCS.  Beware of point 2 below!

2.  Not all longitudes and latitude are the same!  Each model of the earth (geographic coordinate system) will map locations on the surface of the earth to different longitudes and latitudes.  Translating a longitude, latitude point from one geographic coordinate system to another is not a simple problem, so be aware that the underlying geographic coordinate systems may prevent you from translating the points from one PCS to another.

## References:

Snyder, John P. 1987. Map Projections - A Working Manual. U.S. Geological Survey Professional Paper 1395. United States Government Printing Office, Washington, DC.