Lab VI Section I: Custom Coordinate System Definition By Affine Transformation

Geographic Calculator has the ability to define a local, custom coordinate system by computing an affine transformation between point values in an "unknown" coordinate system and their respective values in a known coordinate system. The results may be saved into a Coordinate System Registration (.csr) file and subsequently used to define the local system.

Follow these steps to register a local coordinate system:

1. Open the Geographic Calculator and select the Point Database Conversion tab to open the interface.

2. Click on the Load Data button and specify the control.tsv as the file to load into the point database.

Specifying Data Columns To Use

3. Click on the "Conversion Settings" button. This will display a form where you can specify which columns of data in the point database are to be used to compute the transformation. Select the "Best-Fit" tab to open the Best-Fit-specific settings:

4. Set each input parameter to the following columns:

The remaining parameters should be assigned to empty columns that you add to the point database grid. They can automatically be added by clicking the Add button next to each output parameter and specifying a new column be added after the last column in the list.

Note: A value of "1" in the Point Use Flag column denotes that the record is to be used in the transformation computation. A value of "0" excludes the point from the computation.

Output Coordinate System Specification

Part of the Best-Fit process requires that the points in the known coordinate values must be converted into geodetic coordinates, as signed decimal degrees, on the WGS84 ellipsoid.

5. Ensure that the Destination Coordinate System is in geodetic latitude/longitude using the WGS84 ellipsoid. This can be set by clicking the Define Coordinate System button and selecting the specified values.

6. Ensure that the computed geodetic coordinates are displayed in signed decimal degrees. This can be set via the menu selection Options>Unit Display Settings>Geodetic Degrees.

Transformation Error Plot

7. Click on the Best-Fit button to compute the transformation. If the processing was successful, the error plot tool button and menu item will be enabled.

8. Click on the error plot tool button (or select menu item: "Window > Error Plot") to display a plot of the computed transformation’s fit.

In the plot, the locations of all of the points in the point database are shown, with a line drawn from each signifying the direction and relative magnitude of the point’s residual error (the difference between its file-specified location and its computed location from the transformation). The radio buttons at the bottom of the dialog box allow you to alternate between the display of the residual errors from the forward transformation and those of the reverse transformation.

Points which were used to compute the coordinate system transformation are shown with a circle and are normally drawn in black. Those points which were excluded are shown with a triangle and are normally drawn in blue. A point whose residual error has a magnitude exceeding the criteria specified by the Best-Fit conversion settings (in this case three times the root-mean-square of the residual errors) are drawn in red.

Placing the mouse over the point symbols pops up the name of the point next to it. Clicking on the point symbol pops up information about the point, including the numerical values of its residual errors. The root-mean-square value of the residual error vectors is displayed at the bottom of the plot.

Excluding Points From The Transformation

As you may have noticed in the plot for this particular dataset, the points with the largest errors (points 3, 5, 7 and 9) fall outside of the main cluster of points in the display. The clustered point error vectors suggest that the transformation affected these points as a group to better fit with the outside point values. To see how the exclusion of the latter would affect the transformation:

9. Dismiss the error plot error viewer.

10. In the point database grid, change the use point column values in the first four records (points 3, 5, 7 and 9) from "1" to "0". This will exclude them from use in computing the transformation.

11. Click on the Best-Fit button to compute the transformation without the excluded points.

12. Click on the error plot tool button (or select menu item: Window>Error Plot) to display a plot of the computed transformation's fit.

The effect of excluding the points should be readily apparent in the new plot. The clustered points now fit much better to the computed transformation (which is also reflected in a lower root-mean-square residual error), while the excluded points have greater errors. This means that the transformation has a better local fit around the clustered points at the expense of accuracy farther out from them.

While excluding points is useful to remove suspect points from the transformation, care must be taken to not exclude so many points that the transoformation may not be accurate or reliable throughout the area of interest.

Saving the Coordinate System Registration

To save the results as a Coordinate System Registration (.csr) file:

13. Dismiss the error plot error viewer.

14. Click the Save Data button beneath the point database grid.

15. In the dialog that pops up, specify a name under which to save the coordinate system registration data. Be sure to either include a ".csr" extension at the end of the file name, or select the extension in the file filter dropdown list.  It is a good idea to save the .csr file into the same data directory where the Geographic Calculator stores the other files used for coordinate system parameters (typically: C:\Program Files\Blue Marble Geo\Geographic Calculator\data)

Note: You will only be allowed to save the data in a .csr file if a transformation was successfully computed and none of the data or settings were manipulated since the computation.  If you do not see the .csr file type listed, you will need to click the Best-Fit button again.