Helmert 2D + Vertical Displacement

This type of transformation is a combination of the Helmert 4-parameter transformation and a displacement in Z. This translation in Z is calculated as the mean of the differences between the source and target points with this component. At least two pairs of points with X and Y coordinates and one with the Z coordinate 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

Tz = Translation Z