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.