RE: [Algorithms] Bounding cones.

[Paul Du B. <du...@do...>]

Of the 3 algorithms mentioned in Johnstone, covariance is the
2nd one suggested..

The 3rd (exact) algorithm uses voronoi regions.  It's solving
for the largest empty region in S(3) but of course because of
the geometry that's pretty much the same thing as finding the
smallest enclosing region.

To paraphrase for your case, find the point in S(2) farthest away
from any of your cones; the opposite point is the center of your
bounding cone.  This farthest point will be some vertex in the
voronoi diagram.  Either compute the full thing (tricky) or
find all possible voronoi verts (intersections of bisectors)
and check for distance from your cones.

Since you have O(n^2) bisectors, that's O(n^4) intersections
and O(n^5) circle-circle distance checks.  Hm...maybe it's
better in practice.  If it's not... computing the full diagram
sounds like a fun and interesting problem.

p