Plane-AABB Intersection.

[Michael J. Aftosmis]

I don't know if I agree with your assessment that actually doing the
clipping and computing the volume is "overkill" in 3D. There are
very effecient algorithms to do it. If you think of your AABB
as a coordinate aligned clipping window you can use a
sutherland-hodgeman algorithm to do it. We do this all the time in 
Cart3D.
(http://www.nas.nasa.gov:~aftosmis/cart3d/). Even doing all the clipping
in software, its not hard to code this so that you can generate 2-10 
million
clipped polyhedra per minute, getting all the volumes, volume 
centroids, face areas, and face centroids along the way.

If you're intent on an approximate method, there are some
"volume-of-fluid" approaches from LLBL that may be of interest to
you. Perhaps one of them will join the discussion.
-Michael


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