generating randomly oriented non-intersecting cylinders in a unit cell

Hi all,
Im trying to think of a way of generating non-intersecting randomly oriented cylinders within a unit cell volume for micromechanical analysis.
Several research papers suggest a monte-carlo approach was used by displacing cylinders by vectors until the "condition was satisfied" - the condition is never stated.
My initial thought was to treat each cylinder as a line segment, and calculate the minimum distance between line segments, if that distance is > twice the radius of the cylinder, then they should not intersect. However, this also means that co-linear cylinders cannot be closer than twice the radius axially, which is not necessarily a condition i would like to impose.
Anyone have any thoughts on this?

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Would also like help on this!
@Sam Bottum: I do not understand the original question. If the cylinders cannot intersect, 2 parallel cylinders must have a distance of the double radius. Whay is this condition not necessary?
Please open a new question and post, what you exactly need.
The idea may well be that the cylinders have finite length, and for the simplest case of coaxial cylinders, if their spacing along the axis is large enough they will not intersect.

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