nOrderTransform enables the user to transform ArcView shape files by a polynomial transformation of any order. This not only allows shifting, scaling and rotating, but can be as complex as any order polynomial.

A transformation is defined from two sets of control points, the initial set representing positions in the data to be transformed and the result set representing where those positions should appear after the transformation. These positions are taken from two shape point files. They are matched by a user specified attribute. These files should be in the ArcView view prior to running nOrderTransform.

From these points, a polynomial transformation of a user specified order is determined using the least squares method. The resultant transformation is applied to each input point and the error is calculated between the transformed point and the desired position for that point. The minimum and maximum "residual errors" are displayed. Details for each point can be viewed through clicking the Details button.

The transformation is then applied to the requested dataset producing a transformed dataset of the same type with the same attributes. The dataset to which the transformation is to be applied must be in the ArcView view prior to running nOrderTransform. The resultant data set will be added to the view.

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Installation Instructions

nOrderTransform can be downloaded from www.spatial-online.com.. The file will be called nOrderTransform.exe.

In order to install nOrderTransform, save nOrderTransform.exe to temporary space on your disk. Double click it to run the install. An install wizard will appear to guide you through the installation process.

To find nOrderTransform in ArcView, activate the project window and from the file menu, choose Extensions. In the Extensions dialog, click the box beside nOrderTransform. When a view is open, a Transform menu item will appear to evoke nOrderTransform.

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Control Values

Prior to evoking nOrderTransform, the initial control file, result control file and file to be transformed must be in the current view. When the view is active, a Transform menu item will appear. It offers a choice of running the module or evoking your default browser with this help file.

When the product is running in trial mode, the following registration screen will appear.

Clicking the purchase button will evoke your browser with www.spatial-online.com to enable you to purchase the product on-line, through the Fax or via Purchase Order. When you purchase the product, you will be required to supply your site code (just below the Purchase button). In return, you will get a product key. Insert that key into the Text Box next to Product Key and click OK to register the product. Once you have done this, this registration box will no longer appear.

To run the product in trial mode, click the Run in Demo Mode button. Below the button, the remaining trial period is shown.

Clicking the Cancel button will stop the process.

The first dialog to appear is the one below.

The top left input specifies the order of the polynomial that will be derived and used. It defaults to a first order polynomial, that is a function of the form a + bX + cY for determining each of X and Y. A second order polynomial function has the form a + bX + cY + dX^2 + eXY + fY^2, etc. A minimum of 3 control points are required for a first order polynomial, a minimum of 6 for a second order polynomial. For order n, a minimum of (n+1)(n+2)/2 are required. In general, more than the minimum number of control points are preferable. This will minimize the problems that occur when one of the control points is not quite correct.

The left-most drop down box on the next line specifies the shape file of the initial control points, that is those that align with the data to be transformed. It will default to the first point shape file in your view. The subsequent line specifies the shape file for the resultant control points, that is those that indicate where the initial control points should be mapped to. These files can be chosen from the drop down boxes which contain all the point themes that were in the view when the function was evoked. The values of the attribute specified for each are used to match the two sets of control points. They can be chosen from drop down boxes listing the attributes available for each control file.

The next line specifies the file to be transformed. It can be chosen from a drop down box listing all the shape files that were in the view when the function was evoked.

The last input line specifies the output file that is to be produced, that is the resultant of applying the transformation to the input file. A default name is generated from the input file, with a numeric value appended if the file already exists. Any file in the same directory as the input file can be specified.

There are three buttons across the bottom. The rightmost one, labeled Help, will bring up this help file in your default browser. The second button, labeled Cancel, will cause the process to halt. These buttons are always available and can be clicked at any point. The leftmost button, labeled Transform, is available when the process is awaiting input or confirmation from the user. In this step, it is requesting confirmation of the input parameters described above.

When the input values have been specified, and the Transform button clicked, the files will be verified to ensure that the control files are different and that the output file can be written to. When this is successful, the dialog below will appear.

The input boxes have been grayed and can no longer be altered. The transformation polynomial has been computed using the Least Squares technique to minimize the sum of the squares of the "residual" errors. The residual error for an initial control point is the distance between the corresponding resultant control point and the position obtained by applying the transformation to the initial control point. If there are the minimum number of control points, these should be zero. If there are more control points, these are likely to be more than zero, but should be fairly small.

The minimum and maximum residual error is shown on the dialog. If you wish to see the individual residual errors for each point, click the details button and the dialog below will be seen. The label used to match the initial and resultant control points is shown along with the residual error. One point with a residual error much larger than the other points tends to indicate that the control point needs further examination.

If the residual errors are not acceptable, press Cancel to end the process and rework the control points. If they are acceptable, press Transform to have the transformation polynomial applied to the file chosen. While the transformation is occurring, the following dialog will be visible.

The transformation is done in two steps. The file is scanned in the initial step. The message appearing in the bottom left corner of the dialog will be as above and the progress bar will indicate where in the scanning the process is. In the next step, the message will indicate that the file is being written and the progress bar will show how far through the the writing the process is. The cancel button will stop the processing.

When the process is complete, the newly produced shape file will be added to the current ArcView view. The extents of the view will be reset to the extents of the newly transformed data.

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Frequently Asked Questions

• What order polynomial should I use?
A first order polynomial will perform a shift, scale and any variety of linear transformation. A second order polynomial will also allow warping. Higher orders will provide additional warping. It is preferable to utilize the lowest order that will provide for the type of transformation you require as high order transformations can have unexpected results, especially at the extremities of the data.
• How many control points do I need?
In general, more control points are better. They prevent small errors in the control points being exaggerated. It is important that control points be placed not only where the required shifting is highest, but also where there is little required shifting.
• Where should the control points be?
The control points should be as evenly spaced throughout the data as possible.
• Why did my map warp a long ways from the control points.
The transformation is applied to all the input map. Specifying data only where the modifications are extreme will definitely result in some unusual movements. Also, if the order of the polynomial is high, you are more likely to get a slight error causing some substantial problems, often far away from the control error.