CGAL users discussion list

[Oleg <>]

I'll try it. Thank you!

Oleg

Monday, March 11, 2013, 19:39, you wrote:
> 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.

---

View this message in context: Re[8]: Triangulation optimization around special points
Sent from the cgal-discuss mailing list archive at Nabble.com.