CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

On 09/04/2012 02:24 PM, babaOroms wrote:
> Hi everybody,
> I have a question before going in depth in my code.
> I have a set of 3D points in the same plane. With the CGAL framework, it's
> impossible to do 3D polygons so I have chosen to do a 3D polyhedron with my
> 3D points. The result is on this picture :
> http://cgal-discuss.949826.n4.nabble.com/file/n4655791/poly1.png
> The construction of this polyhedron is :
>
> template<class HDS>
> void Build_polygon<HDS>::operator()( HDS&  hds )
> {
>      if (!polygon)
>          return;
>
>      // Postcondition: `hds' is a valid polyhedral surface.
>      CGAL::Polyhedron_incremental_builder_3<HDS>  B( hds, true);
>      typedef typename HDS::Vertex   Vertex;
>      typedef typename Vertex::Point Point;
>
>      B.begin_surface( polygon->points().count(), 1, 0); //Surface with
> several points
>
>      foreach (RPoint3d* p, polygon->points()) { //iterates all points
>          B.add_vertex(Point(p->x(), p->y(), p->z()));
>      }
>      B.begin_facet();
>      for (int i = 0; i<  polygon->points().count(); i++)
>          B.add_vertex_to_facet( i);
>      B.end_facet();
>      B.end_surface();
> }
>
> Now I need to have the intersection between this polyhedron and a plane :
> Tree tree(polyhedron()->facets_begin(),polyhedron()->facets_end());
> Point p((FT)0.0, (FT)0.0, z);
> Plane plane(p,normal);
> std::list<Object_and_primitive_id>  intersections;
> tree.all_intersections(plane,std::back_inserter(intersections));
>
> This code crash but if I declare several polyhedron of 3 points instead, the
> intersection works.
If the polyhedron is not triangulated and Tree::Primitive::Datum is a
triangle, then this can not work.

> The result of the intersection I need is a segment.
Note that the intersection might be several segments.

What you need to use is a AABB_tree with 
AABB_polyhedron_segment_primitive as primitive [0].

Then compute all the intersections. You will have a set of points
(and segments if the plane contains a segment of the polygon).

You can sort the points using a dot product with the left-down most
point.

Then you can get the segments using adjacent points, taking care that 
the plane might go through a segment endpoint

[0] 
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/AABB_tree_ref/Class_AABB_polyhedron_segment_primitive.html

Sebastien.

> So to resume, is the polyhedron the best way to have a segment as result ?
> Does exists another class instead ?
>
> Laurent Rineau said to me in other topic that I can do 3D triangulation of
> my polyhedron. The result is not that I am expected (see the following
> picture) :
> http://cgal-discuss.949826.n4.nabble.com/file/n4655791/poly2.png
> The triangulation gives facets at the exterior of my polehydron.
> The good news is that the intersections algorithm works.
>
> Thanks in advance for your advices
>
>
>
> --
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> http://cgal-discuss.949826.n4.nabble.com/Is-it-the-right-way-to-do-that-tp4655791.html
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