Geodata transformations

Geodata transforms are mathematical algorithms that perform geometric transformation. Geodata transforms convert an image location (column and row) in a raster to a spatial reference coordinate (x, y, and possibly z) and vice versa. These calculations are used to determine which pixels to access and where to display them in a map frame.

The simplest and most commonly used transformation is an affine transformation, a special type of polynomial transformation that uses six coefficients to establish the origin and pixel sizes in each direction. World files are examples of an affine transformation. The following is an example of how an affine transformation is used to calculate (x,y) from (row, col):

Assume a tagged image file format (TIFF) image has a dimension of 10000 columns x 5000 rows in GCS_WGS84 (degrees) coordinates (parenthesis indicate the coefficient):

   x = A0 + A1 * column + A2 * row

   y = B0 + B1 * column + B2 * row

A transformation has both forward and inverse directions. For inverse transformation, assuming there is no rotation between the coordinate systems (for example, the two terms are zero), the inverse can be easily illustrated using the following equations:

   column = (x - A0) / A1      

   row     = (y - B0) / B2

Or, rewritten to conform to the affine model:

   column = (-A0)/A1 + (1/A1) * x   = 5000 + 27.7778 * (-176.38) = 100

   row     = (-B0)/B2 + (1/B2) * y    = 2500 + (-27.7778) * (82.78) = 200

Notice that these inverse coefficients are very different than those in the world file:

27.7778      (A1)

0.0            (A2)

0.0            (B1)

-27.7778    (B2)

5000.0       (A0)

2500.0       (B0)

Now, (A0, B0) represents the pixel location at the map coordinate system origin (0,0). Other coefficients represent pixels per map unit (pixels per degree in this case).

ArcGIS supports many types of geodata transformations, from basic polynomial transformation to sensor models—such as RPC and frame cameras. These transformations are implemented as a set of GeodataXform classes, including PolynomialXform, AdjustXform, SplineXform, RPCXform, and FrameXform.

ArcGIS has an open framework to handle new geodata transformations. All GeodataXform classes implement a set of required interfaces—IGeodataXform, IClone, and IPersist—and interfaces to serialize them as persist streams.

You can also create a custom geodata transform in ArcGIS by implementing the required interfaces and substituting your own transformation algorithms. Because some of the underlying classes use particular data structures, it is not possible to use .NET languages to create a custom geodata transformation. Instead, VC++ must be used. For additional information, see the VC++ sample Create a custom geodata transform, available in the Visual C++ (VC++) software development kit (SDK).

Any GeodataXform, whether built-in or custom, can be saved within a raster dataset by using the IGeoDataSchemaEdit2 interface or applying the transformation to a Raster object using the IRaster2 interface.

A custom GeodataXform can be accessed and transformation triggered automatically in ArcGIS. If the GeodataXfom is stored in a format with a unique extension and is supported by an existing format driver in ArcGIS, a RasterXforms.dat file is needed in the ArcGIS bin directory to reference the file extension and the class ID of the custom GeodataXform. If the custom GeodataXform is associated with a new raster format, you must implement the ICustomXform interface for the ArcGIS software to recognize the custom GeodataXform when accessing the new format data and applying the transformation automatically. For more information, see the ArcGIS Image Management Resource Center code gallery.