# Generating randomly oriented non-intersecting cylinders in a unit cell

1. Feb 10, 2014

### tricha122

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. (also, i do not know what the monte carlo approach is)

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?

2. Feb 10, 2014

### FactChecker

Their terminology seems vague. One guess might be that they generate a set of randomly oriented cylinders and then move any of them that intersect using a displacement vector that doesn't change their orientation. "The condition" might mean that they have been moved so that none intersect any more. That would result in "non-intersecting randomly oriented cylinders"

3. Feb 11, 2014

### Stephen Tashi

I think you'll get better advice if you describe exactly what is being analyzed and what the analysis attempts to discover. The terminology of doing something "randomly" doesn't refer to a specific mathematical method. If this has something to do with a physical material, you might get some hints from thinking about how the material is fabricated.

Nowadays, "monte-carlo method" usually refers to running a computer simulation of a random process many times and using statistics from those simulations to answer some question.

4. Feb 11, 2014

### tricha122

This is a theoretical study, and I will be biasing the orientation of the fibers using statistical functions, however the Crux of the problem I have is the condition for rejecting intersecting fibers. If I treat them as line segments, I can reject fibers that come within twice the radius of each other.. But for two collinear Fibres this condition would space them axially apart at the ends by at least twice the radius which is not a necessary condition... In that case they could butt up together. I just can't think of how to define that exception to the condition

5. Feb 11, 2014

### Stephen Tashi

Does your question amount to "What is an efficient algorithm for determining whether two cylinders intersect?" ?

6. Feb 11, 2014

### tricha122

Yes I guess you can say that, keeping in mind ill be generating hundreds of cylinders one at a time and ensuring the new cylinder doesn't intersect with any existing cylinders

7. Feb 11, 2014

### FactChecker

Generating randomly oriented cylinders one at a time and rejecting any that intersect will not give uniform random orientations in the final result. It is not the same as generating them and then moving them if they intersect.

8. Feb 11, 2014

### tricha122

It is the same if you iterate the centroid and maintain the orientation (which I would say is similar to generating a full set of cylinders and relocating them) - but easier for me to process in my head. It still doesn't address the endpoint issue.

9. Feb 11, 2014

### Stephen Tashi

10. Feb 12, 2014

### FactChecker

Agree. Detecting an intersection will probably have to be by brute force, checking each side of the new cylinder and making sure that it does not cross the near sides of any close cylinders.