Geodesic Midpoints

Finds the midpoint along geodesic paths.

Here "geodesic paths" refers to paths of shortest distance along the surface of a sphere. Midpoints along these paths are equidistant from the endpoints both in straight-line distance and in distance along the surface of the sphere. In the case in which a given pair of points are antipodes, there are an infinite number of geodesics between them, and thus an infinite number of geodesic midpoints. In this case, the midpoint on the equator with longitude closest to 0 is arbitrarily selected.