Reference System Transition

GeoDLL supports three basic forms for Reference Systems Transitions:

Helmert Transformation with 7 Parameter

Molodensky Transformation with 3 Parameter

NTv2-Transformation

In addition, the following settings are supported:

Without Reference System Transition on standard ellipsoids

Without Reference System Transition and ellipsoid tansition

Without Reference System Transition on user defined ellipsoids

User-defined geodetic Reference System

Helmert and Molodensky

The Geodetic Development Kit performs Reference Systems Transitions via three-dimensional Cartesian transformation by Helmert or Molodensky using different possible transformations methods:

Internal sign changes of the three rotation parameters support the following transformation methods:

The following seven parameters are used for the Helmert transformation:

3 Translations

3 Rotations

1 scale factor

The Molodensky transformation uses only three parameters:

3 Translations

GeoDLL calculates Reference System Transitions with Helmert transformation parameters as Forward and Backward Transformations. With a Forward Transformation, starting from the source system, first the rotations and then the translations are performed. With a Backward Transformation, leading to the target system, in reverse order first the translations and then the rotations are calculated.

Forward and Backward Transformations are executed each across the current dynamic reference system WGS84. This has the advantage that Reference System Transitions between WGS84 and other predefined Reference Systems can consider the current continental drift. So GPS measurements can be converted directly into arbitrary Coordinate Reference Systems.

On the other hand, with Reference System Transitions between two predefined reference systems, the WGS84 parameters are recalculated internally. The transition via WGS84 is only used to give the Reference Systems a common basis.

The situation is different when using user-defined Reference Systems. In this case, the transition is not calculated via the current WGS84 parameters, but directly using the user-defined parameters.

Normally, geodesic software only supports very small rotation angles when transforming with seven Helmert transformation parameters. In GeoDLL, the fast, simplified rotation matrix is resolved for small rotation angles up to 5 seconds. At larger angles, the slower, complete rotation matrix is resolved to maintain accuracy. In this way, both the high accuracy and the high calculation speed is guaranteed.

For the Source Coordinate System and the Target Coordinate System, any Helmert or Molodensky Reference Systems can be combined with each other. GeoDLL independently calculates the required transformation parameters.

NTv2

In addition to the described methods GeoDLL supports Reference System Transitions with higher accuracy by using grid files according to worldwide NTv2 standard and the American HARN standard.

NTv2 means "National Transformation Version 2". The NTv2 method uses binary files to perform accurate calculations from one geodetic Reference System to an other. A NTv2 file contains the differences between the two Reference Systems as geographic seconds shift values in a grid. A bilinear interpolation is used to calculate the exact coordinates for a point in the target Reference System.

NTv2 is designed to check multiple grids for the most accurate information. A NTv2 file contains one or more low density base grids (parent). Certain areas such as cities can have high density local sub grids. The sub grids overlay portions of the base grids. If a point is within one of the high density sub grids, NTv2 will use the high density grid, otherwise, the point ‘falls through’ to the suitable low density grid. The sub grids may overlap each other. In this case, the sub grid that has the closest mesh width is found.

NTv2 Reference Systems are identified by the suffix "NTv2" in the designation. When setting an NTv2 Reference System for the Source or Destination Coordinate System, on the other side must be set the equivalent Reference system of the associated NTv2 file. The combination of NTv2 Reference Systems with Helmert or Molodensky Reference Systems is not possible.

You can download the NTv2 files supported by GeoDLL directly from the KilletSoft Internet site https://www.killetsoft.de/p_gdln_e.htm#download or use the download links to the original sources there.