Add a GridGenerator function for flow past a cylinder.

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diff --git a/doc/news/changes/major/20180704DavidWells b/doc/news/changes/major/20180704DavidWells
new file mode 100644 (file)
index 0000000..0a093f6
--- /dev/null
+++ b/doc/news/changes/major/20180704DavidWells
@@ -0,0 +1,6 @@
+New: A new function GridGenerator::channel_with_cylinder has been added. This
+function generates a grid corresponding to the classic flow past a cylinder test
+problem, and uses manifolds to blend between the description of the cylinder and
+the Cartesian bulk geometry.
+<br>
+(2018/07/04, David Wells)

diff --git a/include/deal.II/grid/grid_generator.h b/include/deal.II/grid/grid_generator.h
index bd277e3592cff21f4b349be3aadac69ca98bae95..4582bc531d1251b111b4de68b8647a696021a355 100644 (file)
--- a/include/deal.II/grid/grid_generator.h
+++ b/include/deal.II/grid/grid_generator.h
@@ -367,6 +367,99 @@ namespace GridGenerator
                     const unsigned int       n_slices          = 2,
                     const bool               colorize          = false);
 
+  /**
+   * Generate a grid consisting of a channel with a cylinder. This is a common
+   * benchmark for Navier-Stokes solvers. The geometry consists of a channel
+   * of size $[0, 2.2] \times [0, 0.41] \times [0, 0.41] $ (where the $z$
+   * dimension is omitted in 2D) with a cylinder, parallel to the $z$ axis
+   * with diameter $0.1$, centered at $(0.2, 0.2, 0)$. The channel has three
+   * distinct regions:
+   * <ol>
+   *   <li>If @p n_shells is greater than zero, then there are that many shells
+   *   centered around the cylinder,</li>
+   *   <li>a blending region between the shells and the rest of the
+   *   triangulation, and</li>
+   *   <li>a bulk region consisting of Cartesian cells.</li>
+   * </ol>
+   * Since the cylinder is slightly offset from the center of the channel,
+   * this geometry results in vortex shedding at moderate Reynolds
+   * numbers. Here is the grid (after one global refinement) in 2D:
+   *
+   * @image html channel_with_cylinder_2d.png
+   *
+   * and in 3D:
+   *
+   * @image html channel_with_cylinder_3d.png
+   *
+   * The resulting Triangulation uses three manifolds: a PolarManifold (in 2D)
+   * or CylindricalManifold (in 3D) with manifold id $0$, a
+   * TransfiniteInterpolationManifold with manifold id $1$, and a FlatManifold
+   * everywhere else. For more information on this topic see @ref
+   * GlossManifoldIndicator "the glossary entry on manifold indicators".  The
+   * cell faces on the cylinder and surrounding shells have manifold ids of
+   * $0$, while the cell volumes adjacent to the shells (or, if they do not
+   * exist, the cylinder) have a manifold id of $1$. Put another way: this
+   * grid uses TransfiniteInterpolationManifold to smoothly transition from
+   * the shells (generated with GridGenerator::concentric_hyper_shells) to the
+   * bulk region. All other cell volumes and faces have manifold id
+   * numbers::flat_manifold_id and use FlatManifold. All cells with id
+   * numbers::flat_manifold_id are rectangular prisms aligned with the
+   * coordinate axes.
+   *
+   * The picture below shows part of the 2D grid (using all default arguments
+   * to this function) after two global refinements. The cells with manifold
+   * id $0$ are orange (the polar manifold id), cells with manifold id $1$ are
+   * yellow (the transfinite interpolation manifold id), and the ones with
+   * manifold id numbers::flat_manifold_id are cyan:
+   *
+   * @image html channel_with_cylinder_2d_manifolds.png
+   *
+   * @param tria Triangulation to create. Must be empty upon calling this
+   * function.
+   *
+   * @param shell_region_width Width of the layer of shells around the cylinder.
+   * This value should be between $0$ and $0.05$; the default value is $0.03$.
+   *
+   * @param n_shells Number of shells to use in the shell layer.
+   *
+   * @param skewness Parameter controlling how close the shells are
+   * to the cylinder: see the mathematical definition given in
+   * GridGenerator::concentric_hyper_shells.
+   *
+   * @param colorize Assign different boundary ids if set to true. For more
+   * information on boundary indicators see
+   * @ref GlossBoundaryIndicator "this glossary entry".
+   * The left boundary (at $x = 0$) is assigned an id of $0$, the right
+   * boundary (at $x = 2.2$) is assigned an id of $1$, the cylinder boundary
+   * is assigned an id of $2$, and the channel walls are assigned an id of
+   * $3$.
+   *
+   * See the original paper for more information:
+   * @code{.bib}
+   * @inbook{schafer1996,
+   * author    = {Sch{\"a}fer, M. and Turek, S. and Durst, F. and Krause, E.
+   *              and Rannacher, R.},
+   * title     = {Benchmark Computations of Laminar Flow Around a Cylinder},
+   * bookTitle = {Flow Simulation with High-Performance Computers II: DFG
+   *              Priority Research Programme Results 1993--1995},
+   * year      = {1996},
+   * publisher = {Vieweg+Teubner Verlag},
+   * address   = {Wiesbaden},
+   * pages     = {547--566},
+   * isbn      = {978-3-322-89849-4},
+   * doi       = {10.1007/978-3-322-89849-4_39},
+   * url       = {https://doi.org/10.1007/978-3-322-89849-4_39}
+   * }
+   * @endcode
+   */
+  template <int dim>
+  void
+  channel_with_cylinder(Triangulation<dim> &tria,
+                        const double        shell_region_width = 0.03,
+                        const unsigned int  n_shells           = 2,
+                        const double        skewness           = 2.0,
+                        const bool          colorize           = false);
+
   /**
    * A general quadrilateral in 2d or a general hexahedron in 3d. It is the
    * responsibility of the user to provide the vertices in the right order (see
@@ -954,7 +1047,7 @@ namespace GridGenerator
   torus(Triangulation<dim, spacedim> &tria, const double R, const double r);
 
   /**
-   * This class produces a square in the <i>xy</i>-plane with a cylindrical
+   * This function produces a square in the <i>xy</i>-plane with a cylindrical
    * hole in the middle. The square and the circle are centered at the
    * origin. In 3d, this geometry is extruded in $z$ direction to the interval
    * $[0,L]$.
@@ -1564,8 +1657,28 @@ namespace GridGenerator
                                         const double,
                                         const unsigned int,
                                         const bool);
-#endif
 
+  template <>
+  void channel_with_cylinder(Triangulation<1> &,
+                             const double,
+                             const unsigned int,
+                             const double,
+                             const bool);
+
+  template <>
+  void channel_with_cylinder(Triangulation<2> &,
+                             const double,
+                             const unsigned int,
+                             const double,
+                             const bool);
+
+  template <>
+  void channel_with_cylinder(Triangulation<3> &,
+                             const double,
+                             const unsigned int,
+                             const double,
+                             const bool);
+#endif
 } // namespace GridGenerator
 
 

diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc
index c995c397812c937454ac661e8f077c1655c2864e..ffe84275ee5b624989983e8519d2e56fe47c3c28 100644 (file)
--- a/source/grid/grid_generator.cc
+++ b/source/grid/grid_generator.cc
@@ -26,7 +26,6 @@
 #include <deal.II/grid/tria_iterator.h>
 
 #include <cmath>
-#include <iostream>
 #include <limits>
 
 DEAL_II_NAMESPACE_OPEN
@@ -1931,6 +1930,19 @@ namespace GridGenerator
   }
 
 
+
+  template <>
+  void channel_with_cylinder(Triangulation<1> & /*tria*/,
+                             const double /*shell_region_width*/,
+                             const unsigned int /*n_shells*/,
+                             const double /*skewness*/,
+                             const bool /*colorize*/)
+  {
+    Assert(false, ExcNotImplemented());
+  }
+
+
+
   namespace internal
   {
     // helper function to check if point is in 2D box
@@ -1957,9 +1969,10 @@ namespace GridGenerator
           length = std::min(length, cell->line(n)->diameter());
       return length;
     }
-
   } // namespace internal
 
+
+
   template <>
   void plate_with_a_hole(Triangulation<2> &       tria,
                          const double             inner_radius,
@@ -2187,6 +2200,253 @@ namespace GridGenerator
 
 
 
+  template <>
+  void channel_with_cylinder(Triangulation<2> & tria,
+                             const double       shell_region_width,
+                             const unsigned int n_shells,
+                             const double       skewness,
+                             const bool         colorize)
+  {
+    Assert(0.0 <= shell_region_width && shell_region_width < 0.05,
+           ExcMessage("The width of the shell region must be less than 0.05 "
+                      "(and preferably close to 0.03)"));
+    const types::manifold_id polar_manifold_id = 0;
+    const types::manifold_id tfi_manifold_id   = 1;
+
+    // We begin by setting up a grid that is 4 by 22 cells. While not
+    // squares, these have pretty good aspect ratios.
+    Triangulation<2> bulk_tria;
+    GridGenerator::subdivided_hyper_rectangle(bulk_tria,
+                                              {22u, 4u},
+                                              Point<2>(0.0, 0.0),
+                                              Point<2>(2.2, 0.41));
+    // bulk_tria now looks like this:
+    //
+    //   +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
+    //   |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+    //   +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
+    //   |  |XX|XX|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+    //   +--+--O--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
+    //   |  |XX|XX|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+    //   +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
+    //   |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+    //   +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
+    //
+    // Note that these cells are not quite squares: they are all 0.1 by
+    // 0.1025.
+    //
+    // The next step is to remove the cells marked with XXs: we will place
+    // the grid around the cylinder there later. The next loop does two
+    // things:
+    // 1. Determines which cells need to be removed from the Triangulation
+    //    (i.e., find the cells marked with XX in the picture).
+    // 2. Finds the location of the vertex marked with 'O' and uses that to
+    //    calculate the shift vector for aligning cylinder_tria with
+    //    tria_without_cylinder.
+    std::set<Triangulation<2>::active_cell_iterator> cells_to_remove;
+    Tensor<1, 2> cylinder_triangulation_offset;
+    for (const auto &cell : bulk_tria.active_cell_iterators())
+      {
+        if ((cell->center() - Point<2>(0.2, 0.2)).norm() < 0.15)
+          cells_to_remove.insert(cell);
+
+        if (cylinder_triangulation_offset == Tensor<1, 2>())
+          {
+            for (unsigned int vertex_n = 0;
+                 vertex_n < GeometryInfo<2>::vertices_per_cell;
+                 ++vertex_n)
+              if (cell->vertex(vertex_n) == Point<2>())
+                {
+                  // cylinder_tria is centered at zero, so we need to
+                  // shift it up and to the right by two cells:
+                  cylinder_triangulation_offset =
+                    2.0 * (cell->vertex(3) - Point<2>());
+                  break;
+                }
+          }
+      }
+    Triangulation<2> tria_without_cylinder;
+    GridGenerator::create_triangulation_with_removed_cells(
+      bulk_tria, cells_to_remove, tria_without_cylinder);
+
+    // set up the cylinder triangulation. Note that this function sets the
+    // manifold ids of the interior boundary cells to 0
+    // (polar_manifold_id).
+    Triangulation<2> cylinder_tria;
+    GridGenerator::hyper_cube_with_cylindrical_hole(cylinder_tria,
+                                                    0.05 + shell_region_width,
+                                                    0.41 / 4.0);
+    // The bulk cells are not quite squares, so we need to move the left
+    // and right sides of cylinder_tria inwards so that it fits in
+    // bulk_tria:
+    for (auto &cell : cylinder_tria.active_cell_iterators())
+      for (unsigned int vertex_n = 0;
+           vertex_n < GeometryInfo<2>::vertices_per_cell;
+           ++vertex_n)
+        {
+          if (std::abs(cell->vertex(vertex_n)[0] - -0.41 / 4.0) < 1e-10)
+            cell->vertex(vertex_n)[0] = -0.1;
+          else if (std::abs(cell->vertex(vertex_n)[0] - 0.41 / 4.0) < 1e-10)
+            cell->vertex(vertex_n)[0] = 0.1;
+        }
+
+    // Assign interior manifold ids to be the TFI id.
+    for (auto &cell : cylinder_tria.active_cell_iterators())
+      {
+        cell->set_manifold_id(tfi_manifold_id);
+        for (unsigned int face_n = 0; face_n < GeometryInfo<2>::faces_per_cell;
+             ++face_n)
+          if (!cell->face(face_n)->at_boundary())
+            cell->face(face_n)->set_manifold_id(tfi_manifold_id);
+      }
+    if (0.0 < shell_region_width)
+      {
+        Assert(0 < n_shells,
+               ExcMessage("If the shell region has positive width then "
+                          "there must be at least one shell."));
+        Triangulation<2> shell_tria;
+        GridGenerator::concentric_hyper_shells(shell_tria,
+                                               Point<2>(),
+                                               0.05,
+                                               0.05 + shell_region_width,
+                                               n_shells,
+                                               skewness,
+                                               8);
+
+        // Make the tolerance as large as possible since these cells can
+        // be quite close together
+        const double vertex_tolerance =
+          std::min(internal::minimal_vertex_distance(shell_tria),
+                   internal::minimal_vertex_distance(cylinder_tria)) *
+          0.5;
+
+        shell_tria.set_all_manifold_ids(polar_manifold_id);
+        Triangulation<2> temp;
+        GridGenerator::merge_triangulations(
+          shell_tria, cylinder_tria, temp, vertex_tolerance, true);
+        cylinder_tria = std::move(temp);
+      }
+    GridTools::shift(cylinder_triangulation_offset, cylinder_tria);
+
+    // Compute the tolerance again, since the shells may be very close to
+    // each-other:
+    const double vertex_tolerance =
+      std::min(internal::minimal_vertex_distance(tria_without_cylinder),
+               internal::minimal_vertex_distance(cylinder_tria)) /
+      10;
+    GridGenerator::merge_triangulations(
+      tria_without_cylinder, cylinder_tria, tria, vertex_tolerance, true);
+
+    // Ensure that all manifold ids on a polar cell really are set to the
+    // polar manifold id:
+    for (auto &cell : tria.active_cell_iterators())
+      if (cell->manifold_id() == polar_manifold_id)
+        cell->set_all_manifold_ids(polar_manifold_id);
+
+    // Ensure that all other manifold ids (including the interior faces
+    // opposite the cylinder) are set to the flat manifold id:
+    for (const auto &cell : tria.active_cell_iterators())
+      if (cell->manifold_id() != polar_manifold_id &&
+          cell->manifold_id() != tfi_manifold_id)
+        cell->set_all_manifold_ids(numbers::flat_manifold_id);
+
+    // We need to calculate the current center so that we can move it later:
+    // to start get a unique list of (points to) vertices on the cylinder
+    std::vector<Point<2> *> cylinder_pointers;
+    for (const auto &face : tria.active_face_iterators())
+      if (face->manifold_id() == polar_manifold_id)
+        {
+          cylinder_pointers.push_back(&face->vertex(0));
+          cylinder_pointers.push_back(&face->vertex(1));
+        }
+    // de-duplicate
+    std::sort(cylinder_pointers.begin(), cylinder_pointers.end());
+    cylinder_pointers.erase(std::unique(cylinder_pointers.begin(),
+                                        cylinder_pointers.end()),
+                            cylinder_pointers.end());
+
+    // find the current center...
+    Point<2> center;
+    for (const Point<2> *const ptr : cylinder_pointers)
+      center += *ptr / double(cylinder_pointers.size());
+
+    // and recenter at (0.2, 0.2)
+    for (Point<2> *const ptr : cylinder_pointers)
+      *ptr += Point<2>(0.2, 0.2) - center;
+
+    // attach manifolds
+    PolarManifold<2> polar_manifold(Point<2>(0.2, 0.2));
+    tria.set_manifold(polar_manifold_id, polar_manifold);
+    TransfiniteInterpolationManifold<2> inner_manifold;
+    inner_manifold.initialize(tria);
+    tria.set_manifold(tfi_manifold_id, inner_manifold);
+
+    if (colorize)
+      for (auto &face : tria.active_face_iterators())
+        if (face->at_boundary())
+          {
+            const Point<2> center = face->center();
+            // left side
+            if (std::abs(center[0] - 0.0) < 1e-10)
+              face->set_boundary_id(0);
+            // right side
+            else if (std::abs(center[0] - 2.2) < 1e-10)
+              face->set_boundary_id(1);
+            // cylinder boundary
+            else if (face->manifold_id() == polar_manifold_id)
+              face->set_boundary_id(2);
+            // sides of channel
+            else
+              {
+                Assert(std::abs(center[1] - 0.00) < 1.0e-10 ||
+                         std::abs(center[1] - 0.41) < 1.0e-10,
+                       ExcInternalError());
+                face->set_boundary_id(3);
+              }
+          }
+  }
+
+
+
+  template <>
+  void channel_with_cylinder(Triangulation<3> & tria,
+                             const double       shell_region_width,
+                             const unsigned int n_shells,
+                             const double       skewness,
+                             const bool         colorize)
+  {
+    Triangulation<2> tria_2;
+    channel_with_cylinder(
+      tria_2, shell_region_width, n_shells, skewness, colorize);
+    extrude_triangulation(tria_2, 5, 0.41, tria, true);
+
+    // set up the new 3D manifolds
+    const types::manifold_id      cylindrical_manifold_id = 0;
+    const types::manifold_id      tfi_manifold_id         = 1;
+    const PolarManifold<2> *const m_ptr =
+      dynamic_cast<const PolarManifold<2> *>(
+        &tria_2.get_manifold(cylindrical_manifold_id));
+    Assert(m_ptr != nullptr, ExcInternalError());
+    const Point<3>     axial_point(m_ptr->center[0], m_ptr->center[1], 0.0);
+    const Tensor<1, 3> direction{{0.0, 0.0, 1.0}};
+
+    const CylindricalManifold<3> cylindrical_manifold(direction, axial_point);
+    TransfiniteInterpolationManifold<3> inner_manifold;
+    inner_manifold.initialize(tria);
+    tria.set_manifold(cylindrical_manifold_id, cylindrical_manifold);
+    tria.set_manifold(tfi_manifold_id, inner_manifold);
+
+    // From extrude_triangulation: since the maximum boundary id of tria_2 was
+    // 3, the bottom boundary id is 4 and the top is 5: both are walls, so set
+    // them to 3
+    if (colorize)
+      for (auto &face : tria.active_face_iterators())
+        if (face->boundary_id() == 4 || face->boundary_id() == 5)
+          face->set_boundary_id(3);
+  }
+
+
+
   template <int dim, int spacedim>
   void
   hyper_cross(Triangulation<dim, spacedim> &   tria,

diff --git a/tests/grid/channel_flow.cc b/tests/grid/channel_flow.cc
new file mode 100644 (file)
index 0000000..9e1ecb1
--- /dev/null
+++ b/tests/grid/channel_flow.cc
@@ -0,0 +1,95 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2018 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+// Test GridGenerator::channel_with_cylinder(). The output generated here is
+// similar to that generated in extrude_copy_manifold.
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/tria.h>
+
+#include "../tests.h"
+
+template <int dim>
+void
+test()
+{
+  Triangulation<dim> triangulation;
+  GridGenerator::channel_with_cylinder(triangulation, 0.03, 4, 2.0, true);
+
+  std::map<types::manifold_id, std::vector<Point<dim>>>
+    manifold_to_face_centers;
+  std::map<types::boundary_id, std::vector<Point<dim>>>
+    boundary_to_face_centers;
+
+  for (const auto &face : triangulation.active_face_iterators())
+    {
+      manifold_to_face_centers[face->manifold_id()].push_back(face->center());
+      boundary_to_face_centers[face->boundary_id()].push_back(face->center());
+    }
+
+  deallog << "face centers:" << std::endl;
+  for (std::pair<const types::manifold_id, std::vector<Point<dim>>> &key :
+       manifold_to_face_centers)
+    {
+      if (key.first == numbers::flat_manifold_id)
+        continue;
+      deallog << "manifold id: " << key.first << std::endl;
+      for (const Point<dim> &point : key.second)
+        {
+          deallog << point[0] << ", " << point[1];
+          if (dim == 3)
+            deallog << ", " << point[2];
+          deallog << std::endl;
+        }
+    }
+  for (std::pair<const types::boundary_id, std::vector<Point<dim>>> &key :
+       boundary_to_face_centers)
+    {
+      if (key.first == numbers::internal_face_boundary_id)
+        continue;
+      deallog << "boundary id: " << key.first << std::endl;
+      for (const Point<dim> &point : key.second)
+        {
+          deallog << point[0] << ", " << point[1];
+          if (dim == 3)
+            deallog << ", " << point[2];
+          deallog << std::endl;
+        }
+    }
+
+  // reenable if we want to look at pictures
+  if (false)
+    {
+      std::ofstream out("out-" + std::to_string(dim) + ".vtu");
+      GridOut       grid_out;
+      grid_out.write_vtu(triangulation, out);
+    }
+}
+
+
+int
+main()
+{
+  initlog();
+
+  deallog.push("2d");
+  test<2>();
+  deallog.pop();
+
+  deallog.push("3d");
+  test<3>();
+  deallog.pop();
+}

diff --git a/tests/grid/channel_flow.output b/tests/grid/channel_flow.output
new file mode 100644 (file)
index 0000000..1618d8b
--- /dev/null
+++ b/tests/grid/channel_flow.output
@@ -0,0 +1,1163 @@
+
+DEAL:2d::face centers:
+DEAL:2d::manifold id: 0
+DEAL:2d::0.268284, 0.171716
+DEAL:2d::0.268284, 0.228284
+DEAL:2d::0.228284, 0.268284
+DEAL:2d::0.171716, 0.268284
+DEAL:2d::0.131716, 0.228284
+DEAL:2d::0.131716, 0.171716
+DEAL:2d::0.171716, 0.131716
+DEAL:2d::0.228284, 0.131716
+DEAL:2d::0.272810, 0.200000
+DEAL:2d::0.256009, 0.176800
+DEAL:2d::0.251484, 0.251484
+DEAL:2d::0.256009, 0.223200
+DEAL:2d::0.223200, 0.256009
+DEAL:2d::0.200000, 0.272810
+DEAL:2d::0.176800, 0.256009
+DEAL:2d::0.148516, 0.251484
+DEAL:2d::0.143991, 0.223200
+DEAL:2d::0.127190, 0.200000
+DEAL:2d::0.143991, 0.176800
+DEAL:2d::0.148516, 0.148516
+DEAL:2d::0.200000, 0.127190
+DEAL:2d::0.176800, 0.143991
+DEAL:2d::0.251484, 0.148516
+DEAL:2d::0.223200, 0.143991
+DEAL:2d::0.260959, 0.200000
+DEAL:2d::0.248055, 0.180095
+DEAL:2d::0.243105, 0.243105
+DEAL:2d::0.248055, 0.219905
+DEAL:2d::0.219905, 0.248055
+DEAL:2d::0.200000, 0.260959
+DEAL:2d::0.180095, 0.248055
+DEAL:2d::0.156895, 0.243105
+DEAL:2d::0.151945, 0.219905
+DEAL:2d::0.139041, 0.200000
+DEAL:2d::0.151945, 0.180095
+DEAL:2d::0.156895, 0.156895
+DEAL:2d::0.200000, 0.139041
+DEAL:2d::0.180095, 0.151945
+DEAL:2d::0.243105, 0.156895
+DEAL:2d::0.219905, 0.151945
+DEAL:2d::0.254066, 0.200000
+DEAL:2d::0.244242, 0.181675
+DEAL:2d::0.238230, 0.238230
+DEAL:2d::0.244242, 0.218325
+DEAL:2d::0.218325, 0.244242
+DEAL:2d::0.200000, 0.254066
+DEAL:2d::0.181675, 0.244242
+DEAL:2d::0.161770, 0.238230
+DEAL:2d::0.155758, 0.218325
+DEAL:2d::0.145934, 0.200000
+DEAL:2d::0.155758, 0.181675
+DEAL:2d::0.161770, 0.161770
+DEAL:2d::0.200000, 0.145934
+DEAL:2d::0.181675, 0.155758
+DEAL:2d::0.238230, 0.161770
+DEAL:2d::0.218325, 0.155758
+DEAL:2d::0.250916, 0.200000
+DEAL:2d::0.242678, 0.182322
+DEAL:2d::0.236003, 0.236003
+DEAL:2d::0.242678, 0.217678
+DEAL:2d::0.217678, 0.242678
+DEAL:2d::0.200000, 0.250916
+DEAL:2d::0.182322, 0.242678
+DEAL:2d::0.163997, 0.236003
+DEAL:2d::0.157322, 0.217678
+DEAL:2d::0.149084, 0.200000
+DEAL:2d::0.157322, 0.182322
+DEAL:2d::0.163997, 0.163997
+DEAL:2d::0.200000, 0.149084
+DEAL:2d::0.182322, 0.157322
+DEAL:2d::0.236003, 0.163997
+DEAL:2d::0.217678, 0.157322
+DEAL:2d::manifold id: 1
+DEAL:2d::0.290000, 0.202500
+DEAL:2d::0.278284, 0.282034
+DEAL:2d::0.200000, 0.293750
+DEAL:2d::0.121716, 0.282034
+DEAL:2d::0.110000, 0.202500
+DEAL:2d::0.121716, 0.122966
+DEAL:2d::0.200000, 0.111250
+DEAL:2d::0.278284, 0.122966
+DEAL:2d::boundary id: 0
+DEAL:2d::0.00000, 0.0512500
+DEAL:2d::0.00000, 0.153750
+DEAL:2d::0.00000, 0.256250
+DEAL:2d::0.00000, 0.358750
+DEAL:2d::boundary id: 1
+DEAL:2d::2.20000, 0.0512500
+DEAL:2d::2.20000, 0.153750
+DEAL:2d::2.20000, 0.256250
+DEAL:2d::2.20000, 0.358750
+DEAL:2d::boundary id: 2
+DEAL:2d::0.242678, 0.182322
+DEAL:2d::0.242678, 0.217678
+DEAL:2d::0.217678, 0.242678
+DEAL:2d::0.182322, 0.242678
+DEAL:2d::0.157322, 0.217678
+DEAL:2d::0.157322, 0.182322
+DEAL:2d::0.182322, 0.157322
+DEAL:2d::0.217678, 0.157322
+DEAL:2d::boundary id: 3
+DEAL:2d::0.0500000, 0.00000
+DEAL:2d::0.150000, 0.00000
+DEAL:2d::0.250000, 0.00000
+DEAL:2d::0.350000, 0.00000
+DEAL:2d::0.450000, 0.00000
+DEAL:2d::0.550000, 0.00000
+DEAL:2d::0.650000, 0.00000
+DEAL:2d::0.750000, 0.00000
+DEAL:2d::0.850000, 0.00000
+DEAL:2d::0.950000, 0.00000
+DEAL:2d::1.05000, 0.00000
+DEAL:2d::1.15000, 0.00000
+DEAL:2d::1.25000, 0.00000
+DEAL:2d::1.35000, 0.00000
+DEAL:2d::1.45000, 0.00000
+DEAL:2d::1.55000, 0.00000
+DEAL:2d::1.65000, 0.00000
+DEAL:2d::1.75000, 0.00000
+DEAL:2d::1.85000, 0.00000
+DEAL:2d::1.95000, 0.00000
+DEAL:2d::2.05000, 0.00000
+DEAL:2d::2.15000, 0.00000
+DEAL:2d::0.0500000, 0.410000
+DEAL:2d::0.150000, 0.410000
+DEAL:2d::0.250000, 0.410000
+DEAL:2d::0.350000, 0.410000
+DEAL:2d::0.450000, 0.410000
+DEAL:2d::0.550000, 0.410000
+DEAL:2d::0.650000, 0.410000
+DEAL:2d::0.750000, 0.410000
+DEAL:2d::0.850000, 0.410000
+DEAL:2d::0.950000, 0.410000
+DEAL:2d::1.05000, 0.410000
+DEAL:2d::1.15000, 0.410000
+DEAL:2d::1.25000, 0.410000
+DEAL:2d::1.35000, 0.410000
+DEAL:2d::1.45000, 0.410000
+DEAL:2d::1.55000, 0.410000
+DEAL:2d::1.65000, 0.410000
+DEAL:2d::1.75000, 0.410000
+DEAL:2d::1.85000, 0.410000
+DEAL:2d::1.95000, 0.410000
+DEAL:2d::2.05000, 0.410000
+DEAL:2d::2.15000, 0.410000
+DEAL:3d::face centers:
+DEAL:3d::manifold id: 0
+DEAL:3d::0.268284, 0.171716, 0.0512500
+DEAL:3d::0.268284, 0.228284, 0.0512500
+DEAL:3d::0.228284, 0.268284, 0.0512500
+DEAL:3d::0.171716, 0.268284, 0.0512500
+DEAL:3d::0.131716, 0.228284, 0.0512500
+DEAL:3d::0.131716, 0.171716, 0.0512500
+DEAL:3d::0.171716, 0.131716, 0.0512500
+DEAL:3d::0.228284, 0.131716, 0.0512500
+DEAL:3d::0.262147, 0.174258, 0.00000
+DEAL:3d::0.256009, 0.176800, 0.0512500
+DEAL:3d::0.272810, 0.200000, 0.0512500
+DEAL:3d::0.262147, 0.225742, 0.00000
+DEAL:3d::0.256009, 0.223200, 0.0512500
+DEAL:3d::0.225742, 0.262147, 0.00000
+DEAL:3d::0.251484, 0.251484, 0.0512500
+DEAL:3d::0.223200, 0.256009, 0.0512500
+DEAL:3d::0.200000, 0.272810, 0.0512500
+DEAL:3d::0.174258, 0.262147, 0.00000
+DEAL:3d::0.176800, 0.256009, 0.0512500
+DEAL:3d::0.148516, 0.251484, 0.0512500
+DEAL:3d::0.137853, 0.225742, 0.00000
+DEAL:3d::0.143991, 0.223200, 0.0512500
+DEAL:3d::0.127190, 0.200000, 0.0512500
+DEAL:3d::0.137853, 0.174258, 0.00000
+DEAL:3d::0.143991, 0.176800, 0.0512500
+DEAL:3d::0.148516, 0.148516, 0.0512500
+DEAL:3d::0.174258, 0.137853, 0.00000
+DEAL:3d::0.176800, 0.143991, 0.0512500
+DEAL:3d::0.200000, 0.127190, 0.0512500
+DEAL:3d::0.225742, 0.137853, 0.00000
+DEAL:3d::0.223200, 0.143991, 0.0512500
+DEAL:3d::0.251484, 0.148516, 0.0512500
+DEAL:3d::0.252032, 0.178448, 0.00000
+DEAL:3d::0.248055, 0.180095, 0.0512500
+DEAL:3d::0.260959, 0.200000, 0.0512500
+DEAL:3d::0.252032, 0.221552, 0.00000
+DEAL:3d::0.248055, 0.219905, 0.0512500
+DEAL:3d::0.221552, 0.252032, 0.00000
+DEAL:3d::0.243105, 0.243105, 0.0512500
+DEAL:3d::0.219905, 0.248055, 0.0512500
+DEAL:3d::0.200000, 0.260959, 0.0512500
+DEAL:3d::0.178448, 0.252032, 0.00000
+DEAL:3d::0.180095, 0.248055, 0.0512500
+DEAL:3d::0.156895, 0.243105, 0.0512500
+DEAL:3d::0.147968, 0.221552, 0.00000
+DEAL:3d::0.151945, 0.219905, 0.0512500
+DEAL:3d::0.139041, 0.200000, 0.0512500
+DEAL:3d::0.147968, 0.178448, 0.00000
+DEAL:3d::0.151945, 0.180095, 0.0512500
+DEAL:3d::0.156895, 0.156895, 0.0512500
+DEAL:3d::0.178448, 0.147968, 0.00000
+DEAL:3d::0.180095, 0.151945, 0.0512500
+DEAL:3d::0.200000, 0.139041, 0.0512500
+DEAL:3d::0.221552, 0.147968, 0.00000
+DEAL:3d::0.219905, 0.151945, 0.0512500
+DEAL:3d::0.243105, 0.156895, 0.0512500
+DEAL:3d::0.246148, 0.180885, 0.00000
+DEAL:3d::0.244242, 0.181675, 0.0512500
+DEAL:3d::0.254066, 0.200000, 0.0512500
+DEAL:3d::0.246148, 0.219115, 0.00000
+DEAL:3d::0.244242, 0.218325, 0.0512500
+DEAL:3d::0.219115, 0.246148, 0.00000
+DEAL:3d::0.238230, 0.238230, 0.0512500
+DEAL:3d::0.218325, 0.244242, 0.0512500
+DEAL:3d::0.200000, 0.254066, 0.0512500
+DEAL:3d::0.180885, 0.246148, 0.00000
+DEAL:3d::0.181675, 0.244242, 0.0512500
+DEAL:3d::0.161770, 0.238230, 0.0512500
+DEAL:3d::0.153852, 0.219115, 0.00000
+DEAL:3d::0.155758, 0.218325, 0.0512500
+DEAL:3d::0.145934, 0.200000, 0.0512500
+DEAL:3d::0.153852, 0.180885, 0.00000
+DEAL:3d::0.155758, 0.181675, 0.0512500
+DEAL:3d::0.161770, 0.161770, 0.0512500
+DEAL:3d::0.180885, 0.153852, 0.00000
+DEAL:3d::0.181675, 0.155758, 0.0512500
+DEAL:3d::0.200000, 0.145934, 0.0512500
+DEAL:3d::0.219115, 0.153852, 0.00000
+DEAL:3d::0.218325, 0.155758, 0.0512500
+DEAL:3d::0.238230, 0.161770, 0.0512500
+DEAL:3d::0.243460, 0.181998, 0.00000
+DEAL:3d::0.242678, 0.182322, 0.0512500
+DEAL:3d::0.250916, 0.200000, 0.0512500
+DEAL:3d::0.243460, 0.218002, 0.00000
+DEAL:3d::0.242678, 0.217678, 0.0512500
+DEAL:3d::0.218002, 0.243460, 0.00000
+DEAL:3d::0.236003, 0.236003, 0.0512500
+DEAL:3d::0.217678, 0.242678, 0.0512500
+DEAL:3d::0.200000, 0.250916, 0.0512500
+DEAL:3d::0.181998, 0.243460, 0.00000
+DEAL:3d::0.182322, 0.242678, 0.0512500
+DEAL:3d::0.163997, 0.236003, 0.0512500
+DEAL:3d::0.156540, 0.218002, 0.00000
+DEAL:3d::0.157322, 0.217678, 0.0512500
+DEAL:3d::0.149084, 0.200000, 0.0512500
+DEAL:3d::0.156540, 0.181998, 0.00000
+DEAL:3d::0.157322, 0.182322, 0.0512500
+DEAL:3d::0.163997, 0.163997, 0.0512500
+DEAL:3d::0.181998, 0.156540, 0.00000
+DEAL:3d::0.182322, 0.157322, 0.0512500
+DEAL:3d::0.200000, 0.149084, 0.0512500
+DEAL:3d::0.218002, 0.156540, 0.00000
+DEAL:3d::0.217678, 0.157322, 0.0512500
+DEAL:3d::0.236003, 0.163997, 0.0512500
+DEAL:3d::0.268284, 0.171716, 0.153750
+DEAL:3d::0.268284, 0.228284, 0.153750
+DEAL:3d::0.228284, 0.268284, 0.153750
+DEAL:3d::0.171716, 0.268284, 0.153750
+DEAL:3d::0.131716, 0.228284, 0.153750
+DEAL:3d::0.131716, 0.171716, 0.153750
+DEAL:3d::0.171716, 0.131716, 0.153750
+DEAL:3d::0.228284, 0.131716, 0.153750
+DEAL:3d::0.262147, 0.174258, 0.102500
+DEAL:3d::0.256009, 0.176800, 0.153750
+DEAL:3d::0.272810, 0.200000, 0.153750
+DEAL:3d::0.262147, 0.225742, 0.102500
+DEAL:3d::0.256009, 0.223200, 0.153750
+DEAL:3d::0.225742, 0.262147, 0.102500
+DEAL:3d::0.251484, 0.251484, 0.153750
+DEAL:3d::0.223200, 0.256009, 0.153750
+DEAL:3d::0.200000, 0.272810, 0.153750
+DEAL:3d::0.174258, 0.262147, 0.102500
+DEAL:3d::0.176800, 0.256009, 0.153750
+DEAL:3d::0.148516, 0.251484, 0.153750
+DEAL:3d::0.137853, 0.225742, 0.102500
+DEAL:3d::0.143991, 0.223200, 0.153750
+DEAL:3d::0.127190, 0.200000, 0.153750
+DEAL:3d::0.137853, 0.174258, 0.102500
+DEAL:3d::0.143991, 0.176800, 0.153750
+DEAL:3d::0.148516, 0.148516, 0.153750
+DEAL:3d::0.174258, 0.137853, 0.102500
+DEAL:3d::0.176800, 0.143991, 0.153750
+DEAL:3d::0.200000, 0.127190, 0.153750
+DEAL:3d::0.225742, 0.137853, 0.102500
+DEAL:3d::0.223200, 0.143991, 0.153750
+DEAL:3d::0.251484, 0.148516, 0.153750
+DEAL:3d::0.252032, 0.178448, 0.102500
+DEAL:3d::0.248055, 0.180095, 0.153750
+DEAL:3d::0.260959, 0.200000, 0.153750
+DEAL:3d::0.252032, 0.221552, 0.102500
+DEAL:3d::0.248055, 0.219905, 0.153750
+DEAL:3d::0.221552, 0.252032, 0.102500
+DEAL:3d::0.243105, 0.243105, 0.153750
+DEAL:3d::0.219905, 0.248055, 0.153750
+DEAL:3d::0.200000, 0.260959, 0.153750
+DEAL:3d::0.178448, 0.252032, 0.102500
+DEAL:3d::0.180095, 0.248055, 0.153750
+DEAL:3d::0.156895, 0.243105, 0.153750
+DEAL:3d::0.147968, 0.221552, 0.102500
+DEAL:3d::0.151945, 0.219905, 0.153750
+DEAL:3d::0.139041, 0.200000, 0.153750
+DEAL:3d::0.147968, 0.178448, 0.102500
+DEAL:3d::0.151945, 0.180095, 0.153750
+DEAL:3d::0.156895, 0.156895, 0.153750
+DEAL:3d::0.178448, 0.147968, 0.102500
+DEAL:3d::0.180095, 0.151945, 0.153750
+DEAL:3d::0.200000, 0.139041, 0.153750
+DEAL:3d::0.221552, 0.147968, 0.102500
+DEAL:3d::0.219905, 0.151945, 0.153750
+DEAL:3d::0.243105, 0.156895, 0.153750
+DEAL:3d::0.246148, 0.180885, 0.102500
+DEAL:3d::0.244242, 0.181675, 0.153750
+DEAL:3d::0.254066, 0.200000, 0.153750
+DEAL:3d::0.246148, 0.219115, 0.102500
+DEAL:3d::0.244242, 0.218325, 0.153750
+DEAL:3d::0.219115, 0.246148, 0.102500
+DEAL:3d::0.238230, 0.238230, 0.153750
+DEAL:3d::0.218325, 0.244242, 0.153750
+DEAL:3d::0.200000, 0.254066, 0.153750
+DEAL:3d::0.180885, 0.246148, 0.102500
+DEAL:3d::0.181675, 0.244242, 0.153750
+DEAL:3d::0.161770, 0.238230, 0.153750
+DEAL:3d::0.153852, 0.219115, 0.102500
+DEAL:3d::0.155758, 0.218325, 0.153750
+DEAL:3d::0.145934, 0.200000, 0.153750
+DEAL:3d::0.153852, 0.180885, 0.102500
+DEAL:3d::0.155758, 0.181675, 0.153750
+DEAL:3d::0.161770, 0.161770, 0.153750
+DEAL:3d::0.180885, 0.153852, 0.102500
+DEAL:3d::0.181675, 0.155758, 0.153750
+DEAL:3d::0.200000, 0.145934, 0.153750
+DEAL:3d::0.219115, 0.153852, 0.102500
+DEAL:3d::0.218325, 0.155758, 0.153750
+DEAL:3d::0.238230, 0.161770, 0.153750
+DEAL:3d::0.243460, 0.181998, 0.102500
+DEAL:3d::0.242678, 0.182322, 0.153750
+DEAL:3d::0.250916, 0.200000, 0.153750
+DEAL:3d::0.243460, 0.218002, 0.102500
+DEAL:3d::0.242678, 0.217678, 0.153750
+DEAL:3d::0.218002, 0.243460, 0.102500
+DEAL:3d::0.236003, 0.236003, 0.153750
+DEAL:3d::0.217678, 0.242678, 0.153750
+DEAL:3d::0.200000, 0.250916, 0.153750
+DEAL:3d::0.181998, 0.243460, 0.102500
+DEAL:3d::0.182322, 0.242678, 0.153750
+DEAL:3d::0.163997, 0.236003, 0.153750
+DEAL:3d::0.156540, 0.218002, 0.102500
+DEAL:3d::0.157322, 0.217678, 0.153750
+DEAL:3d::0.149084, 0.200000, 0.153750
+DEAL:3d::0.156540, 0.181998, 0.102500
+DEAL:3d::0.157322, 0.182322, 0.153750
+DEAL:3d::0.163997, 0.163997, 0.153750
+DEAL:3d::0.181998, 0.156540, 0.102500
+DEAL:3d::0.182322, 0.157322, 0.153750
+DEAL:3d::0.200000, 0.149084, 0.153750
+DEAL:3d::0.218002, 0.156540, 0.102500
+DEAL:3d::0.217678, 0.157322, 0.153750
+DEAL:3d::0.236003, 0.163997, 0.153750
+DEAL:3d::0.268284, 0.171716, 0.256250
+DEAL:3d::0.268284, 0.228284, 0.256250
+DEAL:3d::0.228284, 0.268284, 0.256250
+DEAL:3d::0.171716, 0.268284, 0.256250
+DEAL:3d::0.131716, 0.228284, 0.256250
+DEAL:3d::0.131716, 0.171716, 0.256250
+DEAL:3d::0.171716, 0.131716, 0.256250
+DEAL:3d::0.228284, 0.131716, 0.256250
+DEAL:3d::0.262147, 0.174258, 0.205000
+DEAL:3d::0.256009, 0.176800, 0.256250
+DEAL:3d::0.272810, 0.200000, 0.256250
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+DEAL:3d::1.75000, 0.0512500, 0.410000
+DEAL:3d::1.85000, 0.0512500, 0.410000
+DEAL:3d::1.95000, 0.0512500, 0.410000
+DEAL:3d::2.05000, 0.0512500, 0.410000
+DEAL:3d::2.15000, 0.0512500, 0.410000
+DEAL:3d::0.0500000, 0.153750, 0.410000
+DEAL:3d::0.350000, 0.153750, 0.410000
+DEAL:3d::0.450000, 0.153750, 0.410000
+DEAL:3d::0.550000, 0.153750, 0.410000
+DEAL:3d::0.650000, 0.153750, 0.410000
+DEAL:3d::0.750000, 0.153750, 0.410000
+DEAL:3d::0.850000, 0.153750, 0.410000
+DEAL:3d::0.950000, 0.153750, 0.410000
+DEAL:3d::1.05000, 0.153750, 0.410000
+DEAL:3d::1.15000, 0.153750, 0.410000
+DEAL:3d::1.25000, 0.153750, 0.410000
+DEAL:3d::1.35000, 0.153750, 0.410000
+DEAL:3d::1.45000, 0.153750, 0.410000
+DEAL:3d::1.55000, 0.153750, 0.410000
+DEAL:3d::1.65000, 0.153750, 0.410000
+DEAL:3d::1.75000, 0.153750, 0.410000
+DEAL:3d::1.85000, 0.153750, 0.410000
+DEAL:3d::1.95000, 0.153750, 0.410000
+DEAL:3d::2.05000, 0.153750, 0.410000
+DEAL:3d::2.15000, 0.153750, 0.410000
+DEAL:3d::0.0500000, 0.256250, 0.410000
+DEAL:3d::0.350000, 0.256250, 0.410000
+DEAL:3d::0.450000, 0.256250, 0.410000
+DEAL:3d::0.550000, 0.256250, 0.410000
+DEAL:3d::0.650000, 0.256250, 0.410000
+DEAL:3d::0.750000, 0.256250, 0.410000
+DEAL:3d::0.850000, 0.256250, 0.410000
+DEAL:3d::0.950000, 0.256250, 0.410000
+DEAL:3d::1.05000, 0.256250, 0.410000
+DEAL:3d::1.15000, 0.256250, 0.410000
+DEAL:3d::1.25000, 0.256250, 0.410000
+DEAL:3d::1.35000, 0.256250, 0.410000
+DEAL:3d::1.45000, 0.256250, 0.410000
+DEAL:3d::1.55000, 0.256250, 0.410000
+DEAL:3d::1.65000, 0.256250, 0.410000
+DEAL:3d::1.75000, 0.256250, 0.410000
+DEAL:3d::1.85000, 0.256250, 0.410000
+DEAL:3d::1.95000, 0.256250, 0.410000
+DEAL:3d::2.05000, 0.256250, 0.410000
+DEAL:3d::2.15000, 0.256250, 0.410000
+DEAL:3d::0.0500000, 0.358750, 0.410000
+DEAL:3d::0.150000, 0.358750, 0.410000
+DEAL:3d::0.250000, 0.358750, 0.410000
+DEAL:3d::0.350000, 0.358750, 0.410000
+DEAL:3d::0.450000, 0.358750, 0.410000
+DEAL:3d::0.550000, 0.358750, 0.410000
+DEAL:3d::0.650000, 0.358750, 0.410000
+DEAL:3d::0.750000, 0.358750, 0.410000
+DEAL:3d::0.850000, 0.358750, 0.410000
+DEAL:3d::0.950000, 0.358750, 0.410000
+DEAL:3d::1.05000, 0.358750, 0.410000
+DEAL:3d::1.15000, 0.358750, 0.410000
+DEAL:3d::1.25000, 0.358750, 0.410000
+DEAL:3d::1.35000, 0.358750, 0.410000
+DEAL:3d::1.45000, 0.358750, 0.410000
+DEAL:3d::1.55000, 0.358750, 0.410000
+DEAL:3d::1.65000, 0.358750, 0.410000
+DEAL:3d::1.75000, 0.358750, 0.410000
+DEAL:3d::1.85000, 0.358750, 0.410000
+DEAL:3d::1.95000, 0.358750, 0.410000
+DEAL:3d::2.05000, 0.358750, 0.410000
+DEAL:3d::2.15000, 0.358750, 0.410000
+DEAL:3d::0.284142, 0.162733, 0.410000
+DEAL:3d::0.284142, 0.242267, 0.410000
+DEAL:3d::0.239142, 0.287892, 0.410000
+DEAL:3d::0.160858, 0.287892, 0.410000
+DEAL:3d::0.115858, 0.242267, 0.410000
+DEAL:3d::0.115858, 0.162733, 0.410000
+DEAL:3d::0.160858, 0.117108, 0.410000
+DEAL:3d::0.239142, 0.117108, 0.410000
+DEAL:3d::0.262147, 0.174258, 0.410000
+DEAL:3d::0.262147, 0.225742, 0.410000
+DEAL:3d::0.225742, 0.262147, 0.410000
+DEAL:3d::0.174258, 0.262147, 0.410000
+DEAL:3d::0.137853, 0.225742, 0.410000
+DEAL:3d::0.137853, 0.174258, 0.410000
+DEAL:3d::0.174258, 0.137853, 0.410000
+DEAL:3d::0.225742, 0.137853, 0.410000
+DEAL:3d::0.252032, 0.178448, 0.410000
+DEAL:3d::0.252032, 0.221552, 0.410000
+DEAL:3d::0.221552, 0.252032, 0.410000
+DEAL:3d::0.178448, 0.252032, 0.410000
+DEAL:3d::0.147968, 0.221552, 0.410000
+DEAL:3d::0.147968, 0.178448, 0.410000
+DEAL:3d::0.178448, 0.147968, 0.410000
+DEAL:3d::0.221552, 0.147968, 0.410000
+DEAL:3d::0.246148, 0.180885, 0.410000
+DEAL:3d::0.246148, 0.219115, 0.410000
+DEAL:3d::0.219115, 0.246148, 0.410000
+DEAL:3d::0.180885, 0.246148, 0.410000
+DEAL:3d::0.153852, 0.219115, 0.410000
+DEAL:3d::0.153852, 0.180885, 0.410000
+DEAL:3d::0.180885, 0.153852, 0.410000
+DEAL:3d::0.219115, 0.153852, 0.410000
+DEAL:3d::0.243460, 0.181998, 0.410000
+DEAL:3d::0.243460, 0.218002, 0.410000
+DEAL:3d::0.218002, 0.243460, 0.410000
+DEAL:3d::0.181998, 0.243460, 0.410000
+DEAL:3d::0.156540, 0.218002, 0.410000
+DEAL:3d::0.156540, 0.181998, 0.410000
+DEAL:3d::0.181998, 0.156540, 0.410000
+DEAL:3d::0.218002, 0.156540, 0.410000