CGAL users discussion list

[Hansjoerg Seybold <>]

Hi,
that were the two options which i was thinking of.
I dont care too much about the actual mesh structure of the triangulation,
only about the vertices as they store the data for the (later) interpolation,
so also remeshing would be fine for me if i could get the values for the
"new points" somehow (also some kind fo interpolation i suppose).

How would i use the triangulation hirarchy in the mesh_2? for efficient point
location.

Thank you very much for your help
hj

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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