Plane-AABB Intersection.

Josy P. Pullockara josy at
Sat Oct 4 12:40:41 PDT 2003

On Sat, 2003-10-04 at 04:00, Michael J. Aftosmis wrote:
> I don't know if I agree with your assessment that actually doing the
> clipping and computing the volume is "overkill" in 3D.

Actually, I follow your work (VKI lectures and others) closely. It is a
pleasure to receive a reply from you. I agree that in practise it may
not be an overkill but I "felt" it "may" be in principle :)

> 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.
> ( 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.

Before embarking on the above method described by you in your
publications I wanted to make sure I was not missing other methods that
can just give me volume and area fractions as the two objects (box and
plane) involved are quite simple! (simple - relatively)

> 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.

Do you or others use exact sub-cell information in practise for
computing flows? Since, researchers like Colella, Berger, LeVeque and
others do not "seem" to use sub-cell information, I thought it was not
required to have sub-cell information. I thought it is a general
practise to approximate the intersection by a line/plane.

Thank you very much for your kind suggestions. I will go ahead and
implement the clipping algorithms. I hope some mathematician will not
come up with a proof "it is impossible to obtain the volume fractions
without computing the polytopes" :P
Josy P. Pullockara <josy at>
National Aerospace Laboratories, INDIA.

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