Fast 3D Line Segment (float , no thickness) Intersection Detection.

[Freshmaker]

I think I have described the problem imprecisely. The problem is not the function for the intersection of the lines the problem is the quantity of the comparisons to find the knots.

Ahh I see. My mistake.

As for reducing the total number of comparisons made, some sort of broad phase culling scheme could be implemented. If you have already considered this and ruled it out due to the nature of the problem, then I don't really have any other insights to offer.

Otherwise, various spatial partitioning schemes, and possibly sweep and prune, may be worth investigating. I know that, for instance, KD-trees are often associated with good behavior with respect to shooting rays, and so may be a good starting point.