Convex hull of (longitude, latitude)-points on the surface of a sphere

Question

Standard convex hull algorithms will not work with (longitude, latitude)-points, because standard algorithms assume you want the hull of a set of Cartesian points. Latitude-long

Answer 1

This question has been answered a while ago, but I would like to sum up the results of my research.

The spherical convex hull is basically defined only for non-antipodal points. Supposing all the points are on the same hemisphere, you can compute their convex hull in two main ways:

1. Project the points to a plane using gnomonic/central projection and apply a planar convex hull algorithm. See Lin-Lin Chen, T. C. Woo, "Computational Geometry on the Sphere With Application to Automated Machining" (1992). If the points are on a known hemisphere, you can hard-code on which plane to project the points unto.
2. Adapt planar convex hull algorithms to the sphere. See C. Grima and A. Marquez, "Computational Geometry on Surfaces: Performing Computational Geometry on the Cylinder, the Sphere, the Torus, and the Cone", Springer (2002). This reference seems to give a similar method to the abstract referenced by Li-aung Yip above.

For reference, in Python I am working on an implementation of my own, which currently works only for points on the Northern hemisphere.

See also this question on Math Overflow.