For example if we compare the AGD84 (Australian Geodetic Datum) with GDA94 (Geocentric Datum Australia), the centre of the AGD Datum is 200 metres different to GDA, because it is a best fit to the geoid.
But how is this difference realised (implicitly) given only the Lat/Long/ Ellipsoidal Height of a Point (Johnstone), the semi-major axis (a) and the flattening (f)? I realise that (a) is different by 23 metres, but it is the angle between the 2 datums that makes the most difference, this is what I am trying to get a handle on.
Asking another way, how could I calc the ECEF coords for the centre of the AGD, to see how different it is to GDA?
Asking yet another way, how to determine the shift & angles between the axes of of AGD & GDA?
I already have the GDA manual - http://www.icsm.gov.au/gda/gdatm/gdav2.3.pdf and am working through writing C++ code for this. I also understand how AGD is not very consistent, so a conversion between the 2 datums requires the use of a model, it is just that I am trying to truly understand the mathematical difference between the two.
Sorry for the particularly nerdy question, & thanks in advance for any answers.