Helmert 2D

Also known as 4-parameter similarity transformation. The transformation process involves 3 steps: scaling, rotation and translations. The first two are defined by one parameter each and the translations include 2. At least two pairs of points are necessary.

Formulas:

where:

x', y' = Transformed X,Y coordinates

x,y = Original X,Y coordinates

S = Scale

= Rotation angle

Tx = Translation X

Ty = Translation Y