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[Václav Šmilauer <eudoxos@xxxxxxxx>]

I'd sample the whole space (dimensions x,y,z), then calculate
occupied_volume=(#hits/#samples)*sample_volume=(#hits/(x/dx*y/dy*z/dz))*x*y*z. I did this for tetrahedra once, it worked pretty well. It will be probably quite slow if you do it at every timestep, but will work in all cases.

Less generally, you would consider that there is no situation that 3
bodies occupy one point (can be quite reasonable an assumption). The
you'd sum all particle's volumes (constant) and then for each
interaction, subtract once the volume (some geometry) that is doubled by
the overlap. But it will work on unbounded space only, i.e. you'll get
V_the_whole_spherical_arrangement, not V[red]. 

Vaclav


> Hi, all:
>  
> Is there a way to calculate the total volume of the particles,
> excluding the intersection (overlapped) volume of the particles? In
> addition, if an assembly of particle is intersected with a cubic wall,
> is there a method to accurately calcualte the intersection volume? I
> attached a figure which shows my purpose (I need the V[Red]). If
> anyone can provide a way to go will be very much appreciated. I have
> some thoughts, but no idea whether it is easy to implement.
>  
> (1) Currently I have read some materials about Alpha-Shape theory
> originated from molecular dynamics, however, such theory might not be
> able to solve the intersection with cubic wall.
> (2) Another way is to follow CSG (constructive solid geometry), with
> dividing the whole domain into small grids, then count the number of
> those grids, but I am not sure whether this will be very time
> comsuming, since I need to calcualte the volume at each time step, and
> this is still an approximate way, although we can adjust the
> resolution (the size of the grid)
>  
> I hope I have made my problem clear, any kind of suggestion is
> welcome, thank you very much!
>  
>  
>  
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