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Re: Any idea to calculate the total nooverlapping volume of the particle assembly?


> Are the 3 cases enough? Since there is possibility that the 3 spheres
> share one area (volume in 3D) and a cubic corner will also intersect
> with them, then the situation will be very complicated, it is not just
> a sphere cap, I attached a figure (intersection.gif) about this, a
> possible solution might through Alpha-shape theory as described below:
> http://cnx.org/content/m11616/latest/
> However, whether this theory is able to handle the cubic intersection
> is unknown, although possible. So currently I still think the sampling
> method might be the "best" solution:-|
I know it is simplified. But if the overlap size is (much) smaller than
radii of spheres (which is a condition for DEM convergence, I think),
you cannot get 3 spheres sharing 1 point. And if you create the boxes
such that they encompass the red volume while stretching further away a
bit, you will never get sphere being punched by the box edge as you

I bet this method would be quite fast (at least compared to sampling),
while being comparably o even more precise. But that's just feeling; try
out both and you will see.

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