NavList:

Robin -

I did not get all details during the discussions amongst the experts with prior knowledge re: vectorial methods yielding a direct method. So, this might be a repetition but I would like to fully understand the problem. The issue is this I think:

Imagine Earth as a sphere with radius 1 located at (0,0,0) in space. The two circles surrounding GP1/GP2 and determined by Hc1 / Hc2 define two planes in space which intersect in a straight line. Find on this straight line the points whose distance from (0,0,0) is 1, the radius of Earth. A solution exists only if the minimum distance of the points on that line is < 1.

Could you please confirm that was is indeed the problem discussed. If it is than it sounds conceptually "straight forward" as well. The challenge lies in some fancy - and rather tedious - algebraic footwork like rotations and solutions of n equations with m variables. I could to that with MAPLE but the stereographic projection you discussed with much detail and clarity offers obviously a much cleaner and simpler solution.

Regards
H