I have been having all sorts of problems with converting Australian projections 
between AGD84 and GDA94, both as spherical and cartesian coordinates. 

I have MapInfo data in AGD84. I go through the conversion process to GDA94 using 
various methods (FME some time ago, and now via ESRI ArcTools) and end up with a 
dataset projected in GDA94. However, when I overlay this data with the original AGD84 
data, there is only about a 3 metre offset, not the 200 metre offset that it should 
be. 

But if during the conversion process, I set the coordinate system to GDA94 again, and 
then overlay the original GDA94 data with the converted data, there is the 200 metre 
(or so offset).

In a nutshell, my processing steps are:

  1.. From MapInfo, export the source AGD84 table as MID/MIF format.
  2.. In ArcToolBox, convert the MIF to a Shapefile, assign the source projection 
(AGD84) and then specify the projection going to (GDA94).
  3.. Go back to MapInfo (v7.5) and import the Shapefile, selecting GDA94 as the 
projection. This results in only a 3 metre offset. But at this stage, if I import the 
Shapefile and select AGD84 (the original projection), the 200 metre offset is apparent.
Are there any ideas what is going on? Will sum.
Many thanks,
Bill

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