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helmert3d

About

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]. The tool helmparms3d reads two 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.

Development

Build:

make

Install:

sudo make install

Uninstall:

sudo make uninstall

Use

Parameter computation:

helmparms3d [xyz_src_infilename] [xyz_dest_infilename] [parms_outfilename]

Transformation:

helmert3d [xyz_src_infilename] [param_infilename] [xyz_transformed_outfilename]

Test:

helmdiff3d [xyz_dest_infilename] [xyz_transformed_infilename] [xyz_diff_outfilename]

Files

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]

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