antarctica - Intersection algorithm that correctly handles 180° meridian and poles?

Is there a well known intersection algorithm that correctly handles 180 meridian and poles?

For example, let's say we have a list of latitude and longitude values that represent Antarctica. Let's say we also have a simple polygon that represents an airplane. We want to know if the airplane is over Antarctica.

Generic 2D polygon intersection does not work in this case if you simply use latitude for y and longitude for x, because the flat coordinate system will have edges at -180 and 180 longitude, and -90 and 90 latitude. Antarctica will go off the page on three of the edges.