CGAL 3D conversions.

[luca-heltai]

@fdrmrc, I tried implementing deal.II cells to cgal polyhedron translations, and deal.II two-dimensional triangulation to

It seems to work for single cells. Now I'd like to use the intersections, but I'm not able (yet) to construct a valid triangulation from a polyhedron to feed to the CGAL::Polygon_mesh_processing::corefine_and_compute_boolean_operations. I'll look into it later on. Do you have an idea on how to do that?

[fdrmrc]

Looking at the docs, the issue should be that you're passing a C3T3 instead of a CGAL::surface_mesh. tm1,tm2 have to be surfaces (https://doc.cgal.org/latest/Polygon_mesh_processing/group__PMP__corefinement__grp.html#ga70346bbfd568de05220767cdcbcd6f68).

[fdrmrc]

The only way I can think of now is to add a wrapper for surfaces, as we can't use HDS (https://doc.cgal.org/latest/Surface_mesh/classCGAL_1_1Surface__mesh.html)

  template <typename CGALPointType, int dim, int spacedim>
  void
  to_cgal(const typename dealii::Triangulation<dim, spacedim> &tria,
          const dealii::Mapping<dim, spacedim> &               mapping,
          CGAL::Surface_mesh<CGALPointType> &                                     surface_mesh);

[luca-heltai]

would this allow us to use intersection and refinement algorithms?

[luca-heltai]

Also, I was trying to support tetrahedral mesh generation, that's why I was using the C3T3 meshes.

[fdrmrc]

would this allow us to use intersection and refinement algorithms?

In all the examples they're using surfaces, so yes, that would work. But it seems too strange that Polyhedrons are not supported.

[luca-heltai]

Once we have a surface mesh, it should be easy enough to get a tetra mesh.

[fdrmrc]

I've added a first wrapper for Surface_mesh<CGALPointType>, tested only with cubes. The previously commented test now compiles, but it's still not robust, (see next comment)

[fdrmrc]

Tests still don't work if you perform the second (commented) rotation.

fsi-suite/gtests/cgal_triangulation.cc

Lines 182 to 183 in 45d1d85

	GridTools::rotate(numbers::PI_4, 0, tria);
	// GridTools::rotate(numbers::PI_4, 1, tria);

The thrown exception is

[ctest] C++ exception with description "CGAL ERROR: assertion violation!
[ctest] Expr: (size_ == 2 && (v == first || v == second) ) || v==first
[ctest] File: /usr/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersection_impl.h
[ctest] Line: 131" thrown in the test body.

That's only related to machine precision. If you use exact arithmetic, everything works fine.

Is there something more to do in this PR? @luca-heltai