Affine 2D

Also known as 6-parameter transformation. It is the general case of the 4-parameter Helmert transformation, where different scales are used for the X and Y axes and where, moreover, these axes are not orthogonal. At least three pairs of points are necessary.

Formulas:

where:

x', y' = Transformed X,Y coordinates

x,y = Original X,Y coordinates

Sx = Scale X

Sy = Scale Y

= Rotation angle

= Othogonality correction angle

Tx = Translation X

Ty = Translation Y