Transformation, Coordinate

A coordinate transformation is a calculation that converts coordinates from one system to another. Coordinate transformations are needed in GIS because data often have different projections, coordinate systems, and datums. To perform analyses, all data must overlay accurately in coordinate space.

A coordinate transformation might be as simple as shifting each coordinate in one or two directions, for example, x and y, by a specified distance. This is sometimes done when GIS data are just slightly off in a particular direction. Coordinate transformations can also be very complex, such as when data are in different projected coordinate systems with different datums. In this case, it may be necessary to shift, rotate, warp, and scale the coordinates using more than one kind of coordinate transformation. In most cases, GIS software can handle the types of transformation required to process those data so they overlay correctly.

There are many kinds of coordinate transformations, including geographic, Euclidean or planar, and datum, among others. The variations in these types of [Page 483]transformations relate to the model or space to which the coordinate system refers. A Euclidean system can be a 2D or 3D planar system. Thus, a Euclidean transformation might convert digitized data to a projected coordinate system, or it may be used to manipulate aerial photographs so that they can be edge matched (joined along the edges). A geographic coordinate system is latitude, longitude, and height. A geographic, or datum, transformation converts coordinates from one datum to another, for example, from ED50 to ETRS89 or NAD27 to NAD83.

In GIS software, a common coordinate transformation is to convert data between projected coordinate systems. This procedure is often composed of more than one coordinate transformation. For instance, a datum transformation is often embedded in this procedure. To illustrate, the general process is as follows:

• 1.
  Define the projected coordinate system currently being used, which includes the datum.
• 2.
  Unproject the data to geographic coordinates using the same datum.
• 3.
  Transform the data to geographic coordinates in the new datum.
• 4.
  Project the data to the new projection with the new datum.

While knowing about all the numerous types of transformations and understanding the math behind them is the domain of expertise for geodesists, photogrammetrists, and surveyors, it is important that all GIS users understand what types of transformations are being performed on their data by the GIS software to ensure that results are correct. Ideally, it would be possible to check the results of a transformation against control points that have known accuracies. More often, the best you can do is a visual check against data that are assumed to be reliable.

Users should check their software documentation for information about the transformations being used by their software. Any transformations performed on spatial data should be recorded in the metadata in order to document the accuracy of spatial databases. In the documentation of a production workflow, these transformations should also be described and checked because of their critical importance to the accuracy of the geographic data and results of analyses. Knowing the requirements for and results of any coordinate transformation used is the responsibility of all GIS data custodians.

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