CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

I repeat my answer: Use exact arithmetic to compute the intersection
of the polyhedra, that way there is no notion of "almost intersecting"
to handle.

Use for example CGAL::Simple_cartesian<CGAL::Lazy_exact_nt<CGAL::Gmpq> >
which is rather fast and exact and this package [1] to then compute the
intersection of polyline segments. Once done you can switch everything
back to double.


Sebastien.

[1] 
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/AABB_tree/Chapter_main.html

On 03/11/2013 01:17 PM, Oleg wrote:
> Hello Sebastien! Thank you for the reference. I may use it in the
> future, but for now I already can compute intersection of polyhedrons,
> and my problem consists rather in the following. When I compute
> intersections of a few polyhedrons, the mesh becomes essentially
> non-uniform (crowded) around the points, where the intersecting
> polylines intersect between themselves, like the one in the first
> message:
> <http://cgal-discuss.949826.n4.nabble.com/file/n4656843/3balls.gif> .
>
> Laurent suggested that splitting the intersecting polylines at the
> points, where they intersect between themselves, thus turning them
> into "corner points" can help. Now I'm wondering what would be the
> best way to achieve that..
>
> Oleg
>
> Monday, March 11, 2013, 13:10, you wrote:
>
>  > Since snap rounding in 3D is not easy, I think you should compute the
>  > intersecting polyline using exact arithmetic and then simplify the
> output.
>  > For the computation of intersecting polylines, you might want to
>  > have a look at the non-documented function in
>  > CGAL/intersection_of_Polyhedra_3.h
>
>  > template <typename Polyhedron, typename OutputIterator>
>  > OutputIterator
>  > intersection_Polyhedron_3_Polyhedron_3(const Polyhedron& P, const
>  > Polyhedron& Q, OutputIterator out)
>
>  > where out expects object of type std::vector<typename Kernel::Point_3>
>  > representing a polyline
>
>  > Sebastien.
>
>
>  > On 03/07/2013 11:47 AM, Oleg wrote:
>  >> Yes, more general shapes. The final goal is to make uniform meshes for
>  >> bodies composed of general shapes with sharp boundaries between them.
>  >>
>  >> Oleg
>  >>
>  >> Thursday, March 7, 2013, 17:23, you wrote:
>  >> > What is the final goal? Only mesh 3 spheres? mesh n spheres? or more
>  >> > general shapes?
>  >>
>  >> > I ask the question because the answer then varies.
>  >>
>  >> > Sebastien.
>  >>
>  >> > On 03/07/2013 11:16 AM, Oleg wrote:
>  >> >> Thursday, March 7, 2013, 16:53, you wrote:
>  >> >> > Le jeudi 07 mars 2013 00:00:11 Oleg a écrit :
>  >> >> >> Hello everyone! I have a question regarding triangulation
>  >> >> optimization. I
>  >> >> >> make a mesh for 3 balls intersection with 3 1D features. The
> mesh is
>  >> >> uniform
>  >> >> >> everywhere except 2 points where the 3 boundaries intersect:
>  >> >> >>
> <http://cgal-discuss.949826.n4.nabble.com/file/n4656843/3balls.gif>
>  >> >> >> These points don't seem to represent any problem for a manual
>  >> meshing,
>  >> >> >> because the boundaries intersect at large angles. Is there any
> easy
>  >> >> way to
>  >> >> >> optimize the mesh around these points to avoid the unnecessary
>  >> >> crowding? Any
>  >> >> >> ideas will be greatly appreciated.
>  >> >>
>  >> >> > In your example, I assume that you have computed the
> intersections of
>  >> >> spheres
>  >> >> > and set them as 1D features of the domain. When 1D-features
>  >> >> intersect, you
>  >> >> > need to split them first at the intersection points. That will
>  >> make the
>  >> >> > special intersections points as "corner points" of the domain, and
>  >> >> fix the
>  >> >> > crowding you see in the result.
>  >> >>
>  >> >> You're right, that's what I did. I'll try what you recommend,
> thanks!
>  >> >> Just another quick question - what would be the best way to find
>  >> >> intersection points of two polylines? Keeping in mind that the
>  >> >> polylines may not intersect in one exact point but rather pass by
>  >> >> each other at a small distance..?
>  >> >>
>  >> >> Oleg
>  >> >>
>  >> >>
>  >> >>
>  >>
> ------------------------------------------------------------------------
>  >> >> View this message in context: Re[2]: Triangulation optimization
> around
>  >> >> special points
>  >> >>
>  >>
> <http://cgal-discuss.949826.n4.nabble.com/Triangulation-optimization-around-special-points-tp4656843p4656846.html>
>
>  >>
>  >> >> Sent from the cgal-discuss mailing list archive
>  >> >> <http://cgal-discuss.949826.n4.nabble.com/> at Nabble.com.
>  >>
>  >>
>  >>
>  >>
> ------------------------------------------------------------------------
>  >> View this message in context: Re[4]: Triangulation optimization around
>  >> special points
>  >>
> <http://cgal-discuss.949826.n4.nabble.com/Triangulation-optimization-around-special-points-tp4656843p4656848.html>
>
>  >> Sent from the cgal-discuss mailing list archive
>  >> <http://cgal-discuss.949826.n4.nabble.com/> at Nabble.com.
>
>
>
> ------------------------------------------------------------------------
> View this message in context: Re[6]: Triangulation optimization around
> special points
> <http://cgal-discuss.949826.n4.nabble.com/Triangulation-optimization-around-special-points-tp4656843p4656892.html>
> Sent from the cgal-discuss mailing list archive
> <http://cgal-discuss.949826.n4.nabble.com/> at Nabble.com.