﻿ Calculation Accuracy
 Calculation Accuracy

GeoDLL uses Coordinate Transformation formulas based on publications by Schatz, Schuhr and Klotz and Hooijberg. Algorithms used for country-specific transformations are either published or made directly available by the Measurement Authorities of the respective countries or by similar respectable institutions. To achieve the highest precision only strong formula algorithms are used for calculations.

without Reference System Transition have extremely high precision ranging within millimeters. A good example for Coordinate transformations between Gauß-Kruger and UTM Coordinate Systems made with GeoDLL are the results published by the North-Rhine Westphalia Land Survey Commission [see: Transformation von Koordinaten und Höhen in der Landesvermessung, Teil II]. It was confirmed that the differences were within lower millimeter range.

The DLL performs Reference System Transitions by three-dimensional Cartesian Transformation using the following transformations methods:

 • Coordinate Frame Rotation" with seven Helmert transformation parameters
 • Molodensky Transformation with three Transformation parameters.

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

 • Position Vector Transformation with seven Helmert transformation parameters
 • European Standard ISO 19111 with seven Helmert transformation parameters

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.

Calculating bidirectional coordinate transformations with Forward and Backward Transformations like in GeoDLL does not lead in minor deviations, that occur in many GIS systems. A series of tests with bidirectional coordinate transformations between different coordinate reference systems in GeoDLL has revealed a maximum tolerance of 0.5 mm.

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.

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.

Coordinate Transformations involving Reference System Transitions produce a systematic error. This deviation is higher when the calculated coordinates are far away from the Reference System origin. Depending on the Reference System used it can be in decimeter up to meter range [see also: Johannes Ihde: Datumstransformation zwischen den Bezugssystemen ETRF / WGS, DHDN und SYSTEM42, Zeitschrift für das Vermessungswesen 120, 4.1995].

The deviation depends almost exclusively on the quality of the used transformation parameter set. GeoDLL uses only the official parameter sets, which are published by the Measurement Authorities of the individual countries or by similar respectable institutions.

Better resolution can be achieved using local transformation parameter sets. Transformation sets can be obtained from various sources, e.g. the Measurement Authorities of the respective German Federal Republic States or they can be calculated by suitable software, e.g. the program SEVENPAR. They can be imported in GeoDLL as "User defined Geodetic Reference Systems".

The accuracy of the calculations is sufficient for most practical applications - navigation, small-scale maps, environmental protection, local lore and geology, as well as most of the common Surveying projects.