Origin :
GLC.ORG:

The 3D Helmert transformation is a frequently used method in geodesy to produce transformations between different cartesian coordinate systems:

Xt=T+sRX

where

Xt = transformed coordinate vector

X = initial coordinate vector

T = translation vector

R = rotation matrix including rx, ry, rz

rx, ry, rz = rotations around the coordinate axes

s = scale factor

Seven parameters are required for this kind of transformation and can be calculated from a set of at least three point correspondences [Crosilla, F. (1999). Procrustes analysis and geodetic sciences. Technical report, Quo vadis geodesia...?, Department of Geodesy and GeoInformatics, University of Stuttgart]. A simple description of the SVD-based algorithm can be found here: http://dx.doi.org/10.18419/opus-523 on page 148 (A.3.1).

All coordinates must be translated to XYZ coordinates, first, if the coordinate system is not cartesian. Transformations between ellipsoidal (B L H = LAT LON H) and cartesian (XYZ) coordinates can be managed with the tool helmeltrans. The ellipsoid name, as well as both axes of the ellipsoid must be predefined in a seperate textfile (ellipsoid_infile). See also common_ellipsoids.txt for common values.

The tool helmparms3d reads two XYZ point-textfiles and calculates all necessary parameters for Helmert transformation. For further computations these parameters are stored in an additional textfile. The Helmert transformation can then be calculated with helmert3d. Finally the alignment can be tested with helmdiff3d.

Build:

make

Install:

sudo make install

Uninstall:

sudo make uninstall

Parameter computation:

helmparms3d xyz_src_infilename xyz_dest_infilename [parms_outfilename]

Transformation:

helmert3d xyz_src_infilename param_infilename [xyz_transformed_outfilename]

Coordinate system translatation:

helmeltrans {blh|xyz} src_infilename ellipsoid_infilename [outfilename]

Transverse Mercator:

helmtmerc {blh|xyh} src_infilename ellipsoid_infilename zone_infilename [outfilename]

Test:

helmdiff3d xyz_dest_infilename xyz_transformed_infilename [xyz_diff_outfilename]

Helmert parameter file format:

 r11 r12 r13
 r21 r22 r23
 r31 r32 r33
 tx ty tz
 s

XYZ data file format:

 X[1] Y[1] Z[1]
 ..   ..   ..
 ..   ..   ..
 X[n] Y[n] Z[n]

BLH data file format:

 B[1] L[1] H[1]
 ..   ..   ..
 ..   ..   ..
 B[n] L[n] H[n]

xyH data file format:

 x[1] y[1] H[1]
 ..   ..   ..
 ..   ..   ..
 x[n] y[n] H[n]

Ellipsoid data file format:

 name a b

Zone data file format:

 zone_size zone_number [zone_scale] [L0] [x0] [y0]

See ellipsoids : Common Ellipsoids

https://github.com/dr-ni/helmert3d