First, if we define a true coordinate system which accurately models the "plant/company" coordinate system, we can convert "plant/company" coordinates to any other system, including state planes. Tralaine, and most other coordinate conversion programs, can convert from any defined coordinate system to any other. Thus, once we arrive at a suitable definition, we will be able to convert "plant/company" coordinates to lat/longs, UTM’s, state planes, or whatever. Perhaps just as important, we’ll be able to convert coordinates in any other system to "plant/company" coordinates as well.

Second, to accomplish this task, we observe that all projections are designed to do the same job; convert spherical/ellipsoidal latitude and longitude coordinates to cartesian X and Y coordinates (and vice versa). Therefore, we make the statement that any projection can be used as an approximation of any other. Exactly how good this approximation is depends, naturally, on the projections involved. However, the technique described below seems work reasonably well in the case we are addressing here.

Given our assumption above, we usually assume that we can use the Azimuthal Equidistant projection as an approximation of whatever projection (if any) was used to develop the "plant/company" coordinate system. This usually works well as the Azimuthal Equidistant will faithfully compute distances from the origin to points as much as 600 kilometers away quite accurately (even on the ellipsoid). Thus, we start a new coordinate system definition and choose the Azimuthal Equidistant as our projection.

You will need to choose the datum/ellipsoid to be used. For older systems in the US, NAD27 (which implies the Clarke 1866 ellipsoid) is a good guess. You will also need to choose a unit. Usually these "plant/company" coordinate systems are based on the U.S. Survey Foot.

Now, the interesting part. Ideally, we would like to provide the Azimuthal Equidistant projection with the latitude and longitude of the actual original of the "plant/company" coordinate system. However, the exact origin is rarely known. Therefore, we pick one of our known points which is close to the middle of the region covered and designate, somewhat arbitrarily, this point as the origin; and provide the latitude and longitude of that point as the origin latitude and longitude of our "plant/company" coordinate system. "I don’t know the latitude and longitude, all I have is state planes?" you say. No problem. Use the Test dialog of Tralaine and convert the state plane coordinates to latitude and longitude. (Be sure to convert to latitude and longitude of the same datum as that upon which our "plant/company" coordinate system is based.) Finally, enter the "plant/company" coordinates of the designated origin point as the values for False Easting and False Northing.

In many cases, the above is all that is necessary to define a "plant/company" coordinate system. However, in many cases, the above is insufficient. Tralaine has two features built in it to assist in these difficult cases. Mentor Software’s implementation of the Azimuthal Equidistant Projection includes a parameter not normally supported by other vendors; the azimuth of the Y axis relative to true north. You can use this parameter to enter an angle, in degrees east of north, which represents the amount the Y axis of your "plant/company" coordinate system deviates from true north. Determining this may be tricky. (Sounds like a good freebie for a future issue of the Casual Cartographer.) In any case, this parameter can be used to adjust for "plant/company" coordinate systems where the Y axis is not coincident with true north.

Another feature of Tralaine, the Quadrant, was also added specifically for this type of problem. In some "plant/company" coordinate systems, the X coordinate will increase to the west (rather than east as is customary). Or, maybe the Y coordinate increases to the south. Or, maybe, a combination of these. The Quadrant field on the General tab of Tralaine’s Coordinate System Editor can be used accommodate these variations in "plant/company" coordinate systems.