﻿ Function gettranshelmert()
 Prototype and description of the function gettranshelmert() (Function of the unlock requiring group "Transformation Parameter")
 ```gettranshelmert() Calculation of Seven Helmert Parameters and a rotation matrix from identical points in different Reference Systems. Prototype of the DLL function in C++ syntax (attend lower case!): extern "C" __declspec(dllimport) unsigned long __stdcall gettranshelmert( double aCartQ[], double aCartZ[], unsigned long nCount, unsigned short nTyp, unsigned short nIterat, unsigned short *nItNeed, double aHelmert, double aRotMat[]); Prototype of the DLL function in Visual Objects syntax: _DLL FUNCTION gettranshelmert(; aCartQ as real8 ptr,; // 4 Byte aCartZ as real8 ptr,; // 4 Byte nCount as dword,; // 4 Byte nTyp as word,; // 2 Byte nIterat as word,; // 2 Byte nItNeed ref word,; // 4 Byte aHelmert as real8 ptr,; // 4 Byte aRotMat as real8 ptr); // 4 Byte AS logic pascal:geodll32.gettranshelmert // 4 Byte The function calculates Seven Helmert Transformation Parameters and a Rotation Matrix from identical points in different source and target Coordinate Reference Systems. The identical points are stored in arrays as cartesian coordinates. The Helmert transformation is a transformation for three-dimensional Cartesian coordinates. It contains as parameters three translation vectors, three rotation angles and a scale factor. The maximum iteration depth for a very accurate calculation of the transformation parameters is calculated automatically by the function depending on the number of identical points, if the parameter nIterat is set to null. For point clouds with plausible identical points, a few iterations are usually sufficient to achieve the required accuracy and thus to finish the calculation. But if the automatically predefined maximum iteration depth is exceeded, the function terminates with an error message. With a small expansion of a point cloud or with a small number of identical points, it may happen that the expected accuracy is not achieved when passing through the automatically predefined maximum iteration depth. In order to obtain a result anyway, the iteration depth can be specified in the nIterat parameter. The function then terminates the calculation without an error message. In extreme cases, however, the parameters calculated in this way may be inaccurate or even incorrect. In case of doubt, the function gettransmolertensky() should be used instead of the function gettranshelmert(). The Molodensky Transformation provides a useful result even in extreme cases, although it does not have the high accuracy of the Helmert transformation. To check the iteration depth, the function returns in the nItNeed parameter the count of the effective iterations to the calling routine. The rotations are also available as a spatial rotation matrix. For this a rotation matrix with 3 x 3 rotation elements is generated. All KilletSoft geodetic tools and programs use a complete rotation matrix for Helmert transformations. The programs of many other manufacturers use a simplified rotation matrix, which provides accurate results only for small rotation angles. Here is the syntax of the full rotation matrix for the "Coordinate Frame Rotaion" transformation method: Cos(Ry)*Cos(Rz) Cos(Rx)*Sin(Rz) + Sin(Rx)*Sin(Ry)*Cos(Rz) Sin(Rx)*Sin(Rz) - Cos(Rx)*Sin(Ry)*Cos(Rz) -Cos(Ry)*Sin(Rz)" + CRLF Cos(Rx)*Cos(Rz) - Sin(Rx)*Sin(Ry)*Sin(Rz) Sin(Rx)*Cos(Rz) + Cos(Rx)*Sin(Ry)*Sin(Rz) Sin(Ry) -Sin(Rx)*Cos(Ry) Cos(Rx)*Cos(Ry) The syntax of the simplified rotation matrix has this form: 1 Rz -Ry -Rz 1 Rx Ry -Rx 1 For the other transformation methods (except Molodensky) the same syntax applies, only some signs are reversed. Since the function due to the extensive calculations is time-consuming, the event handling during the calculation by interrupting the processing loop can be are allowed bei calling the function seteventloop(). The parameters are passed and/or returned as follows: aCartQ[] Cartesian coordinates X, Y, Z of the source Coordinate Reference (ref) System in a two dimensional array of type double. The first dimension counts the available cartesian source coordinates of the identical points given in nCount. The second dimension is 3 for the X, Y and Z component of a cartesian source coordinate. The length of the arrays aCartQ and aCartZ must be identical. There must be at least three coordinate triples available. The structure of the array is described further below. aCartZ[] Cartesian coordinates X, Y, Z of the target Coordinate Reference (ref) System in a two dimensional array of type double. The first dimension counts the available cartesian target coordinates of the identical points given in nCount. The second dimension is 3 for the X, Y and Z component of a cartesian target coordinate. The length of the arrays aCartQ and aCartZ must be identical. There must be at least three coordinate triples available. The structure of the array is described further below. nCount Count of the available identical points stored as cartesian coordinates in the arrays aCartQ and aCartZ. nTyp Geographic Transformation Method of the Helmert Parameters. 1: Coordinate Frame Rotation 2: Position Vector Transformation 3: European Standard ISO 19111 nIterat Predefined maximum iteration depth for the calculation of the Helmert Transformation Parameters. nIterat = 0: Automatic determination of the iteration depth depending on the number of Cartesian Coordinates. nCount ›= 50000: nIterat = nItMax = 20 nCount ›= 10000: nIterat = nItMax = 30 nCount ›= 5000: nIterat = nItMax = 40 nCount ›= 1000 nIterat = nItMax = 50 nCount ›= 500 nIterat = nItMax = 60 nCount ›= 100 nIterat = nItMax = 70 nCount ›= 50 nIterat = nItMax = 80 nCount ›= 25 nIterat = nItMax = 90 nCount ›= 3 nIterat = nItMax = 100 nIterat ›= 5 and nIterat ‹ nItMax: Maximum iteration depth nIterat ‹ 5 or nIterat ›= nItMax: see nIterat == 0 nItNeed Iteration depth actually required for the calculation. In case of (ref out) an error null is returned. aHelmert Seven Helmert parameters in an array of 7 doubles. (ref out) 1. array element: Translation vector for X-axis [meter] 2. array element: Translation vector for Y-axis [meter] 3. array element: Translation vector for Z-axis [meter] 4. array element: Rotation angle around the X-axis [seconds] 5. array element: Rotation angle around the Y-axis [seconds] 6. array element: Rotation angle around the Z-axis [seconds] 7. array element: Scale correction factor [ppm] ------------------------------------ | T1 | T2 | T3 | R1 | R2 | R3 | SF | ------------------------------------ For the array the calling function must provide memory of the size 7*sizeof(double) bytes. aRotMat Rotation Matrix of the spatial Helmert Transformation in an (ref out) array of 3 times 3 doubles. The syntax of the matrix is described above. ------------------- | w11 | w21 | w31 | | w12 | w22 | w32 | | w13 | w23 | w33 | ------------------- The signs of w can change in dependence of the Transformation Method. For the array the calling function must provide memory of the size 3*3*sizeof(double) bytes. returnVal In case of an error the function returns FALSE, otherwise TRUE. The two dimensional arrays aCartQ[] und aCartZ[] are filled with values of type double and are structured as follows: ---------------------------------------------------------------------- | C1-X | C1-Y | C1-Z | C2-X | C2-Y | C2-Z | ... | Cn-X | Cn-Y | Cn-Z | ---------------------------------------------------------------------- with C1 -› Cn: Coordinates 1 to n X: Cartesian X component Y: Cartesian Y component Z: Cartesian Z component At least three identical points with coordinate triples are needed for the calculation. Unlocking: This function is a component of the unlock requiring function group "Transformation parameter". It is unlocked for unrestricted use together with other functions of the group by passing the unlock parameters, acquired from the software distribution company, trough the function setunlockcode(). Without unlocking at most 25 identical points can be processed. ```