CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

Hansjoerg Seybold wrote:
> 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.
Define a constrained triangulation with hierarchy
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Triangulation_2/Chapter_main.html#Section_35.10
use refine_Delaunay_mesh:
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Mesh_2_ref/Function_refine_Delaunay_mesh_2.html#Cross_link_anchor_1438
Note that you will need to use CGAL::Delaunay_mesh_face_base_2 as face
in your triangulation:
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Mesh_2_ref/Class_Delaunay_mesh_face_base_2.html#Cross_link_anchor_1429

you can also only use a constrained triangulation to have a "minimal"
mesh.

S.


> 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>
>         <http://sloriot.ml>@gmail.com <http://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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>
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