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Helmert Transform

The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917; also called a seven-parameter transformation) is a coordinate transformation method within a three-dimensional space. It is frequently used in geodesy to produce distortion-free transformations from one datum to another using:

    XT =C+ uRX

where

    XT is the transformed vector

    X is the initial vector

The parameters are:

    C is the translation vector. Contains the three translations along the coordinate axes

    u is the scale factor, which is unitless, and as it is usually expressed in ppm, it must be divided by 1,000,000.

    R is the rotation matrix. Consists of three axes (small rotations around the coordinate axes) rx, ry, rz. The rotation matrix is an orthogonal matrix. The rotation is given in radians.