Helmert 3D - MDT25

28.7 Helmert 3D

This transformation is also known as 7-parameter transformation. It transfers points from one 3-dimensional coordinate system to another. It is applied in the process of reducing GPS survey data, and also in photogrammetry. The 7 parameters involved are: three rotations, three translations and a scale factor. The rotation matrix is constructed by three consecutive rotations round X,Y,Z axes. At least three pairs of points are necessary.

Rotation matrix:

where

Formulas:

where:

x\', y', z\' = Transformed X,Y,Z coordinates

x,y,z = Original X,Y,Z coordinates

S = Scale

Tx, Ty, Tz = Translations in X,Y,Z

m~11~...m~33~ = Rotation matrix coefficients