Fix HalfHyperShellBoundary in 3d.

git-svn-id: https://svn.dealii.org/trunk@18215 0785d39b-7218-0410-832d-ea1e28bc413d

diff --git a/deal.II/deal.II/include/grid/tria_boundary_lib.h b/deal.II/deal.II/include/grid/tria_boundary_lib.h
index 265eea60968e29fe4b11959e087abde5caf20a53..bf4ad320c8ed974970d1b3d188033c377f808fb3 100644 (file)
--- a/deal.II/deal.II/include/grid/tria_boundary_lib.h
+++ b/deal.II/deal.II/include/grid/tria_boundary_lib.h
@@ -2,7 +2,7 @@
 //    $Id$
 //    Version: $Name$
 //
-//    Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 by the deal.II authors
+//    Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2009 by the deal.II authors
 //
 //    This file is subject to QPL and may not be  distributed
 //    without copyright and license information. Please refer
@@ -461,7 +461,7 @@ class HyperShellBoundary : public HyperBallBoundary<dim>
  *
  * @ingroup boundary
  *
- * @author Wolfgang Bangerth, 2000
+ * @author Wolfgang Bangerth, 2000, 2009
  */
 template <int dim>
 class HalfHyperShellBoundary : public HyperShellBoundary<dim> 
@@ -471,8 +471,17 @@ class HalfHyperShellBoundary : public HyperShellBoundary<dim>
                                      * Constructor. The center of the
                                      * spheres defaults to the
                                      * origin.
-                                     */
-    HalfHyperShellBoundary (const Point<dim> &center = Point<dim>());
+                                     *
+                                     * If the radii are not specified, the
+                                     * class tries to infer them from the
+                                     * location of points on the
+                                     * boundary. This works in 2d, but not in
+                                     * 3d. As a consequence, in 3d these
+                                     * radii must be given.
+                                     */
+    HalfHyperShellBoundary (const Point<dim> &center = Point<dim>(),
+                           const double inner_radius = -1,
+                           const double outer_radius = -1);
     
                                     /**
                                      * Construct a new point on a line.
@@ -525,6 +534,13 @@ class HalfHyperShellBoundary : public HyperShellBoundary<dim>
     virtual void
     get_normals_at_vertices (const typename Triangulation<dim>::face_iterator &face,
                             typename Boundary<dim>::FaceVertexNormals &face_vertex_normals) const;
+
+  private:
+                                    /**
+                                     * Inner and outer radii of the shell.
+                                     */
+    const double inner_radius;
+    const double outer_radius;
 };
 
 

diff --git a/deal.II/deal.II/source/grid/tria_boundary_lib.cc b/deal.II/deal.II/source/grid/tria_boundary_lib.cc
index 139d4540bb4b70796c9870ade03ca559e97dd6dd..803508b3b79f40a63617e819fbb2096f46c5f1d6 100644 (file)
--- a/deal.II/deal.II/source/grid/tria_boundary_lib.cc
+++ b/deal.II/deal.II/source/grid/tria_boundary_lib.cc
@@ -2,7 +2,7 @@
 //    $Id$
 //    Version: $Name$
 //
-//    Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 by the deal.II authors
+//    Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2009 by the deal.II authors
 //
 //    This file is subject to QPL and may not be  distributed
 //    without copyright and license information. Please refer
@@ -694,7 +694,8 @@ get_normals_at_vertices (const typename Triangulation<dim>::face_iterator &face,
 
 
 template <int dim>
-HyperShellBoundary<dim>::HyperShellBoundary (const Point<dim> &center) :
+HyperShellBoundary<dim>::HyperShellBoundary (const Point<dim> &center)
+               :
                HyperBallBoundary<dim>(center, 0.)
 {
   this->compute_radius_automatically=true;
@@ -707,9 +708,20 @@ HyperShellBoundary<dim>::HyperShellBoundary (const Point<dim> &center) :
 
 
 template <int dim>
-HalfHyperShellBoundary<dim>::HalfHyperShellBoundary (const Point<dim> &center) :
-               HyperShellBoundary<dim> (center) 
-{}
+HalfHyperShellBoundary<dim>::HalfHyperShellBoundary (const Point<dim> &center,
+                                                    const double inner_radius,
+                                                    const double outer_radius)
+               :
+               HyperShellBoundary<dim> (center),
+               inner_radius (inner_radius),
+               outer_radius (outer_radius)
+{
+  if (dim > 2)
+    Assert ((inner_radius >= 0) &&
+           (outer_radius > 0) &&
+           (outer_radius > inner_radius),
+           ExcMessage ("Inner and outer radii must be specified explicitly in 3d."));
+}
 
 
 
@@ -718,19 +730,61 @@ Point<dim>
 HalfHyperShellBoundary<dim>::
 get_new_point_on_line (const typename Triangulation<dim>::line_iterator &line) const 
 {
-                                  // first check whether the two end
-                                  // points of the line are on the
-                                  // axis of symmetry. if so, then
-                                  // return the mid point
-  if ((line->vertex(0)(0) == this->center(0)) &&
-      (line->vertex(1)(0) == this->center(0)))
-    return (line->vertex(0) + line->vertex(1))/2;
+  switch (dim)
+    {
+                                      // in 2d, first check whether the two
+                                      // end points of the line are on the
+                                      // axis of symmetry. if so, then return
+                                      // the mid point
+      case 2:
+      {
+       if ((line->vertex(0)(0) == this->center(0))
+           &&
+           (line->vertex(1)(0) == this->center(0)))
+         return (line->vertex(0) + line->vertex(1))/2;
+       else
+                                          // otherwise we are on the outer or
+                                          // inner part of the shell. proceed
+                                          // as in the base class
+         return HyperShellBoundary<dim>::get_new_point_on_line (line);
+      }
+      
+                                            // in 3d, a line is a straight
+                                            // line if it is on the symmetry
+                                            // plane and if not both of its
+                                            // end points are on either the
+                                            // inner or outer sphere
+      case 3:
+      {
+       
+           if (((line->vertex(0)(0) == this->center(0))
+                &&
+                (line->vertex(1)(0) == this->center(0)))
+               &&
+               !(((std::fabs (line->vertex(0).distance (this->center)
+                              - inner_radius) < 1e-12 * outer_radius)
+                  &&
+                  (std::fabs (line->vertex(1).distance (this->center)
+                              - inner_radius) < 1e-12 * outer_radius))
+                 ||
+                 ((std::fabs (line->vertex(0).distance (this->center)
+                              - outer_radius) < 1e-12 * outer_radius)
+                  &&
+                  (std::fabs (line->vertex(1).distance (this->center)
+                              - outer_radius) < 1e-12 * outer_radius))))
+         return (line->vertex(0) + line->vertex(1))/2;
+       else
+                                          // otherwise we are on the outer or
+                                          // inner part of the shell. proceed
+                                          // as in the base class
+         return HyperShellBoundary<dim>::get_new_point_on_line (line);
+      }
+
+      default:
+           Assert (false, ExcNotImplemented());
+    }
   
-
-                                  // otherwise we are on the outer or
-                                  // inner part of the shell. proceed
-                                  // as in the base class
-  return HyperShellBoundary<dim>::get_new_point_on_line (line);
+  return Point<dim>();
 }
 
 
@@ -755,16 +809,46 @@ Point<dim>
 HalfHyperShellBoundary<dim>::
 get_new_point_on_quad (const typename Triangulation<dim>::quad_iterator &quad) const
 {
-                                  // same thing as for the new point
-                                  // on the line
+                                  // if this quad is on the symmetry plane,
+                                  // take the center point and project it
+                                  // outward to the same radius as the
+                                  // centers of the two radial lines
   if ((quad->vertex(0)(0) == this->center(0)) &&
       (quad->vertex(1)(0) == this->center(0)) &&
       (quad->vertex(2)(0) == this->center(0)) &&
       (quad->vertex(3)(0) == this->center(0)))
-    return (quad->vertex(0) + quad->vertex(1) +
-           quad->vertex(2) + quad->vertex(3)   )/4;
-  
+    {
+      const Point<dim> quad_center = (quad->vertex(0) + quad->vertex(1) +
+                                     quad->vertex(2) + quad->vertex(3)   )/4;
+      const Point<dim> quad_center_offset = quad_center - this->center;
 
+      
+      if (std::fabs (quad->line(0)->center().distance(this->center) -
+                    quad->line(1)->center().distance(this->center))
+         < 1e-12 * outer_radius)
+       {
+                                          // lines 0 and 1 are radial
+         const double needed_radius
+           = quad->line(0)->center().distance(this->center);
+         
+         return (this->center +
+                 quad_center_offset/quad_center_offset.norm() * needed_radius);
+       }
+      else if (std::fabs (quad->line(2)->center().distance(this->center) -
+                         quad->line(3)->center().distance(this->center))
+         < 1e-12 * outer_radius)
+       {
+                                          // lines 2 and 3 are radial
+         const double needed_radius
+           = quad->line(2)->center().distance(this->center);
+         
+         return (this->center +
+                 quad_center_offset/quad_center_offset.norm() * needed_radius);
+       }
+      else
+       Assert (false, ExcInternalError());
+    }
+  
                                   // otherwise we are on the outer or
                                   // inner part of the shell. proceed
                                   // as in the base class
@@ -779,15 +863,59 @@ HalfHyperShellBoundary<dim>::
 get_intermediate_points_on_line (const typename Triangulation<dim>::line_iterator &line,
                                 std::vector<Point<dim> > &points) const
 {
-                                  // check whether center of object is
-                                  // at x==0, since then it belongs
-                                  // to the plane part of the
-                                  // boundary
-  const Point<dim> line_center = line->center();
-  if (line_center(0) == this->center(0))
-    return StraightBoundary<dim>::get_intermediate_points_on_line (line, points);
-  else
-    return HyperShellBoundary<dim>::get_intermediate_points_on_line (line, points);
+  switch (dim)
+    {
+                                      // in 2d, first check whether the two
+                                      // end points of the line are on the
+                                      // axis of symmetry. if so, then return
+                                      // the mid point
+      case 2:
+      {
+       if ((line->vertex(0)(0) == this->center(0))
+           &&
+           (line->vertex(1)(0) == this->center(0)))
+         StraightBoundary<dim>::get_intermediate_points_on_line (line, points);
+       else
+                                          // otherwise we are on the outer or
+                                          // inner part of the shell. proceed
+                                          // as in the base class
+         HyperShellBoundary<dim>::get_intermediate_points_on_line (line, points);
+      }
+      
+                                            // in 3d, a line is a straight
+                                            // line if it is on the symmetry
+                                            // plane and if not both of its
+                                            // end points are on either the
+                                            // inner or outer sphere
+      case 3:
+      {
+       
+           if (((line->vertex(0)(0) == this->center(0))
+                &&
+                (line->vertex(1)(0) == this->center(0)))
+               &&
+               !(((std::fabs (line->vertex(0).distance (this->center)
+                              - inner_radius) < 1e-12 * outer_radius)
+                  &&
+                  (std::fabs (line->vertex(1).distance (this->center)
+                              - inner_radius) < 1e-12 * outer_radius))
+                 ||
+                 ((std::fabs (line->vertex(0).distance (this->center)
+                              - outer_radius) < 1e-12 * outer_radius)
+                  &&
+                  (std::fabs (line->vertex(1).distance (this->center)
+                              - outer_radius) < 1e-12 * outer_radius))))
+         StraightBoundary<dim>::get_intermediate_points_on_line (line, points);
+       else
+                                          // otherwise we are on the outer or
+                                          // inner part of the shell. proceed
+                                          // as in the base class
+         HyperShellBoundary<dim>::get_intermediate_points_on_line (line, points);
+      }
+
+      default:
+           Assert (false, ExcNotImplemented());
+    }
 }
 
 
@@ -798,6 +926,8 @@ HalfHyperShellBoundary<dim>::
 get_intermediate_points_on_quad (const typename Triangulation<dim>::quad_iterator &quad,
                                 std::vector<Point<dim> > &points) const
 {
+  Assert (dim < 3, ExcNotImplemented());
+  
                                   // check whether center of object is
                                   // at x==0, since then it belongs
                                   // to the plane part of the

diff --git a/deal.II/doc/news/changes.h b/deal.II/doc/news/changes.h
index 69566252c335a9c04c0ef177ba47d4c05f6e39ea..9336435948ad18c922d2682792dac11f8a497240 100644 (file)
--- a/deal.II/doc/news/changes.h
+++ b/deal.II/doc/news/changes.h
@@ -662,6 +662,15 @@ inconvenience this causes.
 <h3>deal.II</h3>
 
 <ol>
+  <li>
+  <p>
+  New: The GridGenerator::half_hyper_shell function now also exists in 3d.
+  However, to use it with the HalfHyperShellBoundary class, one has to
+  pass inner and outer radii to the constructor.
+  <br>
+  (Martin Kronbichler, WB, 2009/01/13)
+  </p>
+
   <li>
   <p>
   New: The restriction and embedding matrices for FE_Q are now implemented.

diff --git a/tests/bits/grid_generator_06.cc b/tests/bits/grid_generator_06.cc
new file mode 100644 (file)
index 0000000..7d3dcc2
--- /dev/null
+++ b/tests/bits/grid_generator_06.cc
@@ -0,0 +1,95 @@
+//---------------------------------------------------------------------------
+//    $Id$
+//    Version: $Name$ 
+//
+//    Copyright (C) 2005, 2006, 2009 by the deal.II authors
+//
+//    This file is subject to QPL and may not be  distributed
+//    without copyright and license information. Please refer
+//    to the file deal.II/doc/license.html for the  text  and
+//    further information on this license.
+//
+//---------------------------------------------------------------------------
+
+
+// Test GridGenerator::half_hyper_shell in 2d and 3d, making sure that we get
+// the boundary right. in 3d, we need to specify the inner and outer radii
+
+#include "../tests.h"
+#include <base/logstream.h>
+#include <base/tensor.h>
+#include <grid/tria.h>
+#include <grid/grid_generator.h>
+#include <grid/grid_out.h>
+#include <grid/tria_boundary_lib.h>
+
+#include <fstream>
+#include <iomanip>
+
+
+template<int dim>
+void test_1(std::ostream& out)
+{
+  Point<dim> p1;
+  p1[0] = 2.;
+  if (dim>1) p1[1] = -1.;
+  if (dim>2) p1[2] = 0.;
+  
+  GridOut go;
+  deallog << "half_hyper_shell without specifying radii" << std::endl;
+  Triangulation<dim> tr;
+  GridGenerator::half_hyper_shell(tr, p1, 4., 6.);
+
+  if (dim == 2)
+    {
+                                      // test with now specifying the inner and
+                                      // outer radius
+      static HalfHyperShellBoundary<dim> boundary (p1);
+      tr.set_boundary (0, boundary);
+
+      tr.refine_global (2);
+  
+      go.write_gnuplot(tr, out);
+    }
+}
+
+template<int dim>
+void test_2(std::ostream& out)
+{
+  Point<dim> p1;
+  p1[0] = 2.;
+  if (dim>1) p1[1] = -1.;
+  if (dim>2) p1[2] = 0.;
+  
+  GridOut go;
+  deallog << "half_hyper_shell with specifying radii" << std::endl;
+  Triangulation<dim> tr;
+  GridGenerator::half_hyper_shell(tr, p1, 4., 6.);
+
+                                  // test with now specifying the inner and
+                                  // outer radius
+  static HalfHyperShellBoundary<dim> boundary (p1, 4., 6.);
+  tr.set_boundary (0, boundary);
+
+  tr.refine_global (1);
+  
+  go.write_gnuplot(tr, out);
+}
+
+
+int main()
+{
+  std::ofstream logfile("grid_generator_06/output");
+  deallog.attach(logfile);
+  deallog.depth_console(0);
+  deallog.threshold_double(1.e-10);
+  
+  deallog.push("2d");
+  test_1<2>(logfile);
+  test_2<2>(logfile);
+  deallog.pop();
+  deallog.push("3d");
+  test_1<3>(logfile);
+  test_2<3>(logfile);
+  deallog.pop();
+}

diff --git a/tests/bits/grid_generator_06/cmp/generic b/tests/bits/grid_generator_06/cmp/generic
new file mode 100644 (file)
index 0000000..b17470e
--- /dev/null
+++ b/tests/bits/grid_generator_06/cmp/generic
@@ -0,0 +1,2021 @@
+
+DEAL:1d::hyper_cube
+3.00000 0 0
+7.00000 0 0
+
+DEAL:1d::subdivided_hyper_cube
+1.00000 0 0
+3.00000 0 0
+
+3.00000 0 0
+5.00000 0 0
+
+5.00000 0 0
+7.00000 0 0
+
+DEAL:1d::hyper_rectangle
+2.00000 0 0
+3.00000 0 0
+
+DEAL:1d::subdivided_hyper_rectangle
+2.00000 0 1
+2.50000 0 1
+
+2.50000 0 1
+3.00000 0 1
+
+DEAL:2d::hyper_cube
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       3600    3600
+       8400    3600
+       8400    8400
+       3600    8400
+       3600    3600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    3600
+       8400    3600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       8400    3600
+       8400    8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    8400
+       8400    8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    3600
+       3600    8400
+DEAL:2d::subdivided_hyper_cube
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       1200    1200
+       3600    1200
+       3600    3600
+       1200    3600
+       1200    1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       1200    1200
+       3600    1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       1200    1200
+       1200    3600
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       3600    1200
+       6000    1200
+       6000    3600
+       3600    3600
+       3600    1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    1200
+       6000    1200
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       6000    1200
+       8400    1200
+       8400    3600
+       6000    3600
+       6000    1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       6000    1200
+       8400    1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       8400    1200
+       8400    3600
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       1200    3600
+       3600    3600
+       3600    6000
+       1200    6000
+       1200    3600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       1200    3600
+       1200    6000
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       3600    3600
+       6000    3600
+       6000    6000
+       3600    6000
+       3600    3600
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       6000    3600
+       8400    3600
+       8400    6000
+       6000    6000
+       6000    3600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       8400    3600
+       8400    6000
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       1200    6000
+       3600    6000
+       3600    8400
+       1200    8400
+       1200    6000
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       1200    8400
+       3600    8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       1200    6000
+       1200    8400
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       3600    6000
+       6000    6000
+       6000    8400
+       3600    8400
+       3600    6000
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    8400
+       6000    8400
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       6000    6000
+       8400    6000
+       8400    8400
+       6000    8400
+       6000    6000
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       8400    6000
+       8400    8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       6000    8400
+       8400    8400
+DEAL:2d::hyper_rectangle
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       2400    -1200
+       3600    -1200
+       3600    2400
+       2400    2400
+       2400    -1200
+2 1 0 3 3 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -1200
+       3600    -1200
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    -1200
+       3600    2400
+2 1 0 3 4 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    2400
+       3600    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -1200
+       2400    2400
+DEAL:2d::subdivided_hyper_rectangle
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 2 900 0 25 0.0  0 0 -1 0 0 5
+       2400    -1200
+       3000    -1200
+       3000    0
+       2400    0
+       2400    -1200
+2 1 0 3 3 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -1200
+       3000    -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -1200
+       2400    0
+2 3  0 1 0 2 900 0 25 0.0  0 0 -1 0 0 5
+       3000    -1200
+       3600    -1200
+       3600    0
+       3000    0
+       3000    -1200
+2 1 0 3 3 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3000    -1200
+       3600    -1200
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    -1200
+       3600    0
+2 3  0 1 0 4 900 0 25 0.0  0 0 -1 0 0 5
+       2400    0
+       3000    0
+       3000    1200
+       2400    1200
+       2400    0
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    0
+       2400    1200
+2 3  0 1 0 4 900 0 25 0.0  0 0 -1 0 0 5
+       3000    0
+       3600    0
+       3600    1200
+       3000    1200
+       3000    0
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    0
+       3600    1200
+2 3  0 1 0 4 900 0 25 0.0  0 0 -1 0 0 5
+       2400    1200
+       3000    1200
+       3000    2400
+       2400    2400
+       2400    1200
+2 1 0 3 4 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    2400
+       3000    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    1200
+       2400    2400
+2 3  0 1 0 4 900 0 25 0.0  0 0 -1 0 0 5
+       3000    1200
+       3600    1200
+       3600    2400
+       3000    2400
+       3000    1200
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    1200
+       3600    2400
+2 1 0 3 4 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3000    2400
+       3600    2400
+DEAL:2d::parallelogram
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       0       0
+       2400    -1200
+       6000    1200
+       3600    2400
+       0       0
+2 1 0 3 3 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       0
+       2400    -1200
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -1200
+       6000    1200
+2 1 0 3 4 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    2400
+       6000    1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       0
+       3600    2400
+DEAL:2d::enclosed_hyper_cube
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 6 900 0 25 0.0  0 0 -1 0 0 5
+       2400    2400
+       3600    2400
+       3600    3600
+       2400    3600
+       2400    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    2400
+       3600    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    2400
+       2400    3600
+2 3  0 1 0 5 900 0 25 0.0  0 0 -1 0 0 5
+       3600    2400
+       8400    2400
+       8400    3600
+       3600    3600
+       3600    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    2400
+       8400    2400
+2 3  0 1 0 7 900 0 25 0.0  0 0 -1 0 0 5
+       8400    2400
+       9600    2400
+       9600    3600
+       8400    3600
+       8400    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       8400    2400
+       9600    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       9600    2400
+       9600    3600
+2 3  0 1 0 2 900 0 25 0.0  0 0 -1 0 0 5
+       2400    3600
+       3600    3600
+       3600    8400
+       2400    8400
+       2400    3600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    3600
+       2400    8400
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       3600    3600
+       8400    3600
+       8400    8400
+       3600    8400
+       3600    3600
+2 3  0 1 0 3 900 0 25 0.0  0 0 -1 0 0 5
+       8400    3600
+       9600    3600
+       9600    8400
+       8400    8400
+       8400    3600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       9600    3600
+       9600    8400
+2 3  0 1 0 10 900 0 25 0.0  0 0 -1 0 0 5
+       2400    8400
+       3600    8400
+       3600    9600
+       2400    9600
+       2400    8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    9600
+       3600    9600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    8400
+       2400    9600
+2 3  0 1 0 9 900 0 25 0.0  0 0 -1 0 0 5
+       3600    8400
+       8400    8400
+       8400    9600
+       3600    9600
+       3600    8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    9600
+       8400    9600
+2 3  0 1 0 11 900 0 25 0.0  0 0 -1 0 0 5
+       8400    8400
+       9600    8400
+       9600    9600
+       8400    9600
+       8400    8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       9600    8400
+       9600    9600
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       8400    9600
+       9600    9600
+DEAL:2d::hyper_ball
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -145    -3745
+       4945    -3745
+       3454    -2254
+       1345    -2254
+       -145    -3745
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -145    -3745
+       4945    -3745
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -145    -3745
+       1345    -2254
+       1345    -145
+       -145    1345
+       -145    -3745
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -145    -3745
+       -145    1345
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       1345    -2254
+       3454    -2254
+       3454    -145
+       1345    -145
+       1345    -2254
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       4945    -3745
+       4945    1345
+       3454    -145
+       3454    -2254
+       4945    -3745
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       4945    -3745
+       4945    1345
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -145    1345
+       1345    -145
+       3454    -145
+       4945    1345
+       -145    1345
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -145    1345
+       4945    1345
+DEAL:2d::cylinder
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -3600   -1200
+       3600    -1200
+       3600    1200
+       -3600   1200
+       -3600   -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -3600   -1200
+       3600    -1200
+2 1 0 3 3 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       3600    -1200
+       3600    1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -3600   1200
+       3600    1200
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -3600   -1200
+       -3600   1200
+DEAL:2d::hyper_L
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -1200   -1200
+       0       -1200
+       0       0
+       -1200   0
+       -1200   -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -1200   -1200
+       0       -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -1200   -1200
+       -1200   0
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       0       -1200
+       1200    -1200
+       1200    0
+       0       0
+       0       -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       -1200
+       1200    -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       1200    -1200
+       1200    0
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       0
+       1200    0
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -1200   0
+       0       0
+       0       1200
+       -1200   1200
+       -1200   0
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       0
+       0       1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -1200   1200
+       0       1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -1200   0
+       -1200   1200
+DEAL:2d::hyper_cube_slit
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -2400   -2400
+       0       -2400
+       0       0
+       -2400   0
+       -2400   -2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2400   -2400
+       0       -2400
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       -2400
+       0       0
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2400   -2400
+       -2400   0
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       0       -2400
+       2400    -2400
+       2400    0
+       0       0
+       0       -2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       -2400
+       2400    -2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -2400
+       2400    0
+2 1 0 3 3 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       0
+       2400    0
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       -2400
+       0       0
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -2400   0
+       0       0
+       0       2400
+       -2400   2400
+       -2400   0
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2400   2400
+       0       2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2400   0
+       -2400   2400
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       0       0
+       2400    0
+       2400    2400
+       0       2400
+       0       0
+2 1 0 3 3 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       0
+       2400    0
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    0
+       2400    2400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       0       2400
+       2400    2400
+DEAL:2d::hyper_shell
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       9600    -1200
+       9051    1555
+       6834    636
+       7200    -1200
+       9600    -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       9600    -1200
+       9051    1555
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       7200    -1200
+       6834    636
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       9051    1555
+       7491    3891
+       5794    2194
+       6834    636
+       9051    1555
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       9051    1555
+       7491    3891
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       6834    636
+       5794    2194
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       7491    3891
+       5155    5451
+       4236    3234
+       5794    2194
+       7491    3891
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       7491    3891
+       5155    5451
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       5794    2194
+       4236    3234
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       5155    5451
+       2400    6000
+       2400    3600
+       4236    3234
+       5155    5451
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       5155    5451
+       2400    6000
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       4236    3234
+       2400    3600
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       2400    6000
+       -355    5451
+       563     3234
+       2400    3600
+       2400    6000
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    6000
+       -355    5451
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    3600
+       563     3234
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -355    5451
+       -2691   3891
+       -994    2194
+       563     3234
+       -355    5451
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -355    5451
+       -2691   3891
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       563     3234
+       -994    2194
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -2691   3891
+       -4251   1555
+       -2034   636
+       -994    2194
+       -2691   3891
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2691   3891
+       -4251   1555
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -994    2194
+       -2034   636
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -4251   1555
+       -4800   -1199
+       -2400   -1199
+       -2034   636
+       -4251   1555
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -4251   1555
+       -4800   -1199
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2034   636
+       -2400   -1199
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -4800   -1199
+       -4251   -3955
+       -2034   -3036
+       -2400   -1199
+       -4800   -1199
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -4800   -1199
+       -4251   -3955
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2400   -1199
+       -2034   -3036
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -4251   -3955
+       -2691   -6291
+       -994    -4594
+       -2034   -3036
+       -4251   -3955
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -4251   -3955
+       -2691   -6291
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2034   -3036
+       -994    -4594
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -2691   -6291
+       -355    -7851
+       563     -5634
+       -994    -4594
+       -2691   -6291
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -2691   -6291
+       -355    -7851
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -994    -4594
+       563     -5634
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       -355    -7851
+       2399    -8400
+       2399    -6000
+       563     -5634
+       -355    -7851
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       -355    -7851
+       2399    -8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       563     -5634
+       2399    -6000
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       2399    -8400
+       5155    -7851
+       4236    -5634
+       2399    -6000
+       2399    -8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2399    -8400
+       5155    -7851
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2399    -6000
+       4236    -5634
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       5155    -7851
+       7491    -6291
+       5794    -4594
+       4236    -5634
+       5155    -7851
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       5155    -7851
+       7491    -6291
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       4236    -5634
+       5794    -4594
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       7491    -6291
+       9051    -3955
+       6834    -3036
+       5794    -4594
+       7491    -6291
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       7491    -6291
+       9051    -3955
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       5794    -4594
+       6834    -3036
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       9051    -3955
+       9600    -1200
+       7200    -1200
+       6834    -3036
+       9051    -3955
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       9051    -3955
+       9600    -1200
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       6834    -3036
+       7200    -1200
+DEAL:2d::half_hyper_ball
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       2400    -4800
+       4945    -3745
+       3454    -2254
+       2400    -2254
+       2400    -4800
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -4800
+       4945    -3745
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -4800
+       2400    -2254
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       2400    -2254
+       3454    -2254
+       3454    -145
+       2400    -145
+       2400    -2254
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -2254
+       2400    -145
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       4945    -3745
+       4945    1345
+       3454    -145
+       3454    -2254
+       4945    -3745
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       4945    -3745
+       4945    1345
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       2400    2400
+       2400    -145
+       3454    -145
+       4945    1345
+       2400    2400
+2 1 0 3 2 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    2400
+       2400    -145
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    2400
+       4945    1345
+DEAL:2d::half_hyper_shell
+#FIG 3.2
+Landscape
+Center
+Inches
+A4
+100.00
+Single
+-3
+# generated by deal.II GridOut class
+# reduce first number to scale up image
+1200 2
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       2400    -8400
+       5155    -7851
+       4236    -5634
+       2400    -6000
+       2400    -8400
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -8400
+       5155    -7851
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -6000
+       4236    -5634
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       2400    -8400
+       2400    -6000
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       5155    -7851
+       7491    -6291
+       5794    -4594
+       4236    -5634
+       5155    -7851
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       5155    -7851
+       7491    -6291
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       4236    -5634
+       5794    -4594
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       7491    -6291
+       9051    -3955
+       6834    -3036
+       5794    -4594
+       7491    -6291
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       7491    -6291
+       9051    -3955
+2 1 0 3 1 -1 800 0 -1 0.0  0 0 -1 0 0 2
+       5794    -4594
+       6834    -3036
+2 3  0 1 0 1 900 0 25 0.0  0 0 -1 0 0 5
+       9051    -3955
+       9600    -1200
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+       4.59808 -2.06066 1.06066
+object "cells" class array type int rank 1 shape 8 items 6 data follows
+       0       2       8       10      1       3       9       11
+       0       6       8       14      2       4       10      12
+       2       4       10      12      3       5       11      13
+       1       3       9       11      7       5       15      13
+       6       7       14      15      4       5       12      13
+       8       14      9       15      10      12      11      13
+attribute "element type" string "cubes"
+attribute "ref" string "positions"
+
+object "material" class array type int rank 0 items 6 data follows
+ 0 0 0 0 0 0
+attribute "dep" string "connections"
+
+object "level" class array type int rank 0 items 6 data follows
+ 0 0 0 0 0 0
+attribute "dep" string "connections"
+
+object "deal data" class field
+component "positions" value "vertices"
+component "connections" value "cells"
+object "cell data" class field
+component "positions" value "vertices"
+component "connections" value "cells"
+component "material" value "material"
+component "level" value "level"
+
+object "grid data" class group
+member "cells" value "cell data"
+end