27.7. 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
m11...m33 = Rotation matrix coefficients