I don't understand what you mean.
On second thought, I'll venture a guess, which could be wrong given the sprawling nature of the thread referenced. :-) The basic issue seems to be that Manifold treats a coordinate system definition as the explicit statement of all parameters relevant to a coordinate system. That includes parameters such as offsets and scaling (or units). EPSG 3857 with zero offsets is a clearly defined coordinate system. If everything is the same except offsets are non-zero, that's a different coordinate system, with said non-zero offsets duly noted in the JSON string that exactly specifies the coordinate system. That Manifold explicitly specifies all parameters of interest is a good thing. That provides an explicit statement so you can always look and see exactly what the coordinate system is supposed to be. None of this "Oh, this is what the coordinate system is supposed to be. Except when I use the same words to mean something different." That conflicts with what some other systems do, where they use the same name of a coordinate system to refer to what in actuality are different coordinate systems, different because they use different offsets, different units or other differences. You run into that difference in approach with images, where common practice has two inelegant aspects to it: first, formats are used which do not fully convey all projection info of interest. They'll convey some of it, like offsets, but other parts are talk therapy that must be harvested from metadata or other babble. Second, they'll say an image is in some projection but with changes in the form of offsets, rotation or some other customization of the projection specific to that particular image. In Manifold's case, if you read metadata saying the image is in EPSG:3857 and you tell the system to apply EPSG:3857 it will do that, including the zero offsets that are built into that coordinate system. In the case of Arc, if you tell it to apply EPSG:3857 it doesn't think about offsets so it just leaves those whatever they are. With Manifold, you are free to define a custom version of EPGS:3857 that is specific to a given image where the offsets or other parameters in that customized version are those used in the coordinate system of the image. You can then save that to Favorites and you'll get a one-click ability to apply that correct coordinate system to the image. The inelegance arises from having to deal with inelegant formats and with sloppy application of precise notions. It is in some ways analogous to guys who claim to support EPSG but then ignore axis ordering they explicitly specify using EPSG, that YX thing again. The simplest solution is similar to what was done to live with slacker disregard for EPSG axis ordering: add a checkbox that, in effect, says "don't apply the precise definition of the projection, because we're not being literal: just apply that part of it not involving offsets or scales." That could be labeled "Preserve offsets/scales" or something similar. For guys who work with many images like this, you could put that in a Tools - Option setting, perhaps preserving offsets/scales by default just like the default is to use slacker disregard for EPSG axis ordering. That would avoid having two forms of menu lists applying Favorites in a one-click way, the precise form and the not-quite-literal form.
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