Twostep

This transformation approach works by treating the height and position transformation separately. For the position transformation, the WGS 84 coordinates are first transformed using a classic 3D pre-transformation to obtain preliminary local cartesian coordinates. These are projected onto a preliminary grid using the specified ellipsoid and map projection. Then the two shifts, the rotation and the scale factor of a classic 2D transformation are calculated to transform the preliminary to the “real” local coordinates.

The position transformation requires knowledge of the local map projection and the local ellipsoid. However, as the distortions of the map projection are taken into account, twostep transformations can be used for larger areas than onestep transformations.

The height transformation is a single dimension height approximation.

The height and position transformations are separate and, therefore, errors in height do not propagate into errors in position. Additionally, if knowledge of local heights is not good or non-existent you can still create a transformation for position only. Also, the height points and position points do not have to be the same points.

Because of how the transformation works it is possible to compute transformation parameters with just one point in the local and WGS84 system.

The combinations of the number of points in position and the position transformation parameters that can be calculated from them are as follows:

No. of position points	Transformation parameters computed
1	Classic 2D with shift in X and Y only.
2	Classic 2D with shift in X and Y, rotation about Z and scale.
More than 2	Classic 2D with shift in X and Y, rotation about Z, scale and residuals.

The number of points with height included in the transformation directly affects the type of height transformation produced.

No. of height points	Height transformation based on
0	No height transformation.
1	Constant height transformation.
2	Average constant between the two height points.
3	Plane through the three height points.
More than 3	Average plane.

The advantage:

The advantage:

Errors in local heights do not affect the position transformation.
The points used for determining the position and height transformation do not necessarily have to be the same points.
The distortions of the map projection are taken into account which enables you to use the transformation for larger areas.

The disadvantage:

The disadvantage:

Knowledge of the local projection and local ellipsoid are required.

Other transformation approaches:

Other transformation approaches:

Classic 3D

Onestep

Quick Ground