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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">Hi,</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">1) In the genral case, there is no transitivity when doing A -> B, and A -> C and then C -> B. You will generally not get the same result, if A, B and C are not in the same datum.</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">e.g:</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">GDA94 -> WGS 84 : null transformation (they were coincident in Jan 1st 1994)</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">WGS 84 -> GDA2020: null transformation (they were coincident in Jan 1st 2020)</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">but</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">GDA94 -> GDA2020: ~ 1.8m shift !</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">2) However, in your case, I'm not completely clear why you don't get transitivity in using EPSG:32756 since it uses the same datum as EPSG:4326... This seems related to using the deprecated +init=epsg:XXXX syntax instead of the EPSG:XXXX one (if you the EPSG:XXXX one, you'll need to specify the geographic coordinates in latitude, longitude order).</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">3) The result you get with "cs2cs -d 6 +init=epsg:4326 +to +init=epsg:7856+5711" is the optimal one I believe. Setting PROJ_DEBUG=3 as environment variable, I can see "</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">Using coordinate operation axis order change (geographic3D horizontal) + Inverse of GDA2020 to WGS 84 (2) + GDA2020 to AHD height (1) + Map Grid of Australia zone 56", which is the most reasonable option to me, using AUSGeoid2020 for the vertical adjustment.</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">4) But if you used the non deprecated syntax, "cs2cs -d 6 EPSG:4326 EPSG:7856+5711" you'd get a suboptimal result involving AGD66, GDA94 and AUSGeoid09 internal steps. I've traced that issue in</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">https://github.com/OSGeo/PROJ/issues/2348</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">5) If you are interested in centimer-level accuracy, and have a coordinate epoch associate with your WGS 84 coordinate (since WGS 84 is a dynamic datum), you'd better using EPSG:9057 / "WGS 84 (G1762)" to get a non-null transformation between WGS 84 and GDA2020</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">e.g:</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">echo -33 151 5 2020.6 | cs2cs -d 8 "WGS 84 (G1762)" GDA2020</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">returns</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">-33.00000030 150.99999988 5.00013120 2020.6</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">Even</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">-- </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">Spatialys - Geospatial professional services</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">http://www.spatialys.com</p></body></html>