1065 - OGP Surveying and Positioning Committee

Annex F______________________________________________________________________________________________________________Page F5geographical information processing whilst the definition of the vertical datum may be useful itis not essential. However it is critical that the vertical datum is identified. This is because ifthe datum surface is changed, the values of heights measured from that surface will change.Geocentric Co-ordinatesLatitude, longitude and ellipsoidal height can be easily transformed into a three-dimensionalcartesian co-ordinate frame where the cartesian origin is coincident with the centre of theellipsoid. Such a system is known as a geocentric co-ordinate system. Indeed in moderngeodesy this is the starting point for a reference system definition, with geographical and thenprojected co-ordinates being derived from the geocentric system.Relationship between geocentric and ellipsoidal co-ordinate systemsZNorth PoleGreenwichbPointSemi-Major Axis = Equatorial Radius = aSemi-Minor Axis = Polar Radius = bInverse Flattening = 1/f = a/(a-b)0,0,0 aa λφYEquatorXFigure F-7Equations for changing latitude, longitude and ellipsoidal height to and from geocentric coordinates(using the same geodetic datum) can be found in standard geodetic texts. The onlyparameters required are for the size and shape of the ellipsoid.Geodetic TransformationsGeographic 3D and geocentric co-ordinates in one co-ordinate system can be transformed toanother geodetic co-ordinate system if the relative positions of the two systems can bedescribed. This is frequently achieved through a simple three-dimensional transformationbetween geocentric co-ordinate systems. For geographic 3D co-ordinates, the relationshipbetween ellipsoidal and geocentric co-ordinates is straightforward and can be included in thetransformation process.The same procedures can be used to transform geographic 2D co-ordinates, but exactly onlyif an orthometric height is known or assumed and can first be transformed to an ellipsoidalheight through the application of the geoid height. In practice, for geographical informationprocessing, the method can sometimes be used within the general accuracy requirements ofthe user without knowledge of the geoid height. Alternative methods which transform directlybetween geographic 2D co-ordinate systems are also available.The 3-translation model assumes that the axes of the geocentric co-ordinate systems areparallel, and that the scales of the co-ordinate systems are identical. Both of theseassumptions in general are not true. The 3-translation model is therefore an approximation.The approximation can be improved if a 7-parameter Helmert transformation is used. Thisadds three rotations and a scaling to the three translations. A difficulty with practical____________________________________________________________________________________________UKOOA Guidance Notes on use of co-ordinate systems in data management on the UKCS - December 1999