The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917; also called a seven-parameter transformation) is a 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 is the transformed vector
- X is the initial vector
The parameters are:
- — translation vector. Contains the three translations along the coordinate axes
- — scale factor, which is unitless, and as it is usually expressed in ppm, it must be divided by 1,000,000.
- — rotation matrix. Consists of three axes (small rotations around the coordinate axes), . The rotation matrix is an orthogonal matrix. The rotation is given in radians.
Thus, the Helmert transformation is a similarity transformation.
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