[Algorithms] Checking normals against an halfplane

[Pierre T. <p.t...@wa...>]

Ok, another little algorithm I'm fighting with.

Say I have a set of N normals, centered at the origin, in random directions.
The goal is to:
1) check all of them lie on the same side of a plane passing through the
origin
2) find such a plane

That plane is unknown when the routine is called. I must determine whether
such a plane can exist (this is not always the case). Needless to say, it
must be done in a quick way.


I don't expect a light-speed algorithm to exist, but I know you people
sometimes come up with amazing solutions. Hence, worth trying.

Pierre