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How translate a polygon on Earth?

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Ok, how to translate polygon on sphere(or better Earth ellipsoid) that polygon proportions(sizes, corners angles) stay the same as before translation?

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For a sphere, the answer is to use the verb "rotate" (around the center of the sphere) instead of "translate". For an ellipsoid like Earth, in general you can only rotate around the North-South axis without deforming anything.

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