This window allows the batch transformation of the point coordinates from the coordinate list. You can transform either the entire list or only the selected points. The transformation methods are described in the chapter Coordinates transformation
Before initiating the coordinate's transformation, you must first define the transformation key. As in any other job, add all the identical points with their coordinates in both systems on the list. The program automatically recalculates the transformation key and displays the coordinate's adjustments on the individual points. The identical points can be added or removed from the list arbitrarily.
The number of the identical points is unlimited.
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The transformation key is calculated using the least squares method by the iteration method. If there is too much dissonance in both systems, the iteration process might not convert the adjusted value to the result. This applies on all the other jobs which are solved using the coordinate's transformation. |
If your identical points are located in two files, and if the point pairs have identical numbers, you can let the program automatically search the corresponding point pairs. Enter the files with the identical points in the boxes Input and Output, and press the button (Read points). The program will search the pairs of the identical points and add them to the list automatically.
After pressing the button (XY <-> x'y') the program will exchange the coordinates of the identical points in both systems. You can use this option, for example, in case you, when entering the identical points, switched both coordinate sets by mistake. Using this function you can switch the coordinates without the need to reenter the identical points.
If you want to perform the statistical test of the residual error on the identical points, turn on the option Statistical test. The program will perform an analysis of the residual errors and store the results in a report. The detail description of the statistical test is described in the job Comparing the coordinate lists.
After selecting this switcher, the program will calculate the inverse (back) transformation instead of the enterer transformation. This option cannot be used for the user transformation.
The program allows calculating three types of transformations:
Identity transformation
Transformation which saves the scale (the scale coefficient is equal to one). Therefore, the transformation has three parameters (two translations and rotation). For determination of the transformation key, at least two identical points are required.
Similarity transformation
The transformation key will have the same measurement coefficients in the direction of both the X and Y axes (the transformation changes the dimensions of the objects in all directions evenly; therefore it keeps the similarity of the figures). Two identical points are enough for this transformation.
Affinity transformation (5 parameters)
The transformation key will have various scale coefficients for the X and Y axes. During the transformation, the dimensions change depending on the direction and the similarity of the figures is generally not maintained. This type of transformation requires at least three identical points.
Affinity transformation (6 parameters)
The transformation matrix will be calculated directly. Its elements are not constrained by any geometrical relations, as in the case of the 5-parameter affinity transformation. The transformation key will have different scale coefficients for the direction of the X and Y axes. During the transformation, the dimensions change depending on the direction and the similarity of the figures is not generally maintained. This type of transformation requires at least three identical points.
User-defined transformation
If you select this type of transformation, you do not have to enter identical points, but you can directly enter the result transformation relations. After pressing the button (...) a dialog window is displayed where you can enter the transformation formulas to calculate the individual coordinates. Any mathematical operations, number constants and variables X, Y and Z. The function relations can look, for example, like this:
X: X*0.99877354220+Y*0.04951172994+254.339 Y: X*0.04951172994-Y*0.99877354220-365.471 Z: Z
If the transformation key was determined, you can store it to a file using the button (Store key) for further use.
The point transformation is always from one file to another. Enter the input and output file in the section Coordinate lists. If any points in the input file are selected, the program transforms only these points. If no items are selected, the program transforms the entire coordinate list.