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Jan 26, 2022 at 17:45 comment added Michiel Rademakers @StuSmith: the problem is related to the Mercator Projection. Cartesian calculations are performed on the virtual map cylinder which is "way out in space". Modern Transverse Mercator uses a small cylinder touching the poles, so that the x value is precise, and the y error minimal. The old geographers of the USGS solved the problem by using the Polyconic Projection, which attributes each map its own dedicated little map plane.
Jan 26, 2022 at 17:36 history edited Michiel Rademakers CC BY-SA 4.0
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Jan 26, 2022 at 16:10 comment added Stu Smith Good work. Is there any chance that you can add a graphic or screenshot to your answer that will illustrate what you described? Also, is your problem limited to just EPSG:3857, or all CRSs? Finally, can you draw some conclusions, such as "Here's when to use Cartesian, and here's when to use ellipsoid".
Jan 26, 2022 at 14:29 history edited Michiel Rademakers CC BY-SA 4.0
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Jan 26, 2022 at 14:20 history answered Michiel Rademakers CC BY-SA 4.0