Helmert 2D - GPS v2

17.2 Helmert 2D

It is also known as a 4-parameter similarity transformation. The transformation process includes 3 steps: scaling, rotation and translations.

The first two are defined by a parameter each and the translations include 2. At least two pairs of points are necessary.

Formulas:

x′=(S•cosθ)•x+(S•sinθ)•y+Tx y′=−(S•sinθ)•x+(S•cosθ)•y+ Ty

where:

x′, y′ = x, y transformed coordinates.

x, y = Original x, y coordinates.

S = Scale.

θ = Angle of rotation.

T_x = Translation x.

T_y = Translation y.