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Re: [compgeom-discuss] Calculating the overlap of volumes.

The simplical polytope intersection algorithms in AIAA 97-0196: "Robust and Efficient Cartesian Mesh Generation for Component-Based Geometry" should also do what you're looking for. This paper is available on-line from the Cart3D website's "pulbications" page. The software is available as well. 
http://people.nas.nasa.gov/~aftosmis/cart3d/
The boolean intersection algorithms used in this work use exact arithmetic, floating-point filtering, and automatic tie-breaking. 

A description of your approach would certainly be of interest. 

-Michael

Hello,

We are trying to calculate the overlap of two volumes, specifically a
tetrahedron with an irregular, non convex, non simply connected volume bounded
by axis aligned quadrilaterals.  We need to calculate this as efficiently as
possible and so-far, we are not using any exact arithmetic.  Our current
approach is susceptible to roundoff errors which lead to large numerical
errors.  We are looking for a way to fix this problem that is as efficient as
possible.

I have two main questions:

1. Are there any books or papers that treat similar or relevant problems?

2. Would a description of our approach be of interest to the computational
geometry community or to the meshing community?  (The application is
image-based meshing)

Thanks,
Valerie



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