Geodetic transformations and conversions
Last updated:25 August 2020
Geoscience Australia provides a range of web applications, documents and spreadsheets to help with coordinate transformations, conversions and ellipsoid computations. The documents and spreadsheets are a reference standard. They can be used for computations of small datasets and as a validation source for software development.
Detailed information about the spreadsheets can be found in the Geocentric Datum of Australia 2020 Technical Manual available via the International Committee on Surveying and Mapping (ICSM).
Coordinate transformations
Coordinate transformation is the process of changing coordinates from one reference frame to another. Options for the transformation of coordinates to and from GDA2020 are transformation parameters and transformation grids.
Transformation grids
The transformation grids are National Transformation version 2 (NTv2) files of binary grid shift (.gsb) format used to transform coordinates from one reference frame to another. Transformation grids are the preferred method for transforming between Australian datums. The transformation grids are available from the ICSM website.
NOTE: Two types of transformation grids are available: 1) conformal only and 2) conformal and distortion. The combined conformal and distortion grid models both the conformal transformation (i.e. translation, rotation and scale) and distortion components of the differences in the datums. In the case of GDA94 to GDA2020, the distortion component is caused by the different strategies used by state and territories to propagate GDA94 coordinates and surface movement of parts of the Australian crust. The magnitude of the distortion varies between jurisdictions and can be in the order of decimetres.
Similarity transformation:
A spreadsheet is available on the ICSM Github repository to perform a 7-parameter transformation.
Online web service:
A web service available via the ICSM website allows users to upload a file to be transformed. This transformation will use the transformation grids and send the user an email to download the transformed dataset.
Coordinate conversions
Geographic to / from grid
Two methods are presented to convert Geographic to/from Grid coordinates; Krueger n-series equations and Krueger λ‑series equations (Redfearn's equations). The Krueger λ‑series equations are accurate to better than 1 mm within any zone of the Map Grid of Australia 2020 and can still be used for many purposes. However, for applications where users are working across multiple UTM/MGA zones, Krueger n-series equations are recommended. The Krueger n-series equations are particularly beneficial in software to avoid error build up when conversions are done back and forth between geographic and grid coordinates.
- Online application (n-series):
- Spreadsheet (Krueger both series): A spreadsheet is available on the ICSM GitHub repository to perform geographic to grid conversions, or vice versa.
Coordinate computations
Vincenty's formulae can be used to calculate the ellipsoidal distance and azimuths between two points.
Vincenty's direct: Given the latitude and longitude of a point (1) and the forward geodetic azimuth (1-2) and ellipsoidal distance to a second point (2), calculate the latitude and longitude of the second point and the reverse azimuth (2-1).
Vincenty's inverse: Given the latitude and longitude of two points compute the ellipsoidal distance and forward and reverse azimuths between the points.
Tools available to perform ellipsoid computations are: