Similarity transformations convert the latitude and longitude of a point from one ellipsoid to another which may be centred at a different point and oriented differently. These transformations account for the difference between the ellipsoids underlying the different geodetic datums, but can not account for distortions within the datums themselves.
Note: Two different rotation conventions are in common use for defining similarity transformations, Helmert and Bursa-Wolf. The difference between these two conventions is the signs assigned to the rotation components. The transformations described here and the associated conversion formulae follow the Helmert convention. It is critical that transformation software is checked to ensure the correct rotation directions are being applied.
The seven parameter transformation defines the translation (TX, TY, TZ), rotation (RX, RY, RZ) and scale change (ΔS) between the origins and axes of the ellipsoids used for each datum. It has a nominal accuracy of ±2 metres.
This transformation is formally defined in the LINZ standard LINZS25000: Standard for New Zealand Geodetic Datum 2000, and is summarised in the associated NZGD2000 LINZG25700 Fact sheet.
The seven parameter transformation from CIGD1979 to NZGD2000 is:
|Translation (metres)||Rotation (seconds of arc)||Scale change
This transformation can be reversed (ie to convert from NZGD2000 to CIGD1979) by reversing the signs of the above parameters.