Plane-AABB Intersection.

[Josy P. Pullockara]

Hi,

In Adaptive Cartesian 3D(2D) Methods of Computational Fluid Dynamics, it
is of interest to determine volume(area) fractions when a plane(line)
intersects an AABB(Axis Aligned Bounding Box).

Can anyone give pointers to how one can calculate such volume-fractions
for these Cartesian cells WITHOUT the construction of the complex
polytopes as that would be an overkill especially in 3D.

The figure below shows in 2D a line cutting the Cartesian cell. I need
to know Vp/(Vp + Vn) without having multiple cases for different types
of intersection (could be bad in 3D).

Vp: Volume(3D) or Area(2D) on the positive(normal) side of the plane.
Vn: Volume(3D) or Area(2D) on the negative(normal) side of the plane.

If the below figure is not clear(fixed width fonts) see the attached
files cartesian.jpg or cartesian.eps. I hope the attachments are intact
as many mailing lists do not support attachments.

          /
         / Required: Vp/(Vp+Vn)
   +----+-------+
   |Vp /        |
   |  /         |
   | /          |
   |/     Vn    |
   +            |
  /+------------+
 /
/

If that is not known/possible please provide pointers to efficient ways
to approach this problem.

Thank you very much for your kind attention.
-- 
Josy P. Pullockara

Scientist,                             eMail:josy at ctfd.cmmacs.ernet.in
Computational and Theoretical          Phone:+91-80-505 1627
Fluid Dynamics Division,               Fax  :+91-80-522 0952
National Aerospace Laboratories        Res. :+91-80-524 5053
----------------------------------------------------------------------
Please avoid sending me Word or PowerPoint attachments.
See http://www.fsf.org/philosophy/no-word-attachments.html
-------------- next part --------------
A non-text attachment was scrubbed...
Name: cartesian.jpg
Type: image/jpeg
Size: 6369 bytes
Desc: not available
Url : http://compgeom.poly.edu/pipermail/compgeom-announce/attachments/20031003/ed0d184e/cartesian.jpg
-------------- next part --------------
A non-text attachment was scrubbed...
Name: cartesian.eps
Type: application/postscript
Size: 3676 bytes
Desc: not available
Url : http://compgeom.poly.edu/pipermail/compgeom-announce/attachments/20031003/ed0d184e/cartesian.eps