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Any idea to calculate the total no overlapping volume of the particle assembly?


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!

Attachment: volume.GIF
Description: volume.GIF

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