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I have a feeling that spherical geometry can make this really easy.
Below are some resources as to how you can do this:
https://www.movable-type.co.uk/scripts/latlong.html
https://www.movable-type.co.uk/scripts/latlong-vectors.html#intersection
Algorithm considerations
When looking at the plate-carree projection, and most projections really, there are two major discontinuities. One is the seam at the antimeridian, and the other is the zero-to-180 stretching at each pole.
Antimeridian cutting is itself relatively straightforward, but we would also want to somehow fix the polar issue. Maybe with a dynamic resampling at different angles around the same point? Points within some radius of the pole could also receive this treatment.
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