Parameters calculation

In this section you can calculate the transformation parameters for common points. This section is organized in calculation sheets so that this determination to becomes practical and fast. Furthermore, the buttons [Go to the next step ↓] helps you step by step to quickly enter the necessary data and perform calculations.

for a 1D transformation (calculation with 5 parameters or with 1 parameter);
for a 2D transformation (calculation with 4, 5 or 6 parameters);
for a 3D transformation (calculation with 7, 8, 9, 10 or 12 parameters).

In order to obtain fast the coordinates of the common points in the two systems (A and B), points on the base of which the transformation parameters will be calculated, in the pages with the A system (source) and the B system (destination) coordinate conversions can be performed using the buttons with the 1st, 2nd, 3rd and 4th steps. These conversions have as calculation elements: the A system datum, the B system datum and the parameters of the projection system, values that can be chosen by using the button Options - Parameters calculation Tab.

If coordinate conversions for common points are not required then you can choose the method of calculation without steps, the coordinates of the system A and B will be entered in the corresponding tables.

The transformation parameters are determined for the common points from the A and B system so that the coordinates of points are transformed from A system to B system.

System A (source)

Points can be introduced from files, manually or can be calculated by transforming from a coordinate system to another using the 1st and 2nd steps.

In the case of the conversion from (φ, λ, h) to (X, Y, Z) using step 1, it can be chosen if the ellipsoidal elevations are used or not (geographic 3D or 2D case). This option can be useful when we want to check the influences of the ellipsoidal elevations for a 3D transformation.

For calculating the parameters in the case of the 3D transformation the table of Cartesian coordinates (X, Y, Z) on the ellipsoid from the A system must be completed.

For calculating the parameters in the case of the 1D and 2D transformations the local coordinates table (Nª, Eª, Zª) must be completed.

In the case of 1D and 2D transformations the coordinates of the points can be calculated in a local plane by using a transformation with 7 parameters (Bursa-Wolf method), with 10 parameters (Molodensky-Badekas method) or 7 parameters (Helmert conformal method) for an approximate transformation from the ellipsoid from the A system on the ellipsoid from the B system, after that, the passing from the B system in the projection plane is performed according to the selected projection. The parameters of the approximate transformation can be loaded from a file, from the Clipboard memory or from the EPSG database. For details regarding the manner of loading parameters from the database EPSG see The window of loading parameters from the EPSG database. All these commands regarding the parameters can also be given from the contextual menu that appears by right-clicking the mouse on the box with the parameter group. The description of the buttons and of the contextual menu of the parameters group box can be found at The contextual menu of the parameters group box.

System B (destination)

The points can be introduced from files, manually or can be calculated by transforming from a coordinate system to another using the 3rd and 4th steps.

In the case of conversion from (φ, λ, h) to (X, Y, Z) using step 4, it can be chosen if the ellipsoidal elevations are used or not in the calculation (geographical 3D or 2D case). This option can be useful when we want to check the influences of the ellipsoidal elevations for a 3D transformation.

For calculating the parameters in the case of the 3D transformation the table of Cartesian coordinates (X, Y, Z) on the ellipsoid from the B system must be completed.

For calculating the parameters in the case of the 1D or 2D transformations the table of coordinates from the projection system (N, E, H) must be completed. For the 1D transformation only the column with the H elevations is necessary, the N and E coordinates are ignored.

1D Transformation: Calculation of the parameters for a transformation on height

Transformation method

3D plane rotation with 5 parameters (minimum 3 common points);
translation on the elevation with one parameter (minimum one common point).

Button Load common points (1D)

By using this button you can load the table with the common points. From the A system the (Nª, Eª, Hª) coordinates are taken from the table with the coordinates in the local system and from the B system the H coordinates are taken from the table with coordinates in the projection plane.

Button Visualize A points

Plane visualization (2D) of points from system A.

Button A → B

Plane visualization (2D) of points from system A with level difference displaying from system A to system B for each point.

Button Calculate parameters (1D)

By using this button the transformation parameters of the common selected points will be calculated. To do this calculation minimum 3 common points are necessary. If this calculation was possible then the report for the parameter calculation will be completed.

Button Best combination of k points

This button can be used to find the best combination of k points from the total number of points that are found in the table of common points (regardless if they are selected or not). The analysis of the best combination is made according to the standard deviation of the weight unit S₀ by searching from all the possible combinations C_n^k the one that has the smallest S₀. After identifying the best combination, in the table with the common points the used points will appear as selected and the calculation for these points will be presented in the report.

In the case of using the translation on the elevation method, the standard deviation used to identify the best combination is calculated as a standard deviation from average, so the points with the smallest deviation from average will be identified.

Menu button Report

It displays the contextual menu with commands related to the parameters calculation report.

Save report - it saves the report to a file in one of the formats: Plain Text (txt), Rich Text (rtf) or Web Page (html);
Print report - to print the report it opens the printer setup window or the print preview window for the html format;
Export to Microsoft Word - it exports the report data to Microsoft Word;
Clear report - it clears the report data and all calculated precisions.

Menu button Calculated parameters

It displays the contextual menu with commands related to calculated parameters.

Apply 1D transformation - after determination of the parameters you can perform the transformation of a file with points; in this case the parameters calculated before will be loaded in the 1D Transformations section and you will be transferred to this section;
Save parameters - it saves the calculated parameters to a text file;
Copy (...) parameters - it copies the calculated parameters to Clipboard.

2D Transformation: Calculation of the parameters for a transformation in plane

Transformation method

conformal 2D Helmert transformation with 4 parameters (minimum 2 common points);
conformal 2D Helmert transformation with rotation origin with 6 parameters (minimum 2 common points);
affine 2D non-orthogonal transformation with 5 parameters (minimum 3 common points);
affine 2D non-orthogonal transformation with 6 parameters (minimum 3 common points).

Button Load common points (2D)

By using this button you can load the table with the common points. From the A system the (Nª, Eª) coordinates are taken from the table with the coordinates in the local system and from the B system are taken the (N, E) coordinates from the table with coordinates in the projection plane.

Button Visualize A or B points

Plane visualization (2D) of points from A or B systems.

Button A → B

Plane visualization (2D) of points from A and B systems with the display of the vector and of the horizontal distance from system A to system B for each point.

Button Calculate parameters (2D)

By using this button the transformation parameters of the common selected points will be calculated. If this calculation was possible, the report for the parameter calculation will be completed.

Button Best combination of k points

Menu button Report

It displays the contextual menu with commands related to the parameters calculation report.

Save report - it saves the report to a file in one of the formats: Plain Text (txt), Rich Text (rtf) or Web Page (html);
Print report - to print the report it opens the printer setup window or the print preview window for the html format;
Export to Microsoft Word - it exports the report data to Microsoft Word;
Clear report - it clears the report data and all calculated precisions.

Menu button Calculated parameters

It displays the contextual menu with commands related to calculated parameters.

Apply 2D transformation - after determination of the parameters you can perform the transformation of a file with points; in this case the parameters calculated before this will be loaded in the 2D Transformations section and you will be transferred to this section;
Save parameters - it saves the calculated parameters to a text file;
Copy (...) parameters - it copies the calculated parameters to Clipboard.

3D Transformation: Calculation of the parameters for a transformation in space

Transformation method

conformal 3D transformation the Bursa-Wolf method with 7 parameters;
conformal 3D transformation the Molodenski-Badekas method with 10 parameters;
conformal 3D Helmert transformation with 7 parameters;
affine transformation with 8 parameters;
affine transformation with 9 parameters;
affine transformation with rotation origin with 12 parameters.

Button Load common points (3D)

By using this button you can load the table with the common points. From the A and B systems the (X, Y, Z) coordinates are taken from the tables with the geocentric Cartesian coordinates.

Menu button Visualize A or B points

2D view - view points in plane using a local topocentric projection system;
3D view - view points in space using declared datum from options for the A or B system;
Google Earth view - viewing points is done correctly in Google Earth only for coordinate systems that have as reference ellipsoid WGS84 or ETR89 (GRS80).

Button A → B

Plane visualization (2D) of points from A and B systems with the display of the vector and of the 3D distance from system A to system B for each point.

Button Calculate parameters (3D)

By using this button the transformation parameters of the common selected points will be calculated. To do this calculation, at least 3 common points are necessary. If this calculation was possible, the report for the parameter calculation will be completed.

Button Best combination of k points

This button can be used to find the best combination of k points from the total number of points that are found in the table of common points (regardless if they are selected or not). The analysis of the best combination is made accordingly to the standard deviation of the weight unit S₀ by searching from all the possible combinations C_n^k the one that has the smallest S₀. After identifying the best combination, in the table with the common points the used points will appear as selected and the calculation for these points will be presented in the report.

Menu button Report

It displays the contextual menu with commands related to the parameters calculation report.

Save report - it saves the report to a file in one of the formats: Plain Text (txt), Rich Text (rtf) or Web Page (html);
Print report - to print the report it opens the printer setup window or the print preview window for the html format;
Export to Microsoft Word - it exports the report data to Microsoft Word;
Clear report - it clears the report data and all calculated precisions.

Menu button Calculated parameters

It displays the contextual menu with commands related to calculated parameters.

Apply 3D transformation - after determination of the parameters you can perform the transformation of a file with points; in this case the parameters calculated before this will be loaded in the 3D Transformations section and you will be transferred to this section;
Save parameters - it saves the calculated parameters to a text file;
Copy (...) parameters - it copies the calculated parameters to Clipboard.

General considerations

In all tables the coordinates can be entered manually, loaded from a file or copied from another table. Coordinates from tables can be saved to the file or can be exported to Microsoft Word or Microsoft Excel. The description of the buttons and of the contextual menu of tables can be found at The commands of the coordinate tables.

For information on how to choose the transformation method read the page with Recommendations.

When loading the common points from the two tables of the A and B systems the points must not be in order because the identification will be performed according to the point name (point number). In order for the points to be taken correctly make sure the points names (point number) correlate in the two tables.

In the tables with the common points if, for example, you wish that one of the points is not taken in the calculation of the possible combinations just delete the point from the table by selecting the row and pressing the <Del> key.

Both displaying and saving reports regarding parameters calculation can be made as Text, Rich Text Format or Html. The selection of the display mode can be made from Options - General Tab - View reports.

You can calculate the parameters of a transformation for the points from any coordinate system by completing directly the tables used to extract the common points. In this case the coordinate conversions from the pages with the A and B system aren’t necessary. If the coordinates used to calculate the parameters do not belong to the coordinate systems defined for the A and B system, in the 3D Transformation section the transformations (X, Y, Z) to (φ, λ, h) or to (N, E, Z) aren’t valid from inside the tables, the transformation (X, Y, Z) from the A system to (X, Y, Z) from the B system remaining valid.