Hi Thomas, hi Luca,
I would like to re-generate the ellipsoidal with deal.ii 9.0.1 but the
interfaces of the SphericalManifold class have changed in some release. So
I tried to re-implement the following methods
virtual std::unique_ptr<Manifold<dim,spacedim>> clone() const override;
virtual Point<spacedim> get_intermediate_point(
const Point<spacedim> &p1,
const Point<spacedim> &p2,
const double weight) const override;
virtual void get_new_points(
const ArrayView<const Point<spacedim>> &surrounding_points,
const Table<2,double> &weights,
ArrayView<Point<spacedim>> new_points) const
override;
virtual Point<spacedim> get_new_point(
const ArrayView<const Point<spacedim>> &vertices,
const ArrayView<const double> &weights) const override
;
and two additional methods for the mapping from ellipsoid to sphere:
/*
* map a (cartesian) point on a sphere to a point on an ellipsoid
*/
Point<spacedim> push_forward(const Point<spacedim> &space_point)
const;
/*
* map a (cartesian) point on an ellipsoid to a point on a sphere
*/
Point<spacedim> pull_back(const Point<spacedim> &space_point) const
;
Somehow, my implementation does not work well and the mesh is distorted
especially for points on the y- and z-axis. I am actually using the
ellipsoid as test case and would like generate a mesh consisting of a
sphere with (spherical harmonic) boundary topography.
Does anyone know what is going wrong here and the code by Thomas may used
in a newer version of deal.ii?
Best wishes,
Sebastian
Am Dienstag, 9. August 2016 19:04:07 UTC+2 schrieb thomas stephens:
>
> Luca, Thank you for the help.
>
> I now have a working Ellipsoid class:
>
> template <int dim,int spacedim>
> class Ellipsoid: public SphericalManifold<dim,spacedim>
> {
> public:
>
> Ellipsoid(double,double,double);
>
> Point<spacedim> pull_back(const Point<spacedim> &space_point) const;
>
> Point<spacedim> push_forward(const Point<spacedim> &chart_point) const;
>
> Point<spacedim> get_new_point(const Quadrature<spacedim> &quad) const;
>
> Point<spacedim> grid_transform(const Point<spacedim> &X);
>
> private:
> double a,b,c;
> double max_axis;
> const Point<spacedim> center;
>
> Point<dim> ellipsoid_pull_back(const Point<spacedim> &space_point) const;
>
> Point<spacedim> ellipsoid_push_forward(const Point<dim> &chart_point)
> const;
>
> };
>
>
> with member functions:
>
> template <int dim, int spacedim>
> Ellipsoid<dim,spacedim>::Ellipsoid(double a, double b, double c) :
> SphericalManifold<dim,spacedim>(center), a(a), b(b),c(c), center(0,0,0)
> {
> max_axis = std::max(std::max(a,b),c);
> }
>
>
> template <int dim,int spacedim>
> Point<spacedim> Ellipsoid<dim,spacedim>::pull_back(const Point<spacedim>
> &space_point) const
> {
> Point<dim> chart_point = ellipsoid_pull_back(space_point);
> Point<spacedim> p;
> p[0] = -1; // dummy radius to match return of
> SphericalManifold::pull_back()
> p[1] = chart_point[0];
> p[2] = chart_point[1];
>
> return p;
> }
>
>
> template <int dim,int spacedim>
> Point<spacedim> Ellipsoid<dim,spacedim>::push_forward(const
> Point<spacedim> &chart_point) const
> {
>
> Point<dim> p; //
> p[0] = chart_point[1];
> p[1] = chart_point[2];
>
> Point<spacedim> space_point = ellipsoid_push_forward(p);
> return space_point;
>
> }
>
>
> template <int dim,int spacedim>
> Point<spacedim> Ellipsoid<dim,spacedim>::get_new_point(const
> Quadrature<spacedim> &quad) const
> {
> double u,v,w;
> std::vector< Point<spacedim> > space_points;
> for (unsigned int i=0; i<quad.size(); ++i)
> {
> u = quad.point(i)[0]/a;
> v = quad.point(i)[1]/b;
> w = quad.point(i)[2]/c;
> space_points.push_back(Point<spacedim>(u,v,w));
> }
>
> Quadrature<spacedim> spherical_quad = Quadrature<spacedim>(space_points,
> quad.get_weights());
>
> Point<spacedim> p =
> SphericalManifold<dim,spacedim>::get_new_point(spherical_quad);
> double x,y,z;
> x = a*p[0];
> y = b*p[1];
> z = c*p[2];
>
> Point<spacedim> new_point = Point<spacedim>(x,y,z);
> return new_point;
> }
>
> template <int dim,int spacedim>
> Point<dim> Ellipsoid<dim,spacedim>::ellipsoid_pull_back(const
> Point<spacedim> &space_point) const
> {
> double x,y,z, u,v,w;
>
> // get point on ellipsoid
> x = space_point[0];
> y = space_point[1];
> z = space_point[2];
>
> std::cout << "using a,b,c: " << std::endl;
> std::cout << a << " " << b << " " << c << std::endl;
> std::cout << "from pull_back: " << std::endl;
> std::cout << "space_point: " << std::endl;
> std::cout << x << " " << y << " " << z << std::endl;
>
> // map ellipsoid point onto sphere
> u = x/a;
> v = y/b;
> w = z/c;
>
> std::cout << "pulls back to : " << std::endl;
> std::cout << u << " " << v << " " << w << std::endl;
> std::cout << "on sphere." << std::endl;
>
> Point<spacedim> p(u,v,w);
>
> // use reference_sphere's pull_back function
> Point<spacedim> q = pull_back(p);
> Point<dim> chart_point;
>
>
> std::cout << "sphere pull_back: " << std::endl;
> std::cout << q[0] << " " << q[1] << " " << q[2] << std::endl;
> std::cout << "r theta phi" << std::endl;
> std::cout << "..........." << std::endl;
>
> chart_point[0] = q[1];
> chart_point[1] = q[2];
>
> // return (theta,phi) in the chart domain
> return chart_point;
>
> }
>
> template <int dim,int spacedim>
> Point<spacedim> Ellipsoid<dim,spacedim>::ellipsoid_push_forward(const
> Point<dim> &chart_point) const
> {
> double theta,phi, x,y,z;
>
> phi = chart_point[0];
> theta = chart_point[1];
>
>
> Point<spacedim> p(max_axis,theta,phi);
> // map theta,phi in chart domain onto reference_sphere with radius
> max_axis
> Point<spacedim> X = push_forward(p);
>
> // map point on sphere onto ellipsoid
>
> x = a*X[0];
> y = b*X[1];
> z = c*X[2];
>
> Point<spacedim> space_point(x,y,z);
>
> // return point on ellipsoid
> return space_point;
> }
>
> template<int dim, int spacedim>
> Point<spacedim> Ellipsoid<dim,spacedim>::grid_transform(const
> Point<spacedim> &X)
> {
> // transform points X from sphere onto ellipsoid
> double x,y,z;
>
> x = a*X(0);
> y = b*X(1);
> z = c*X(2);
>
> return Point<spacedim>(x,y,z);
> }
>
> along with the non-member function grid_transform() (which should not be
> necessary, but I cannot seem to bind the member function
> Ellipsoid<dim,spacedim>::grid_transform() to an instance of Ellipsoid and a
> dummy variable, as is done in step-53)
>
> Point<3> grid_transform(const Point<3> &X)
> {
> // transform points X from sphere onto ellipsoid
> double x,y,z;
> double a = 1; double b = 3; double c = 5;
> x = a*X(0);
> y = b*X(1);
> z = c*X(2);
>
> return Point<3>(x,y,z);
> }
>
>
>
> At any rate, this can all be scripted using the following:
>
> void assemble_mesh_and_manifold()
> {
>
> const int dim = 2;
> const int spacedim = 3;
>
> double a,b,c;
> a = 1; b=3; c=5;
>
> Ellipsoid<dim,spacedim> ellipsoid(a,b,c);
>
> Triangulation<dim,spacedim> tria;
>
> // generate coarse spherical mesh
> GridGenerator::hyper_sphere (tria, Point<spacedim>(0.0,0.0,0.0), 1.0);
> for (Triangulation<dim,spacedim>::active_cell_iterator
> cell=tria.begin_active(); cell!=tria.end(); ++cell)
> cell->set_all_manifold_ids(0);
>
> print_mesh_info(tria, "spherical_mesh.vtk");
>
> GridTools::transform(&grid_transform, tria);
> //
>
> //GridTools::transform(std_cxx11::bind(&Ellipsoid<dim,spacedim>::grid_transform,std_cxx11::cref(ellipsoid),std_cxx11::_1),
>
> tria); // error when trying to bind to member function in same way as
> step-53
>
> tria.set_manifold(0,ellipsoid);
>
> tria.refine_global(3);
>
> print_mesh_info(tria, "ellipsoidal_mesh.vtk");
>
> }
>
>
> I have attached the entire .cc file, and the output from the above code
> looks great:
>
>
> <https://lh3.googleusercontent.com/-bwkb9gP-gMw/V6oMwm7nLLI/AAAAAAAAFSU/dWS9t96oEQIsqQPjWEpWfQbPmEMoQBxAwCLcB/s1600/refined_ellipsoidal_mesh0000.png>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> On Tuesday, August 9, 2016 at 3:56:58 AM UTC-4, Luca Heltai wrote:
>>
>> There is nothing wrong with what you are doing.
>>
>> The problem is in the nature of your Manifold, since it contains 3
>> singular points. The first is the center of the ellipsoid, while the second
>> and third are the north and south poles.
>>
>> Try attaching a SphericalManifold to your deformed grid, and see if you
>> like the result. If you do, then hack the SphericalManifold. I don’t know
>> what version of deal.II you are using. Assuming you are not using the
>> latest dev, if you open up the definition of spherical manifold in
>> manifold_lib.cc, you’ll see that SphericalManifold::get_new_point does
>> something special in the case spacedim == 3, i.e., SphericalManifold is not
>> *really* a ChartManifold in 3d.
>>
>> In this case the ChartManifold mechanism cannot be used for the reason
>> above.
>>
>> A quick explanation why things are not working:
>>
>> Consider the top cell, and let us assume for a second that the north pole
>> (z=z_max) is in the center of the cell, and that the four vertices of your
>> ellipsoid lie at the same z (z=h < z_max). When you transform using
>> ChartManifold, the z gets mapped to the angle phi, and every point of the
>> cell will have the same angle phi, and different theta. If you take the
>> average of the four points in the chart manifold coordinates, you’ll see
>> that the average will have an average theta (which is ok), but it will also
>> have the same phi of the four surrounding points… in other words, the
>> average will not be in the middle of the four points (that should be the
>> north pole: a singularity of your mapping). It will lye on the same
>> latitude of the other four points.
>>
>> ChartManifold is doing exactly what you asked it to do, but in the case
>> of maps with singularities, you should not use ChartManifold…
>>
>> My suggestion is to derive EllipsoidManifold from SphericalManifold, and
>> then overload directly get_new_point, by calling internally get_new_point
>> of spherical manifold, and then projecting the result to the ellipsoid...
>>
>> Best,
>>
>> Luca.
>>
>> > On 09 Aug 2016, at 24:13, thomas stephens <[email protected]> wrote:
>> >
>> >
>> >
>> > I am trying to obtain the mesh for a codimension-1 ellipsoid and attach
>> an ellipsoidal manifold to it in order to refine the mesh. My strategy is
>> failing and I have a few questions.
>> >
>> > My strategy:
>> > some definitions:
>> > dim=2; spacedim=3; chartdim=spacedim-1; a=1; b=2;c=3;
>> >
>> > Set up codimension-1 Triangulation:
>> >
>> > Triangulation<dim,spacedim> tria;
>> >
>> >
>> > Use GridGenerator::hyper_sphere() to obtain a codimension 1 mesh:
>> >
>> >
>> > GridGenerator::hyper_sphere (tria, Point<spacedim>(0.0,0.0,0.0), 1.0);
>> >
>> > Use GridTools::transform() to map triangulation of sphere onto
>> triangulation of ellipsoid (I have a question about this, see below).
>> Here, grid_transform has signature Point<spacedim> grid_transform(const
>> Point<spacedim> X)
>> >
>> > GridTools::transform(&grid_transform, tria);
>> >
>> > Next, subclass ChartManifold<dim,spacedim,chartdim> in order to obtain
>> a push_forward() and a pull_back() function for my parametric ellipsoidal
>> manifold description. Then attach that manifold to the triangulation:
>> >
>> > Ellipsoid<dim,spacedim,chartdim> ellipsoid(a,b,c);
>> > tria.set_manifold(0,ellipsoid);
>> >
>> > Now refine the triangulation in order to see a refined ellipsoidal
>> mesh:
>> >
>> > tria.refine_global(1);
>> >
>> > The Result: Complete garbage! I also don't really have an idea why
>> this is not working - I've checked the dimensions on my push_forward() and
>> pull_back() functions, I think that I'm setting the periodicity correctly
>> in my ChartManifold superclass, and I've also checked that my simple math
>> is okay. Let me know what other information would be useful. Below is
>> the refined mesh for a=b=c=1. This should just be a sphere.
>> >
>> >
>> >
>> >
>> > The code:
>> > template <int dim,int spacedim,int chartdim=spacedim-1>
>> > class Ellipsoid: public ChartManifold<dim,spacedim,chartdim>
>> > {
>> > public:
>> >
>> > Ellipsoid(double,double,double);
>> >
>> > Point<chartdim> pull_back(const Point<spacedim> &space_point) const;
>> >
>> > Point<spacedim> push_forward(const Point<chartdim> &chart_point)
>> const;
>> >
>> > private:
>> > double a,b,c;
>> > double max_axis;
>> > const Point<spacedim> center;
>> > SphericalManifold<dim,spacedim> reference_sphere;
>> >
>> > };
>> >
>> >
>> > template <int dim, int spacedim, int chartdim>
>> > Ellipsoid<dim,spacedim,chartdim>::Ellipsoid(double a, double b, double
>> c): ChartManifold<dim,spacedim,chartdim>(Point<chartdim>(2*numbers::PI,
>> 2*numbers::PI)), a(a), b(b),c(c), center(0,0,0), reference_sphere(center)
>>
>> > {
>> > max_axis = std::max(std::max(a,b),c);
>> > }
>> > template <int dim,int spacedim, int chartdim>
>> > Point<chartdim> Ellipsoid<dim,spacedim,chartdim>::pull_back(const
>> Point<spacedim> &space_point) const
>> > {
>> > double x,y,z, u,v,w;
>> >
>> > // get point on ellipsoid
>> > x = space_point[0];
>> > y = space_point[1];
>> > z = space_point[2];
>> >
>> > std::cout << "using a,b,c: " << std::endl;
>> > std::cout << a << " " << b << " " << c << std::endl;
>> > std::cout << "from pull_back: " << std::endl;
>> > std::cout << "space_point: " << std::endl;
>> > std::cout << x << " " << y << " " << z << std::endl;
>> >
>> > // map ellipsoid point onto sphere
>> > u = x/a;
>> > v = y/b;
>> > w = z/c;
>> >
>> > std::cout << "pulls back to : " << std::endl;
>> > std::cout << u << " " << v << " " << w << std::endl;
>> > std::cout << "on sphere." << std::endl;
>> >
>> > Point<spacedim> p(u,v,w);
>> >
>> > // use reference_sphere's pull_back function
>> > Point<spacedim> q = reference_sphere.pull_back(p);
>> > Point<chartdim> chart_point;
>> >
>> >
>> > std::cout << "sphere pull_back: " << std::endl;
>> > std::cout << q[0] << " " << q[1] << " " << q[2] << std::endl;
>> > std::cout << "r theta phi" << std::endl;
>> > std::cout << "..........." << std::endl;
>> >
>> > chart_point[0] = q[1];
>> > chart_point[1] = q[2];
>> >
>> > // return (theta,phi) in the chart domain
>> > return chart_point;
>> >
>> > }
>> > template <int dim,int spacedim, int chartdim>
>> > Point<spacedim> Ellipsoid<dim,spacedim,chartdim>::push_forward(const
>> Point<chartdim> &chart_point) const
>> > {
>> > double theta,phi, x,y,z;
>> >
>> > phi = chart_point[0];
>> > theta = chart_point[1];
>> >
>> >
>> > Point<spacedim> p(max_axis,theta,phi);
>> > // map theta,phi in chart domain onto reference_sphere with radius
>> max_axis
>> > Point<spacedim> X = reference_sphere.push_forward(p);
>> >
>> > // map point on sphere onto ellipsoid
>> >
>> > x = a*X[0];
>> > y = b*X[1];
>> > z = c*X[2];
>> >
>> > Point<spacedim> space_point(x,y,z);
>> >
>> > // return point on ellipsoid
>> > return space_point;
>> > }
>> >
>> >
>> > Point<3> grid_transform (const Point<3> &X)
>> > {
>> > // transform points on sphere onto ellipsoid
>> > double a,b,c;
>> > a = 1.0; b = 1.0; c = 1.0;
>> >
>> > double x,y,z;
>> > x = a*X(0);
>> > y = b*X(1);
>> > z = c*X(2);
>> >
>> > return Point<3>(x,y,z);
>> > }
>> >
>> > void assemble_mesh_and_manifold()
>> > {
>> >
>> > const int dim = 2;
>> > const int spacedim = 3;
>> > const int chartdim = 2;
>> >
>> > double a,b,c;
>> > a = 1; b=1; c=1;
>> >
>> > Ellipsoid<dim,spacedim,chartdim> ellipsoid(a,b,c);
>> >
>> > Triangulation<dim,spacedim> tria;
>> >
>> > // generate coarse spherical mesh
>> > GridGenerator::hyper_sphere (tria, Point<spacedim>(0.0,0.0,0.0),
>> 1.0);
>> > for (Triangulation<dim,spacedim>::active_cell_iterator
>> cell=tria.begin_active(); cell!=tria.end(); ++cell)
>> > cell->set_all_manifold_ids(0);
>> >
>> > print_mesh_info(tria, "spherical_mesh.vtk");
>> >
>> > GridTools::transform(&grid_transform, tria);
>> >
>> > tria.set_manifold(0,ellipsoid);
>> >
>> > tria.refine_global(1);
>> >
>> > print_mesh_info(tria, "ellipsoidal_mesh.vtk");
>> >
>> > }
>> >
>> > int main ()
>> > {
>> > assemble_mesh_and_manifold();
>> > }
>> >
>> > Attached is the .vtk of my refined ellipsoidal mesh and the .cc file
>> that generates this output (mostly reproduced above.
>> >
>> > Thank you,
>> > Tom
>> >
>> > --
>> > The deal.II project is located at http://www.dealii.org/
>> > For mailing list/forum options, see
>> https://groups.google.com/d/forum/dealii?hl=en
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>> > For more options, visit https://groups.google.com/d/optout.
>> > <sphere_to_ellipsoid.cc><ellipsoidal_mesh.vtk>
>>
>>
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#include <deal.II/grid/tria.h>
#include <deal.II/grid/grid_out.h>
#include <deal.II/grid/manifold.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/manifold_lib.h>
#include <deal.II/grid/grid_tools.h>
#include <boost/math/special_functions.hpp>
#include <iostream>
#include <fstream>
#include <functional>
namespace EllipsoidalTest
{
using namespace dealii;
template<int dim,int spacedim>
class EllipsoidalManifold: public SphericalManifold<dim,spacedim>
{
public:
EllipsoidalManifold();
virtual std::unique_ptr<Manifold<dim,spacedim>> clone() const override;
virtual Point<spacedim> get_intermediate_point(
const Point<spacedim> &p1,
const Point<spacedim> &p2,
const double weight) const override;
virtual void get_new_points(
const ArrayView<const Point<spacedim>> &surrounding_points,
const Table<2,double> &weights,
ArrayView<Point<spacedim>> new_points) const override;
virtual Point<spacedim> get_new_point(
const ArrayView<const Point<spacedim>> &vertices,
const ArrayView<const double> &weights) const override;
/*
* mapping a (cartesian) point on a sphere to an ellipsoid
*/
Point<spacedim> push_forward(const Point<spacedim> &space_point) const;
private:
/*
* mapping a (cartesian) point on an ellipsoid to a sphere
*/
Point<spacedim> pull_back(const Point<spacedim> &space_point) const;
const double a = 1.0;
const double b = 2.0;
const double c = 3.0;
double max_axis;
const Point<spacedim> center;
};
template<int dim, int spacedim>
EllipsoidalManifold<dim,spacedim>::EllipsoidalManifold
()
:
SphericalManifold<dim,spacedim>(center),
center()
{
max_axis = std::max(std::max(a,b),c);
}
template <int dim, int spacedim>
std::unique_ptr<Manifold<dim, spacedim>>
EllipsoidalManifold<dim,spacedim>::clone() const
{
return std::make_unique<EllipsoidalManifold<dim,spacedim>>();
}
template <int dim, int spacedim>
Point<spacedim> EllipsoidalManifold<dim,spacedim>::get_intermediate_point
(const Point<spacedim> &p1,
const Point<spacedim> &p2,
const double weight) const
{
const Point<spacedim> p1_on_sphere = pull_back(p1);
const Point<spacedim> p2_on_sphere = pull_back(p2);
const Point<spacedim> intermediate_point_on_sphere
= SphericalManifold<dim,spacedim>::get_intermediate_point
(p1_on_sphere,
p2_on_sphere,
weight);
return push_forward(intermediate_point_on_sphere);
}
template <int dim, int spacedim>
void EllipsoidalManifold<dim,spacedim>::get_new_points
(const ArrayView<const Point<spacedim>> &surrounding_points,
const Table<2,double> &weights,
ArrayView<Point<spacedim>> new_points) const
{
std::vector<Point<spacedim>> surrounding_points_on_sphere;
for (typename ArrayView<const Point<spacedim>>::const_iterator
it = surrounding_points.cbegin();
it != surrounding_points.cend(); ++it)
{
const Point<spacedim> surrounding_point_on_sphere
= pull_back(*it);
surrounding_points_on_sphere.push_back(surrounding_point_on_sphere);
}
AssertDimension(surrounding_points_on_sphere.size(),
surrounding_points.size());
SphericalManifold<dim,spacedim>::get_new_points(
make_array_view(surrounding_points_on_sphere,
0,
surrounding_points_on_sphere.size()),
weights,
new_points);
for (unsigned int i=0; i<new_points.size(); ++i)
new_points[i] = push_forward(new_points[i]);
}
template <int dim, int spacedim>
Point<spacedim> EllipsoidalManifold<dim,spacedim>::get_new_point
(const ArrayView<const Point<spacedim>> &vertices,
const ArrayView<const double> &weights) const
{
std::vector<Point<spacedim>> vertices_on_sphere;
typename ArrayView<const Point<spacedim>>::const_iterator
it = vertices.cbegin(),
endit = vertices.cend();
for (; it!=endit; ++it)
{
const Point<spacedim> vertex_on_sphere = pull_back(*it);
vertices_on_sphere.push_back(vertex_on_sphere);
}
AssertDimension(vertices_on_sphere.size(),vertices.size());
const Point<spacedim> new_point_on_sphere
= SphericalManifold<dim,spacedim>::get_new_point(
make_array_view(vertices_on_sphere,
0,
vertices_on_sphere.size()),
weights);
return push_forward(new_point_on_sphere);
}
template<>
Point<3> EllipsoidalManifold<3,3>::pull_back
(const Point<3> &point_ellipsoid) const
{
const Point<3> point_on_sphere(point_ellipsoid(0) / a,
point_ellipsoid(1) / b,
point_ellipsoid(2) / c);
return point_on_sphere;
}
template<>
Point<3> EllipsoidalManifold<3,3>::push_forward
(const Point<3> &point_on_sphere) const
{
const Point<3> point_on_ellipsoid(point_on_sphere(0) * a,
point_on_sphere(1) * b,
point_on_sphere(2) * c);
return point_on_ellipsoid;
}
template<>
Point<3> EllipsoidalManifold<2,3>::pull_back
(const Point<3> &point_ellipsoid) const
{
const Point<3> point_on_sphere(point_ellipsoid(0) / a,
point_ellipsoid(1) / b,
point_ellipsoid(2) / c);
return point_on_sphere;
}
template<>
Point<3> EllipsoidalManifold<2,3>::push_forward
(const Point<3> &point_on_sphere) const
{
const Point<3> point_on_ellipsoid(point_on_sphere(0) * a,
point_on_sphere(1) * b,
point_on_sphere(2) * c);
return point_on_ellipsoid;
}
void run ()
{
const unsigned int dim = 2;
const unsigned int spacedim = 3;
Triangulation<dim,spacedim> triangulation;
EllipsoidalManifold<dim,spacedim> ellipsoid;
GridGenerator::hyper_sphere(triangulation,
Point<spacedim>(),
1.0);
GridTools::transform(
std::bind(&EllipsoidalManifold<dim,spacedim>::push_forward,
std::cref(ellipsoid),
std::placeholders::_1),
triangulation);
{
const std::string filename = "initial-mesh.vtu";
std::ofstream out (filename.c_str());
GridOut grid_out;
grid_out.write_vtu (triangulation, out);
}
triangulation.reset_all_manifolds();
triangulation.set_all_manifold_ids(0);
triangulation.set_all_manifold_ids_on_boundary(0);
triangulation.set_manifold(0, ellipsoid);
triangulation.refine_global(2);
{
const std::string filename = "final-mesh.vtu";
std::ofstream out (filename.c_str());
GridOut grid_out;
grid_out.write_vtu (triangulation, out);
}
}
}
int main ()
{
try
{
EllipsoidalTest::run();
}
catch (std::exception &exc)
{
std::cerr << std::endl << std::endl
<< "----------------------------------------------------"
<< std::endl;
std::cerr << "Exception on processing: " << std::endl
<< exc.what() << std::endl
<< "Aborting!" << std::endl
<< "----------------------------------------------------"
<< std::endl;
return 1;
}
catch (...)
{
std::cerr << std::endl << std::endl
<< "----------------------------------------------------"
<< std::endl;
std::cerr << "Unknown exception!" << std::endl
<< "Aborting!" << std::endl
<< "----------------------------------------------------"
<< std::endl;
return 1;
}
}
