Helmert 3D - GPS v2

17.4 Helmert 3D

It is also known as the 7-parameter transformation. The parameters involved are: three rotations, three translations and a scale factor. The rotation matrix is constructed by three consecutive turns around the x, y, z horizontal alignment. It is necessary to have at least 3 pairs of points.

Formulas:

x′=S•(m11•x+ m12•y+ m13•z)+ Tx y′=S•(m21•x+ m22•y+ m23•z)+ Ty z′=S•(m31•x+ m32•y+ m33•z)+ Tz

where:

x', y', z' = x, y, z transformed coordinates.

x, y, z = Original x, y, z coordinates.

S = Scale.

Tx = Translation x.

Ty = Translation y.

Tz = Translation z.

m11 ... m33~=~ Coefficients of the rotation matrix.