CGAL users discussion list

["Laurent Rineau (CGAL/GeometryFactory)" <>]

Le Tuesday 01 September 2015 10:26:56 Bryn Lloyd a écrit :
> Dear CGAL/Mesh_3 users and developers
> 
> I have an implicit domain oracle (derived from Labeled_mesh_domain_3)
> with 1D features.
> When I add features to my domain, make_mesh_3 sometimes does not
> discover my domain at all. Without the features the domain is discovered
> (usually).
> 
> 
> Digging into the code of make_mesh_3 I noticed the strategy to add
> initial points seems very different for a mesh with features
> (init_c3t3_with_features) compared to one without features (init_c3t3).
> This is how I understand it:
> 
> No features:
>   - segments between random points on sphere and "center" are
> intersected with domain - intersection points are added to C3T3
> 
> With features:
>     - features (0D,1D) are sampled and points added to C3T3 with
> "protecting balls"
> 
> Conclusions:
> - So it seems the code for domains with features might oversee (partial)
> regions with no features.
> - Also, I guess, if a point on a feature is considered "outside" by the
> oracle, instead of on a surface patch, regions/domains will be missed.

I agree that this code path is surprising.

The issue is that the points returned by the functor Construct_initial_points 
might be in the set of protecting balls of features, or close to that set.
 
> How to solve this?
> - Would it make sense to run the initialization code to add feature
> points and the add my own internal (dimension=3) points?
> - How should I add these points? Can I add the points via
> C3T3::insert(Point), or should I add them via the
> C3T3::insert(Weighted_point)
> - What weight/ball radius should I use? I don't really want to enforce
> these points, but want to help the oracle discover the domains.


Instead of:

C3t3 c3t3 = CGAL::make_mesh_3, can you undocumented functions:


    C3t3 c3t3;
    CGAL::internal::Mesh_3::init_c3t3_with_features(c3t3,domain,criteria);
  
Then here if you want to insert your own initial points *on the boundary of 
the domain*, you can use:

    typedef C3t3::Triangulation::Point Weighted_point;
    const Weighted_point p(Weighted_point::Point(x, y, z));
    Tr::Vertex_handle vh = c3t3.triangulation().insert(p);
    c3t3.set_dimension(vh, 2);

If the points you insert are on 1D features, the `set_dimension` call should 
specify 1 instead of 2.

Then you can call `refine_mesh_3` as usual:

    CGAL::refine_mesh_3<C3t3>(c3t3, domain, criteria);


I am willing to improve the API of Mesh_3, to allow custom initialization of 
the triangulation. What do you think could be a good API?

-- 
Laurent Rineau, PhD
R&D Engineer at GeometryFactory           http://www.geometryfactory.com/
Release Manager of the CGAL Project       http://www.cgal.org/