If I understand this correctly, I think that in general one cannot specify a geographical direction for a projection coordinate, because (of course) the projection axes do not coincide with longitude and latitude axes. For example, in some grids, the positive x-direction might be both north and east at all points, but why would you say it was east rather than north? In other grids, the local direction will vary from point to point. You really need to differentiate the coordinates in geographical space to find the local direction, don't you?
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