This transformation is a rigorous implementation of the standard three-dimensional transformation. The seven provided parameters must indicate the transformation to convert local datum coordinates to WGS84 coordinates. For many typical GIS applications, you can simply change the sign of each of the seven parameters to effect an inverse. However, this technique is not exact. For precise results, a rigorous inversion is necessary in order to determine the appropriate parameters.

Essentially, this transformation proceeds in three phases. First, the geographic coordinates are converted to three-dimensional Cartesian, geocentric coordinates using the ellipsoid of the original datum. Second, the three-dimensional transformation defined by the seven parameters is applied producing a modified set of geocentric Cartesian coordinates. Third, the resulting geocentric coordinates are converted back to geographic form using the WGS84 ellipsoid.

The seven parameters are:

1.  Delta X: the amount the intermediary geocentric X coordinate is translated. This value must be given in meters and the direction of the translation is given by the sign of the value.

2. Delta Y: the amount the intermediary geocentric Y coordinate is translated. This value must be given in meters and the direction of the translation is given by the sign of the value.

3. Delta Z: the amount the intermediary geocentric Z coordinate is translated. This value must be given in meters and the direction of the translation is given by the sign of the value.

4. X Rotation: the amount of rotation about the X axis which is applied to the intermediary geocentric coordinates. This value is given in seconds of arc, and the direction of the rotation is indicated by the sign of the value.

5. Y Rotation: the amount of rotation about the Y axis which is applied to the intermediary geocentric coordinates. This value is given in seconds of arc, and the direction of the rotation is indicated by the sign of the value.

6. Z Rotation: the amount of rotation about the Z axis which is applied to the intermediary geocentric coordinates. This value is given in seconds of arc, and the direction of the rotation is indicated by the sign of the value.

7. Scale: a scale factor that is applied to the intermediary geocentric coordinates. The value is given as a value in parts per million and is the difference of the actual scale factor and unity. For example, a value for the scale parameter of -2.5 produces an actual scale factor of 0.9999985. That is, the actual scale factor used is arrived at by multiplying the parameter value by 1.0x10-06 and adding the result (algebraically) to 1.0.