Yes. This is a problem inherent with the fact that it is not possible to
approximate a sphere with a single chart without singularities.
On the other hand, the manifold you use to describe the top and bottom part of
the sphere are not continuous, so the triangulation gets confused when you add
new points. For spheres, the best option is to use SphericalManifold.
I’m implementing your changes for the sphere, and running all tests, in order
to fix the bug you encounter in the computation of the area. I think the real
problem is somewhere else, but I don’t have any more ideas…
> On 22 Sep 2016, at 12:51, Praveen C <cprav...@gmail.com> wrote:
> This is a bit old question, and I would like to pose it again. The first post
> is here
> I am using PolarManifold and a 90 deg rotated PolarManifold to cover the
> surface of sphere.
> As I posted in this thread, some cells at the corner have bad shape. I think
> this is related to the fact that the cell has one manifold but its edge has a
> different manifold.
> I could get better cell shapes by attaching the rotated PolarManifold to
> top/bottom faces and its edges and PolarManifold for all other entities. The
> code looks like this
> Point<spacedim> center(0.0, 0.0, 0.0);
> GridGenerator::hyper_sphere(triangulation, center, Radius);
> static const PolarManifold<2,3> sphere;
> static const FunctionManifold<3,3,3> rotate("x;-z;y","x;z;-y");
> static const CompositionManifold<2,3,3,3,2,3> rotated_sphere(sphere,
> triangulation.set_manifold (0, sphere);
> triangulation.set_manifold (1, rotated_sphere);
> for (typename Triangulation<dim,spacedim>::active_cell_iterator
> cell!=triangulation.end(); ++cell)
> const Point<spacedim> p = cell->center();
> if(std::fabs(p) > 0.5 * Radius) // north and south faces
> cell->set_all_manifold_ids(1); // cell and edges
> std::cout << "Setting RotatedPolarManifold\n";
> cell->set_manifold_id(0); // set cell only
> std::cout << "Setting PolarManifold\n";
> I get better cell shapes but the grid lines dont seem to be smooth on the
> side faces. See attached figure. Note that the cells on these side faces have
> different manifold compared to some of their edges. Whereas on top/bottom
> faces, the cells and edges have the same manifold.
> Is this an inherent limitation of trying to use two different manifolds ?
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