- determining if great circle segments intersect

[Joseph Bussell]

Greetings Group,
   Could someone please offer an efficient algorithm for determining if
two great circle segments intersect?
Specifically, given:
  Segment A (startLatA,startLonA) - (destLatA, destLonA)
    &
  Segment B (startLatB,startLonB) - (destLatB, destLonB)

bool intersects( Segment& A,  Segment& B )
{
    ???
}

All I want to know is if they share a point.  A bonus would be knowing
where that point is.

Cordially,

Joe Bussell
On Time Systems