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


Thanks Vaclav:

1. in sphere-sphere interaction, it's sum of volumes of 2 spherical
caps: doable analytically, since interaction stores penetration depth
and you know radii of both spheres.

2. in sphere-box interaction (spheres only partially within the red
volume), do the same. You just take one sphere cap.

3. Disregards spheres that don't overlap with red volume.

In this way, you have Yade collider doing all the hard work (contact
detection) and you just take what it calculates. The most difficult
would be to have colliding boxes that don't create any forces then, but
that's entirely programming question.

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:


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:-|


Attachment: intersect.GIF
Description: intersect.GIF

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