CGAL users discussion list

["mikhail.matrosov" <>]

Hi Amy,

Has something changed on this topic during the last four years? Is there a
do_intersect function for tetrahedra in CGAL now?

-----
Best regards, Mikhail Matrosov


Amy Tabb wrote
> Hi Andre,
> 
> Okay, I had responded to the second part about computing the actual 
> intersection, which you knew about, but not the first part, about 
> detecting the intersection.
> 
> The equivalent of the CGAL `do_intersect' function in 3D is what is 
> usually called the `intersection detection' or `intersection 
> counting/reporting' problem.  There has been a lot of work done on this, 
> with different strategies depending on the complexity of the objects 
> involved.  Luckily, the portion of the Handbook of Discrete and 
> Computational Geometry (a pretty expensive and heavy book) that talks 
> about this subject is provided online: 
> http://www.cs.umd.edu/~mount/Papers/crc-intersect.pdf.  Briefly, there 
> are two options described there.  The bounding box preprocessing option 
> associates a bounding box with every polyhedron (or triangle in the 
> mesh); the bounding boxes are first tested for intersection before more 
> complicated intersection tests on the actual objects within the bounding 
> boxes.  CGAL provides such a scheme in this package:
> 
> http://www.cgal.org/Manual/3.4/doc_html/cgal_manual/Box_intersection_d/Chapter_main.html
> 
> There's an example program that I think might be applicable to your 
> problem, in section 51.5 of the above web page.
> 
> The other option is to detect the intersection of convex polyhedra via a 
> Dobkin-Kirkpatrick decomposition; this is a more complicated option.
> 
> Good luck.
> 
> Best
> Amy





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