## Defining Custom Datums

Most coordinate systems use one of MapInfo's predefined datums, listed in this appendix. If you need to use a datum that isn't in the list, and you know what the datum's mathematical parameters are, then you can define the coordinate system using a custom datum. MapInfo uses the following information to define a datum:

- An ellipsoid, also called a spheroid. This is an ellipse rotated around its minor axis to form a three-dimensional surface. The ellipsoid is described by two mathematical parameters: the length, in meters, of its semi-major axis (denoted by the letter a) and its degree of flattening (denoted by the letter f). MapInfo supports over 40 predefined ellipsoids, which are listed in the next table.
- Three shift parameters specifying the distance, in meters, to shift the ellipsoid along each of its axes. These parameters are usually denoted by dX, dY, and dZ. You may also see them denoted by DX, DY, and DZ, or by u, v, and w.
- Three rotation parameters specifying the angle, in arc-seconds, to rotate the ellipsoid around each of its axes. These parameters are usually denoted by EX, EY, and EZ. You may also see them denoted by eX, eY, and eZ, or by e, y, and w.
- A scale correction factor specifying the amount, in parts per million, to adjust the size of the ellipsoid. This parameter is denoted by the letter m, or sometimes k.
- The longitude of the prime meridian, in degrees east of Greenwich. The prime meridian specifies which location on earth is assigned longitude 0×. Most datums use Greenwich as the prime meridian, so this parameter is usually zero. However, some datums use a different location as the prime meridian. For example, the NTF datum uses Paris as its prime meridian, which is 2.33722917 degrees east of Greenwich. If you use the NTF datum in a coordinate system, all longitudes in that coordinate system are relative to Paris instead of Greenwich.
You can define a custom datum in any coordinate system definition. Appendix F describes how to define a coordinate system. To define a custom datum in a coordinate system, you use datum number 9999 followed by the datum parameters, in this order:

9999, EllipsoidNumber, dX, dY, dZ, EX, EY, EZ, m, PrimeMeridian

Some datums specify only an ellipsoid and shift parameters (dX, dY, dZ), with no rotation parameters, scale correction, or prime meridian. In those cases, you can use datum number 999 instead of 9999, to simplify the definition:

999, EllipsoidNumber, dX, dY, dZ

The ellipsoid number must be chosen from the following list. Currently, there is no way to define a custom ellipsoid. If you need to use an ellipsoid that does not appear on this list, please notify MapInfo Technical Support so that we can add your ellipsoid to a future MapInfo Professional version.

Two ellipsoids have been added. These are: Everest Pakistan #50, and ATS 77 (Average Terrestrial System) #51.

The ellipsoid names for Everest ellipsoids have been standardized according to NIMA specs to conform to the most current standards used in the GIS and mapping communities. The name changes are summarized in this table:

The additions and the new names are reflected in this table.

The shift and rotation parameters describe the ellipsoid's orientation in space, as compared to the WGS 84 datum. It's important to make sure that these parameters have the correct signs (positive or negative). Usually, a document describing a local datum will list the parameters required to convert coordinates from the local datum to WGS 84. (This is the same as saying that the parameters were derived by subtracting the local datum from WGS 84.) In that case, you can use the parameters exactly as they appear in the document. However, if you have a document that lists parameters for converting coordinates in the opposite direction - from WGS 84 to the local datum - then you must reverse the signs of the shift, rotation, and scale correction parameters.

It's also very important to list the parameters in the correct order. Some documents list the rotation parameters with EZ first, like this: EZ, EY, EX. In those cases, you must reverse the order of the rotation parameters when defining the custom datum. This is especially easy to overlook when your document uses Greek letters to denote the parameters. If the document lists the parameters in order as w, y, e, then you must reverse their order in the custom datum definition.

Here's an example of a local datum description (we'll call it LD-1) as it might appear in a technical article:

This datum uses the International ellipsoid, which is number 4 in the ellipsoid table above. The other parameters describe a conversion from WGS 84 to the local datum, so we must reverse their signs. No prime meridian is listed, so we can assume that Greenwich is used. The custom datum definition in MapInfo would look like this:

9999, 4, -93.5, -103.5, -123.3, 0.25, -0.11, -0.07, 2.1, 0

You can insert this string of numbers in place of the datum number in any line in the MAPINFOW.PRJ file. For example, you could define the following coordinate systems using this custom datum:

Note:Strings must be entered on a single line."Longitude / Latitude (LD-1)", 1, 9999, 4, -93.5, -103.5, -123.3, 0.25, - 0.11, -0.07, 2.1, 0"UTM Zone 30 (LD-1)", 8, 9999, 4, -93.5, -103.5, -123.3, 0.25, -0.11, - 0.07, 2.1, 0, 7, -3, 0, 0.9996, 500000, 0Here's another sample local datum description, called LD-2 this time:

This datum uses the Krassovsky ellipsoid, which is number 3 in the ellipsoid table above. We do not need to reverse the signs of the parameters, since they describe a conversion from the local datum to WGS 84. However, the rotation parameters are listed with w first, so we must reverse their order in the custom datum definition:

Here's a final example, LD-3, that provides only the ellipsoid and shift parameters:

This datum uses the Clarke 1880 ellipsoid, which is number 6 in the ellipsoid table above. We do not need to reverse the signs of the parameters or worry about the order of the rotation parameters (since they aren't present). In this case, you can use datum number 999 instead of 9999 in the custom datum definition. These two definitions are equivalent, and you can use either one:

As with the other custom datum definitions, you would insert one of these definitions in place of the datum number in a MAPINFOW.PRJ line, as follows:

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