Re: [Update REQ 5390]: Hello (spherical convex hulls)

["Stuart Levy" <slevy>]

Rather than thinking about computing real convex hulls on the surface of
a sphere, you might try either of a couple other things:

   - Compute them directly in 3 dimensions, then project the resulting 3-D
	convex hull points back onto the sphere.   Then you needn't think about
	whether some pole appears inside the region, while computing the hull.

   - Or, maybe you can find a convenient *reference point* about which the
	interesting data are distributed.  Maybe you'd know that,
	in practice, all the data points will lie within 90 degrees of that
	reference point.  Do a coordinate transformation to put that point
	at some convenient spot -- say at the origin of a polar-coordinate
	grid on the plane, where the coordinates are
	  (distance from reference point, compass bearing from reference point)
	(That's an equidistant-azimuthal mapping.)
	Then turn those polar coordinates into 2-D rectangular coordinates.
	Take the ordinary 2-D convex hull in that coordinate system, then
	map that back onto the sphere.
	I can make this more explicit if you like.