The Attribute Transfer Tool Field Mapping can be set up to transfer the Source Shape field over to the Target Shape field. In ArcGIS Pro 2.9 at least, when the Source Feature's polygon or polyline Shape contains true curves those true curves are not transferred to the Target Feature's Shape. Instead, the Transfer Attribute tool transfers a Densified curve made up of straight line segments.
Here is an example of a feature containing numerous true curves segments within its geometry. If I use the Attribute Transfer tool to transfer the Shape of this feature back to itself, the feature is densified. This should not be occurring.
In ArcMap, true curves in the source geometry are transferred to the target feature's geometry when the Transfer Attributes tool is used. Below is the same Attribute Transfer set up in ArcMap and the result of transferring the shape of the same feature with true curves back to itself.
When I transfer the above features shape to another feature it retains any true curves that came from the source.
ArcMap does not allow transfers from a feature back to itself. This difference may be required in Pro since the Attribute Transfer tool Field Mapping also controls ArcGIS Pro's Copy/Paste behavior, which I have discussed in another post.
The Attribute Transfer tool in ArcGIS Pro needs to be made equivalent to the ArcMap version in its behavior of preserving True Curves. This is in addition to numerous other behavior differences that I have described in other posts.
I am no longer authorized to contact Esri Support in my organization, since I retired and now work through the Temporary Assistance Program. However, I know someone who can submit a case and I will work with them to do that. However, I will be upgrading to ArcGIS Pro 3.2 next week. So I will wait until I can confirm that this issue has still not been addressed in that version before submitting a case.
You should also check out these two ideas for other issues related to the Transfer Attributes tool. Please up vote them if you agree with the issues I raise.
It looks like this was a bug fixed in ArcGIS Pro 3.0: https://support.esri.com/en-us/bug/the-transfer-attributes-editing-tool-does-not-transfer-bug-000146...
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