Helmert 2D vertical displacement and slopes - MDT25

28.9 Helmert 2D + Vertical Displacement and Slopes

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