As in the previous transformation, this is a combination of the Helmert 4-parameter transformation and a translation in Z calculated from a displacement and the inclinations of the X and Y components. At least two pairs of points with X and Y coordinates and three 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
Px = Slope X
Py = Slope Y
X0 = Original X coordinate of the first pair of points
Y0 = Original Y coordinate of the first pair of points