CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

Hansjoerg Seybold wrote:
> Hi,
> thanks a lot for the answer.
> Yes, i want to use the results from another program to postprocess
> with a cgal.
> The mesh is only flat 2d, so it is a simple 2d triangulation problem.
> The mesh has a complex geometry of holes, which i want to exclude from
> the calculation of the interpolation.
>
> I could try to load the mesh vertices and create a delaunay triangulation,
> but then i need a way to mark/exclude the hole parts,
> thus i was thinking of using the 2d mesh class with triangulation hierarchy
You cannot use directly Delaunay_triangulation as your input mesh is 
probably not Delaunay.

A solution is to use Triangulation_2 and
Triangulation_data_structure_2 but it may be tricky to
make a copy of your mesh (mimicking the function copy_tds
in CGAL/Triangulation_data_structure_2 is probably the easiest way).

To add a tag into faces see:
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Triangulation_2_ref/Class_Triangulation_face_base_with_info_2.html

Another alternative if remeshing is acceptable for your application is 
to use Mesh_2 with constrained edges and excluded parts (see
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Mesh_2/Chapter_main.html)


S.

> cheers hj
>
>
> On Mon, Jan 24, 2011 at 9:31 AM, Sebastien Loriot (GeometryFactory) 
> <sloriot.ml <http://sloriot.ml>@gmail.com <http://gmail.com>> wrote:
>
>     Hansjoerg Seybold wrote:
>
>         Hello,
>         Hello I would like to calculate interpolated values from
>         vertices on a 2d mesh.
>         My problem is as follows:
>         - I have a mesh given by vertices and constraints (i know the
>         boundary and the partitioning of the space (holes) )
>
>         -  With this information i would like to create a cgal mesh to
>         perform interpolation operations of lets say the velocity field
>         stored in the
>           vertices.
>
>         I saw the cgal interpolation page and the point location page
>         for the triangulation.
>         Is it also possible to use the triangulation hierarchy on a mesh
>         for efficient point location.
>         I need a mesh to determine what is inside and what is outside as
>         the domain has holes or is there a simpler way to perform
>         interpolation/and determining inside/outside like in the mesh case.
>          Thank you very much
>           hj
>
>      From what I understand, you have a surface mesh with hole that you
>     computed (not using CGAL surface mesher) and you want:
>     1) determine whether a point is on your surface
>     2) use CGAL::surface_neighbor_coordinates_3 only on points detected on
>       your surface
>
>     For 1) using AABB_tree and closest_point_and_primitive might help
>     
> (http://www.cgal.org/Manual/latest/doc_html/cgal_manual/AABB_tree/Chapter_main.html#Section_62.6).
>
>     Using the triangulation hierarchy will be complicated as you first need
>     to have a your surface included into a 3D triangulation.
>
>     S.
>
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