Three new test cases to verify the transfinite manifold

diff --git a/source/grid/manifold_lib.cc b/source/grid/manifold_lib.cc
index ca94d1a519b71c83de75f505f48b178cb4166264..c61028bc39ccb6f00bd98f6c04f601d69403df32 100644 (file)
--- a/source/grid/manifold_lib.cc
+++ b/source/grid/manifold_lib.cc
@@ -2092,16 +2092,16 @@ TransfiniteInterpolationManifold<dim, spacedim>::pull_back(
       // and we should fail as early as possible. Since we cannot really
       // distinguish the two, we must continue here in any case.
       if (alpha <= 1e-4)
-        return outside;
-      // must_recompute_jacobian = true;
+        must_recompute_jacobian = true;
 
       // update the inverse Jacobian with "Broyden's good method" and
       // Sherman-Morrison formula for the update of the inverse, see
       // https://en.wikipedia.org/wiki/Broyden%27s_method
-      const Tensor<1, dim> delta_x = alpha * update;
+      // J^{-1}_n = J^{-1}_{n-1} + (delta x_n - J^{-1}_{n-1} delta f_n) /
+      // (delta x_n^T J_{-1}_{n-1} delta f_n) delta x_n^T J^{-1}_{n-1}
 
-      // switch sign in residual as compared to the wikipedia article because
-      // we use a negative definition of the residual with respect to the
+      // switch sign in residual as compared to the formula above because we
+      // use a negative definition of the residual with respect to the
       // Jacobian
       const Tensor<1, spacedim> delta_f = old_residual - residual;
 
@@ -2110,8 +2110,12 @@ TransfiniteInterpolationManifold<dim, spacedim>::pull_back(
         for (unsigned int e = 0; e < dim; ++e)
           Jinv_deltaf[e] += inv_grad[d][e] * delta_f[d];
 
-      // prevent division by zero
-      if (delta_x * Jinv_deltaf != 0)
+      const Tensor<1, dim> delta_x = alpha * update;
+
+      // prevent division by zero. This number should be scale-invariant
+      // because Jinv_deltaf carries no units and x is in reference
+      // coordinates.
+      if (std::abs(delta_x * Jinv_deltaf) > 1e-12)
         {
           const Tensor<1, dim> factor =
             (delta_x - Jinv_deltaf) / (delta_x * Jinv_deltaf);
@@ -2345,65 +2349,73 @@ TransfiniteInterpolationManifold<dim, spacedim>::compute_chart_points(
 
 
 
-  auto compute_chart_point = [&](const typename Triangulation<dim, spacedim>::
-                                   cell_iterator &  cell,
-                                 const unsigned int i) {
-    Point<dim> guess;
-    // an optimization: keep track of whether or not we used the affine
-    // approximation so that we don't call pull_back with the same
-    // initial guess twice (i.e., if pull_back fails the first time,
-    // don't try again with the same function arguments).
-    bool used_affine_approximation = false;
-    // if we have already computed three points, we can guess the fourth
-    // to be the missing corner point of a rectangle
-    if (i == 3 && surrounding_points.size() >= 8)
-      guess = chart_points[1] + (chart_points[2] - chart_points[0]);
-    else if (use_structdim_2_guesses && 3 < i)
-      guess = guess_chart_point_structdim_2(i);
-    else if (use_structdim_3_guesses && 4 < i)
-      guess = guess_chart_point_structdim_3(i);
-    else if (dim == 3 && i > 7 && surrounding_points.size() == 26)
-      {
-        if (i < 20)
-          guess =
-            0.5 *
-              chart_points[GeometryInfo<dim>::line_to_cell_vertices(i - 8, 0)] +
-            0.5 *
-              chart_points[GeometryInfo<dim>::line_to_cell_vertices(i - 8, 1)];
-        else
-          guess =
-            0.25 *
-            (chart_points[GeometryInfo<dim>::face_to_cell_vertices(i - 20, 0)] +
-             chart_points[GeometryInfo<dim>::face_to_cell_vertices(i - 20, 1)] +
-             chart_points[GeometryInfo<dim>::face_to_cell_vertices(i - 20, 2)] +
-             chart_points[GeometryInfo<dim>::face_to_cell_vertices(i - 20, 3)]);
-      }
-    else
-      {
-        guess =
-          cell->real_to_unit_cell_affine_approximation(surrounding_points[i]);
-        used_affine_approximation = true;
-      }
-    chart_points[i] = pull_back(cell, surrounding_points[i], guess);
-
-    // the initial guess may not have been good enough: if applicable,
-    // try again with the affine approximation (which is more accurate
-    // than the cheap methods used above)
-    if (chart_points[i][0] == internal::invalid_pull_back_coordinate &&
-        !used_affine_approximation)
-      {
-        guess =
-          cell->real_to_unit_cell_affine_approximation(surrounding_points[i]);
-        chart_points[i] = pull_back(cell, surrounding_points[i], guess);
-      }
+  auto compute_chart_point =
+    [&](const typename Triangulation<dim, spacedim>::cell_iterator &cell,
+        const unsigned int point_index) {
+      Point<dim> guess;
+      // an optimization: keep track of whether or not we used the affine
+      // approximation so that we don't call pull_back with the same
+      // initial guess twice (i.e., if pull_back fails the first time,
+      // don't try again with the same function arguments).
+      bool used_affine_approximation = false;
+      // if we have already computed three points, we can guess the fourth
+      // to be the missing corner point of a rectangle
+      if (point_index == 3 && surrounding_points.size() >= 8)
+        guess = chart_points[1] + (chart_points[2] - chart_points[0]);
+      else if (use_structdim_2_guesses && 3 < point_index)
+        guess = guess_chart_point_structdim_2(point_index);
+      else if (use_structdim_3_guesses && 4 < point_index)
+        guess = guess_chart_point_structdim_3(point_index);
+      else if (dim == 3 && point_index > 7 && surrounding_points.size() == 26)
+        {
+          if (point_index < 20)
+            guess =
+              0.5 * (chart_points[GeometryInfo<dim>::line_to_cell_vertices(
+                       point_index - 8, 0)] +
+                     chart_points[GeometryInfo<dim>::line_to_cell_vertices(
+                       point_index - 8, 1)]);
+          else
+            guess =
+              0.25 * (chart_points[GeometryInfo<dim>::face_to_cell_vertices(
+                        point_index - 20, 0)] +
+                      chart_points[GeometryInfo<dim>::face_to_cell_vertices(
+                        point_index - 20, 1)] +
+                      chart_points[GeometryInfo<dim>::face_to_cell_vertices(
+                        point_index - 20, 2)] +
+                      chart_points[GeometryInfo<dim>::face_to_cell_vertices(
+                        point_index - 20, 3)]);
+        }
+      else
+        {
+          guess = cell->real_to_unit_cell_affine_approximation(
+            surrounding_points[point_index]);
+          used_affine_approximation = true;
+        }
+      chart_points[point_index] =
+        pull_back(cell, surrounding_points[point_index], guess);
+
+      // the initial guess may not have been good enough: if applicable,
+      // try again with the affine approximation (which is more accurate
+      // than the cheap methods used above)
+      if (chart_points[point_index][0] ==
+            internal::invalid_pull_back_coordinate &&
+          !used_affine_approximation)
+        {
+          guess = cell->real_to_unit_cell_affine_approximation(
+            surrounding_points[point_index]);
+          chart_points[point_index] =
+            pull_back(cell, surrounding_points[point_index], guess);
+        }
 
-    if (chart_points[i][0] == internal::invalid_pull_back_coordinate)
-      {
-        for (unsigned int d = 0; d < dim; ++d)
-          guess[d] = 0.5;
-        chart_points[i] = pull_back(cell, surrounding_points[i], guess);
-      }
-  };
+      if (chart_points[point_index][0] ==
+          internal::invalid_pull_back_coordinate)
+        {
+          for (unsigned int d = 0; d < dim; ++d)
+            guess[d] = 0.5;
+          chart_points[point_index] =
+            pull_back(cell, surrounding_points[point_index], guess);
+        }
+    };
 
   // check whether all points are inside the unit cell of the current chart
   for (unsigned int c = 0; c < nearby_cells.size(); ++c)

diff --git a/tests/manifold/transfinite_manifold_08.cc b/tests/manifold/transfinite_manifold_08.cc
new file mode 100644 (file)
index 0000000..2ef1060
--- /dev/null
+++ b/tests/manifold/transfinite_manifold_08.cc
@@ -0,0 +1,146 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 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.
+//
+// ---------------------------------------------------------------------
+
+
+// This test verifies that the transfinite interpolation works on a cylinder
+// with oblique faces
+
+#include <deal.II/grid/grid_reordering.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/tria.h>
+
+#include "../tests.h"
+
+
+int
+main()
+{
+  initlog();
+  deallog << std::setprecision(9);
+
+  const double       radius = 1.;
+  const double       length = 3.;
+  constexpr int      dim    = 3;
+  Triangulation<dim> tria;
+
+  // position of auxiliary point to achieve an angle of 120 degrees in corner
+  // of inner cell
+  const double ycord =
+    0.55 * radius * std::cos(numbers::PI / 12) /
+    (std::sin(numbers::PI / 12) + std::cos(numbers::PI / 12));
+  // vertices for quarter of circle
+  std::vector<Point<3>> vertices{{0, 0, 0},
+                                 {0.55 * radius, 0, 0},
+                                 {ycord, ycord, 0},
+                                 {radius, 0, 0},
+                                 {radius * std::sqrt(0.5),
+                                  radius * std::sqrt(0.5),
+                                  0}};
+
+  // create additional vertices for other three quarters of circle -> gives 17
+  // vertices in total
+  for (unsigned int a = 1; a < 4; ++a)
+    {
+      Tensor<2, 3> transform;
+      transform[0][0] = a == 2 ? -1. : 0;
+      transform[1][0] = a == 2 ? 0 : (a == 1 ? 1 : -1);
+      transform[0][1] = -transform[1][0];
+      transform[1][1] = transform[0][0];
+      transform[2][2] = 1;
+      for (unsigned int i = 1; i < 5; ++i)
+        vertices.push_back(Point<3>(transform * vertices[i]));
+    }
+  const unsigned int n_base_vertices = vertices.size();
+  for (unsigned int i = 0; i < n_base_vertices; ++i)
+    {
+      Point<3> new_point;
+      for (unsigned int d = 0; d < 2; ++d)
+        new_point[d] = vertices[i][d];
+      new_point[2] =
+        length - std::tan(numbers::PI / 8) * std::abs(vertices[i][0]) / radius;
+      vertices.push_back(new_point);
+    }
+
+  // create cells for mesh on z=0; the first four elements are at the
+  // center of the circle
+  std::vector<CellData<3>> cell_data(12);
+  cell_data[0].vertices[0] = 0;
+  cell_data[0].vertices[1] = 1;
+  cell_data[0].vertices[2] = 5;
+  cell_data[0].vertices[3] = 2;
+  cell_data[1].vertices[0] = 9;
+  cell_data[1].vertices[1] = 0;
+  cell_data[1].vertices[2] = 6;
+  cell_data[1].vertices[3] = 5;
+  cell_data[2].vertices[0] = 10;
+  cell_data[2].vertices[1] = 13;
+  cell_data[2].vertices[2] = 9;
+  cell_data[2].vertices[3] = 0;
+  cell_data[3].vertices[0] = 13;
+  cell_data[3].vertices[1] = 14;
+  cell_data[3].vertices[2] = 0;
+  cell_data[3].vertices[3] = 1;
+
+  // the next 8 elements describe the rim; we take one quarter of the circle
+  // in each loop iteration
+  for (unsigned int a = 0; a < 4; ++a)
+    {
+      cell_data[4 + a * 2].vertices[0] = 1 + a * 4;
+      cell_data[4 + a * 2].vertices[1] = 3 + a * 4;
+      cell_data[4 + a * 2].vertices[2] = 2 + a * 4;
+      cell_data[4 + a * 2].vertices[3] = 4 + a * 4;
+      cell_data[5 + a * 2].vertices[0] = 2 + a * 4;
+      cell_data[5 + a * 2].vertices[1] = 4 + a * 4;
+      AssertIndexRange(4 + a * 4, vertices.size());
+      cell_data[5 + a * 2].vertices[2] = a == 3 ? 1 : 5 + a * 4;
+      cell_data[5 + a * 2].vertices[3] = a == 3 ? 3 : 7 + a * 4;
+    }
+
+  // create extrusion of the base mesh
+  for (unsigned int i = 0; i < cell_data.size(); ++i)
+    for (unsigned int v = 0; v < 4; ++v)
+      cell_data[i].vertices[4 + v] = n_base_vertices + cell_data[i].vertices[v];
+
+  SubCellData subcell_data;
+  tria.create_triangulation(vertices, cell_data, subcell_data);
+
+  // set manifolds on circumferential direction (face ids between 0 and 4)
+  tria.set_all_manifold_ids(1);
+  for (auto &cell : tria.active_cell_iterators())
+    for (unsigned int f = 0; f < 4; ++f)
+      if (cell->at_boundary(f))
+        cell->face(f)->set_all_manifold_ids(2);
+
+  // attach 3 cylindrical manifolds to mesh
+  tria.set_manifold(2,
+                    CylindricalManifold<dim>(Point<dim>{0, 0, 1},
+                                             Point<dim>{0, 0, 0}));
+  TransfiniteInterpolationManifold<dim> transfinite;
+  transfinite.initialize(tria);
+  tria.set_manifold(1, transfinite);
+
+  for (unsigned int l = 0; l < 2; ++l)
+    {
+      for (auto &cell : tria.active_cell_iterators())
+        {
+          deallog << "Face centers:" << std::endl;
+          for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
+            deallog << cell->face(f)->center(true) << std::endl;
+          deallog << std::endl;
+        }
+      tria.refine_global();
+    }
+}

diff --git a/tests/manifold/transfinite_manifold_08.output b/tests/manifold/transfinite_manifold_08.output
new file mode 100644 (file)
index 0000000..771e783
--- /dev/null
+++ b/tests/manifold/transfinite_manifold_08.output
@@ -0,0 +1,865 @@
+
+DEAL::Face centers:
+DEAL::-5.30227280e-16 0.275000000 1.50000000
+DEAL::0.491885662 0.216885662 1.39812714
+DEAL::0.275000000 2.18441115e-16 1.44304564
+DEAL::0.216885662 0.491885662 1.45508151
+DEAL::0.245942831 0.245942831 -1.37045863e-16
+DEAL::0.245942831 0.245942831 2.89812714
+DEAL::
+DEAL::Face centers:
+DEAL::-0.491885662 0.216885662 1.39812714
+DEAL::-5.30227280e-16 0.275000000 1.50000000
+DEAL::-0.275000000 1.39701736e-15 1.44304564
+DEAL::-0.216885662 0.491885662 1.45508151
+DEAL::-0.245942831 0.245942831 -9.14863125e-15
+DEAL::-0.245942831 0.245942831 2.89812714
+DEAL::
+DEAL::Face centers:
+DEAL::-0.491885662 -0.216885662 1.39812714
+DEAL::4.80570453e-15 -0.275000000 1.50000000
+DEAL::-0.216885662 -0.491885662 1.45508151
+DEAL::-0.275000000 1.39701736e-15 1.44304564
+DEAL::-0.245942831 -0.245942831 8.47816049e-15
+DEAL::-0.245942831 -0.245942831 2.89812714
+DEAL::
+DEAL::Face centers:
+DEAL::4.80570453e-15 -0.275000000 1.50000000
+DEAL::0.491885662 -0.216885662 1.39812714
+DEAL::0.216885662 -0.491885662 1.45508151
+DEAL::0.275000000 2.18441115e-16 1.44304564
+DEAL::0.245942831 -0.245942831 -9.01166560e-15
+DEAL::0.245942831 -0.245942831 2.89812714
+DEAL::
+DEAL::Face centers:
+DEAL::0.491885662 0.216885662 1.39812714
+DEAL::0.923879533 0.382683432 1.32322330
+DEAL::0.775000000 1.29803225e-12 1.33949224
+DEAL::0.570439053 0.570439053 1.38185820
+DEAL::0.707882597 0.299784547 4.89758830e-18
+DEAL::0.707882597 0.299784547 2.72135045
+DEAL::
+DEAL::Face centers:
+DEAL::0.216885662 0.491885662 1.45508151
+DEAL::0.382683432 0.923879533 1.42677670
+DEAL::0.570439053 0.570439053 1.38185820
+DEAL::-1.27183200e-12 0.775000000 1.50000000
+DEAL::0.299784547 0.707882597 5.24541063e-15
+DEAL::0.299784547 0.707882597 2.88185820
+DEAL::
+DEAL::Face centers:
+DEAL::-0.216885662 0.491885662 1.45508151
+DEAL::-0.382683432 0.923879533 1.42677670
+DEAL::-1.27183200e-12 0.775000000 1.50000000
+DEAL::-0.570439053 0.570439053 1.38185820
+DEAL::-0.299784547 0.707882597 -3.20075600e-15
+DEAL::-0.299784547 0.707882597 2.88185820
+DEAL::
+DEAL::Face centers:
+DEAL::-0.491885662 0.216885662 1.39812714
+DEAL::-0.923879533 0.382683432 1.32322330
+DEAL::-0.570439053 0.570439053 1.38185820
+DEAL::-0.775000000 -1.29805149e-12 1.33949224
+DEAL::-0.707882597 0.299784547 -1.88042954e-20
+DEAL::-0.707882597 0.299784547 2.72135045
+DEAL::
+DEAL::Face centers:
+DEAL::-0.491885662 -0.216885662 1.39812714
+DEAL::-0.923879533 -0.382683432 1.32322330
+DEAL::-0.775000000 -1.29805149e-12 1.33949224
+DEAL::-0.570439053 -0.570439053 1.38185820
+DEAL::-0.707882597 -0.299784547 -6.83084261e-20
+DEAL::-0.707882597 -0.299784547 2.72135045
+DEAL::
+DEAL::Face centers:
+DEAL::-0.216885662 -0.491885662 1.45508151
+DEAL::-0.382683432 -0.923879533 1.42677670
+DEAL::-0.570439053 -0.570439053 1.38185820
+DEAL::1.27205404e-12 -0.775000000 1.50000000
+DEAL::-0.299784547 -0.707882597 3.20049840e-15
+DEAL::-0.299784547 -0.707882597 2.88185820
+DEAL::
+DEAL::Face centers:
+DEAL::0.216885662 -0.491885662 1.45508151
+DEAL::0.382683432 -0.923879533 1.42677670
+DEAL::1.27205404e-12 -0.775000000 1.50000000
+DEAL::0.570439053 -0.570439053 1.38185820
+DEAL::0.299784547 -0.707882597 -3.20075600e-15
+DEAL::0.299784547 -0.707882597 2.88185820
+DEAL::
+DEAL::Face centers:
+DEAL::0.491885662 -0.216885662 1.39812714
+DEAL::0.923879533 -0.382683432 1.32322330
+DEAL::0.570439053 -0.570439053 1.38185820
+DEAL::0.775000000 1.29803225e-12 1.33949224
+DEAL::0.707882597 -0.299784547 -3.36413850e-21
+DEAL::0.707882597 -0.299784547 2.72135045
+DEAL::
+DEAL::Face centers:
+DEAL::0.00000000 0.137500000 0.750000000
+DEAL::0.260471416 0.122971416 0.723027302
+DEAL::0.137500000 -4.62690180e-16 0.735761409
+DEAL::0.122971416 0.260471416 0.737265893
+DEAL::0.130235708 0.130235708 4.78157171e-15
+DEAL::0.130235708 0.130235708 1.47302730
+DEAL::
+DEAL::Face centers:
+DEAL::0.260471416 0.122971416 0.723027302
+DEAL::0.520942831 0.108442831 0.696054604
+DEAL::0.412500000 0.00000000 0.707284226
+DEAL::0.368914247 0.231414247 0.711797679
+DEAL::0.390707123 0.115707123 2.10191468e-15
+DEAL::0.390707123 0.115707123 1.41908191
+DEAL::
+DEAL::Face centers:
+DEAL::-3.15595785e-16 0.412500000 0.750000000
+DEAL::0.231414247 0.368914247 0.726036270
+DEAL::0.122971416 0.260471416 0.737265893
+DEAL::0.108442831 0.520942831 0.738770377
+DEAL::0.115707123 0.390707123 0.00000000
+DEAL::0.115707123 0.390707123 1.47603627
+DEAL::
+DEAL::Face centers:
+DEAL::0.231414247 0.368914247 0.726036270
+DEAL::0.462828493 0.325328493 0.702072540
+DEAL::0.368914247 0.231414247 0.711797679
+DEAL::0.325328493 0.462828493 0.716311131
+DEAL::0.347121370 0.347121370 -2.88404277e-28
+DEAL::0.347121370 0.347121370 1.42810881
+DEAL::
+DEAL::Face centers:
+DEAL::4.12652653e-16 0.137500000 2.25000000
+DEAL::0.260471416 0.122971416 2.16908191
+DEAL::0.137500000 0.00000000 2.20728423
+DEAL::0.122971416 0.260471416 2.21179768
+DEAL::0.130235708 0.130235708 1.47302730
+DEAL::0.130235708 0.130235708 2.94605460
+DEAL::
+DEAL::Face centers:
+DEAL::0.260471416 0.122971416 2.16908191
+DEAL::0.520942831 0.108442831 2.08816381
+DEAL::0.412500000 5.05415827e-13 2.12185268
+DEAL::0.368914247 0.231414247 2.13539304
+DEAL::0.390707123 0.115707123 1.41908191
+DEAL::0.390707123 0.115707123 2.83816381
+DEAL::
+DEAL::Face centers:
+DEAL::-5.13348455e-13 0.412500000 2.25000000
+DEAL::0.231414247 0.368914247 2.17810881
+DEAL::0.122971416 0.260471416 2.21179768
+DEAL::0.108442831 0.520942831 2.21631113
+DEAL::0.115707123 0.390707123 1.47603627
+DEAL::0.115707123 0.390707123 2.95207254
+DEAL::
+DEAL::Face centers:
+DEAL::0.231414247 0.368914247 2.17810881
+DEAL::0.462828493 0.325328493 2.10621762
+DEAL::0.368914247 0.231414247 2.13539304
+DEAL::0.325328493 0.462828493 2.14893339
+DEAL::0.347121370 0.347121370 1.42810881
+DEAL::0.347121370 0.347121370 2.85621762
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 0.108442831 0.696054604
+DEAL::-0.260471416 0.122971416 0.723027302
+DEAL::-0.412500000 -4.93226320e-13 0.707284226
+DEAL::-0.368914247 0.231414247 0.711797679
+DEAL::-0.390707123 0.115707123 4.64289854e-15
+DEAL::-0.390707123 0.115707123 1.41908191
+DEAL::
+DEAL::Face centers:
+DEAL::-0.260471416 0.122971416 0.723027302
+DEAL::0.00000000 0.137500000 0.750000000
+DEAL::-0.137500000 1.01078312e-15 0.735761409
+DEAL::-0.122971416 0.260471416 0.737265893
+DEAL::-0.130235708 0.130235708 9.06618681e-15
+DEAL::-0.130235708 0.130235708 1.47302730
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 0.325328493 0.702072540
+DEAL::-0.231414247 0.368914247 0.726036270
+DEAL::-0.368914247 0.231414247 0.711797679
+DEAL::-0.325328493 0.462828493 0.716311131
+DEAL::-0.347121370 0.347121370 -4.48665788e-15
+DEAL::-0.347121370 0.347121370 1.42810881
+DEAL::
+DEAL::Face centers:
+DEAL::-0.231414247 0.368914247 0.726036270
+DEAL::-3.15595785e-16 0.412500000 0.750000000
+DEAL::-0.122971416 0.260471416 0.737265893
+DEAL::-0.108442831 0.520942831 0.738770377
+DEAL::-0.115707123 0.390707123 4.54235320e-15
+DEAL::-0.115707123 0.390707123 1.47603627
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 0.108442831 2.08816381
+DEAL::-0.260471416 0.122971416 2.16908191
+DEAL::-0.412500000 4.95027443e-13 2.12185268
+DEAL::-0.368914247 0.231414247 2.13539304
+DEAL::-0.390707123 0.115707123 1.41908191
+DEAL::-0.390707123 0.115707123 2.83816381
+DEAL::
+DEAL::Face centers:
+DEAL::-0.260471416 0.122971416 2.16908191
+DEAL::4.12652653e-16 0.137500000 2.25000000
+DEAL::-0.137500000 9.68081742e-16 2.20728423
+DEAL::-0.122971416 0.260471416 2.21179768
+DEAL::-0.130235708 0.130235708 1.47302730
+DEAL::-0.130235708 0.130235708 2.94605460
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 0.325328493 2.10621762
+DEAL::-0.231414247 0.368914247 2.17810881
+DEAL::-0.368914247 0.231414247 2.13539304
+DEAL::-0.325328493 0.462828493 2.14893339
+DEAL::-0.347121370 0.347121370 1.42810881
+DEAL::-0.347121370 0.347121370 2.85621762
+DEAL::
+DEAL::Face centers:
+DEAL::-0.231414247 0.368914247 2.17810881
+DEAL::-5.13348455e-13 0.412500000 2.25000000
+DEAL::-0.122971416 0.260471416 2.21179768
+DEAL::-0.108442831 0.520942831 2.21631113
+DEAL::-0.115707123 0.390707123 1.47603627
+DEAL::-0.115707123 0.390707123 2.95207254
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 -0.325328493 0.702072540
+DEAL::-0.231414247 -0.368914247 0.726036270
+DEAL::-0.325328493 -0.462828493 0.716311131
+DEAL::-0.368914247 -0.231414247 0.711797679
+DEAL::-0.347121370 -0.347121370 8.88131786e-15
+DEAL::-0.347121370 -0.347121370 1.42810881
+DEAL::
+DEAL::Face centers:
+DEAL::-0.231414247 -0.368914247 0.726036270
+DEAL::5.25661235e-13 -0.412500000 0.750000000
+DEAL::-0.108442831 -0.520942831 0.738770377
+DEAL::-0.122971416 -0.260471416 0.737265893
+DEAL::-0.115707123 -0.390707123 1.79927373e-14
+DEAL::-0.115707123 -0.390707123 1.47603627
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 -0.108442831 0.696054604
+DEAL::-0.260471416 -0.122971416 0.723027302
+DEAL::-0.368914247 -0.231414247 0.711797679
+DEAL::-0.412500000 -4.93226320e-13 0.707284226
+DEAL::-0.390707123 -0.115707123 1.67760332e-14
+DEAL::-0.390707123 -0.115707123 1.41908191
+DEAL::
+DEAL::Face centers:
+DEAL::-0.260471416 -0.122971416 0.723027302
+DEAL::-4.45339299e-15 -0.137500000 0.750000000
+DEAL::-0.122971416 -0.260471416 0.737265893
+DEAL::-0.137500000 1.01078312e-15 0.735761409
+DEAL::-0.130235708 -0.130235708 8.86183199e-15
+DEAL::-0.130235708 -0.130235708 1.47302730
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 -0.325328493 2.10621762
+DEAL::-0.231414247 -0.368914247 2.17810881
+DEAL::-0.325328493 -0.462828493 2.14893339
+DEAL::-0.368914247 -0.231414247 2.13539304
+DEAL::-0.347121370 -0.347121370 1.42810881
+DEAL::-0.347121370 -0.347121370 2.85621762
+DEAL::
+DEAL::Face centers:
+DEAL::-0.231414247 -0.368914247 2.17810881
+DEAL::-5.18724356e-13 -0.412500000 2.25000000
+DEAL::-0.108442831 -0.520942831 2.21631113
+DEAL::-0.122971416 -0.260471416 2.21179768
+DEAL::-0.115707123 -0.390707123 1.47603627
+DEAL::-0.115707123 -0.390707123 2.95207254
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 -0.108442831 2.08816381
+DEAL::-0.260471416 -0.122971416 2.16908191
+DEAL::-0.368914247 -0.231414247 2.13539304
+DEAL::-0.412500000 4.95027443e-13 2.12185268
+DEAL::-0.390707123 -0.115707123 1.41908191
+DEAL::-0.390707123 -0.115707123 2.83816381
+DEAL::
+DEAL::Face centers:
+DEAL::-0.260471416 -0.122971416 2.16908191
+DEAL::-2.25561463e-15 -0.137500000 2.25000000
+DEAL::-0.122971416 -0.260471416 2.21179768
+DEAL::-0.137500000 9.68081742e-16 2.20728423
+DEAL::-0.130235708 -0.130235708 1.47302730
+DEAL::-0.130235708 -0.130235708 2.94605460
+DEAL::
+DEAL::Face centers:
+DEAL::5.25661235e-13 -0.412500000 0.750000000
+DEAL::0.231414247 -0.368914247 0.726036270
+DEAL::0.108442831 -0.520942831 0.738770377
+DEAL::0.122971416 -0.260471416 0.737265893
+DEAL::0.115707123 -0.390707123 0.00000000
+DEAL::0.115707123 -0.390707123 1.47603627
+DEAL::
+DEAL::Face centers:
+DEAL::0.231414247 -0.368914247 0.726036270
+DEAL::0.462828493 -0.325328493 0.702072540
+DEAL::0.325328493 -0.462828493 0.716311131
+DEAL::0.368914247 -0.231414247 0.711797679
+DEAL::0.347121370 -0.347121370 -4.69954171e-15
+DEAL::0.347121370 -0.347121370 1.42810881
+DEAL::
+DEAL::Face centers:
+DEAL::-4.45339299e-15 -0.137500000 0.750000000
+DEAL::0.260471416 -0.122971416 0.723027302
+DEAL::0.122971416 -0.260471416 0.737265893
+DEAL::0.137500000 -4.62690180e-16 0.735761409
+DEAL::0.130235708 -0.130235708 8.62667606e-15
+DEAL::0.130235708 -0.130235708 1.47302730
+DEAL::
+DEAL::Face centers:
+DEAL::0.260471416 -0.122971416 0.723027302
+DEAL::0.520942831 -0.108442831 0.696054604
+DEAL::0.368914247 -0.231414247 0.711797679
+DEAL::0.412500000 0.00000000 0.707284226
+DEAL::0.390707123 -0.115707123 4.05482801e-15
+DEAL::0.390707123 -0.115707123 1.41908191
+DEAL::
+DEAL::Face centers:
+DEAL::-5.18724356e-13 -0.412500000 2.25000000
+DEAL::0.231414247 -0.368914247 2.17810881
+DEAL::0.108442831 -0.520942831 2.21631113
+DEAL::0.122971416 -0.260471416 2.21179768
+DEAL::0.115707123 -0.390707123 1.47603627
+DEAL::0.115707123 -0.390707123 2.95207254
+DEAL::
+DEAL::Face centers:
+DEAL::0.231414247 -0.368914247 2.17810881
+DEAL::0.462828493 -0.325328493 2.10621762
+DEAL::0.325328493 -0.462828493 2.14893339
+DEAL::0.368914247 -0.231414247 2.13539304
+DEAL::0.347121370 -0.347121370 1.42810881
+DEAL::0.347121370 -0.347121370 2.85621762
+DEAL::
+DEAL::Face centers:
+DEAL::-2.25561463e-15 -0.137500000 2.25000000
+DEAL::0.260471416 -0.122971416 2.16908191
+DEAL::0.122971416 -0.260471416 2.21179768
+DEAL::0.137500000 0.00000000 2.20728423
+DEAL::0.130235708 -0.130235708 1.47302730
+DEAL::0.130235708 -0.130235708 2.94605460
+DEAL::
+DEAL::Face centers:
+DEAL::0.260471416 -0.122971416 2.16908191
+DEAL::0.520942831 -0.108442831 2.08816381
+DEAL::0.368914247 -0.231414247 2.13539304
+DEAL::0.412500000 5.05415827e-13 2.12185268
+DEAL::0.390707123 -0.115707123 1.41908191
+DEAL::0.390707123 -0.115707123 2.83816381
+DEAL::
+DEAL::Face centers:
+DEAL::0.520942831 0.108442831 0.696054604
+DEAL::0.750864056 0.151766577 0.675041867
+DEAL::0.662500000 2.19576823e-12 0.681395879
+DEAL::0.599884130 0.258335105 0.689700592
+DEAL::0.635903443 0.130104704 -2.09755240e-18
+DEAL::0.635903443 0.130104704 1.37109647
+DEAL::
+DEAL::Face centers:
+DEAL::0.750864056 0.151766577 0.675041867
+DEAL::0.980785280 0.195090322 0.654029131
+DEAL::0.887500000 1.08765619e-12 0.658096366
+DEAL::0.815881065 0.341233990 0.670974632
+DEAL::0.865824668 0.173428449 2.18504223e-14
+DEAL::0.865824668 0.173428449 1.32907100
+DEAL::
+DEAL::Face centers:
+DEAL::0.462828493 0.325328493 0.702072540
+DEAL::0.647149053 0.440449363 0.685633357
+DEAL::0.599884130 0.258335105 0.689700592
+DEAL::0.502105188 0.502105188 0.698005305
+DEAL::0.554988773 0.382888928 7.44911645e-15
+DEAL::0.554988773 0.382888928 1.38770590
+DEAL::
+DEAL::Face centers:
+DEAL::0.647149053 0.440449363 0.685633357
+DEAL::0.831469612 0.555570233 0.669194174
+DEAL::0.815881065 0.341233990 0.670974632
+DEAL::0.638772917 0.638772917 0.683852899
+DEAL::0.739309332 0.498009798 1.96559562e-14
+DEAL::0.739309332 0.498009798 1.35482753
+DEAL::
+DEAL::Face centers:
+DEAL::0.520942831 0.108442831 2.08816381
+DEAL::0.750864056 0.151766577 2.02512560
+DEAL::0.662500000 1.58504737e-12 2.04418764
+DEAL::0.599884130 0.258335105 2.06910178
+DEAL::0.635903443 0.130104704 1.37109647
+DEAL::0.635903443 0.130104704 2.74219294
+DEAL::
+DEAL::Face centers:
+DEAL::0.750864056 0.151766577 2.02512560
+DEAL::0.980785280 0.195090322 1.96208739
+DEAL::0.887500000 1.46303299e-12 1.97428910
+DEAL::0.815881065 0.341233990 2.01292390
+DEAL::0.865824668 0.173428449 1.32907100
+DEAL::0.865824668 0.173428449 2.65814200
+DEAL::
+DEAL::Face centers:
+DEAL::0.462828493 0.325328493 2.10621762
+DEAL::0.647149053 0.440449363 2.05690007
+DEAL::0.599884130 0.258335105 2.06910178
+DEAL::0.502105188 0.502105188 2.09401592
+DEAL::0.554988773 0.382888928 1.38770590
+DEAL::0.554988773 0.382888928 2.77541179
+DEAL::
+DEAL::Face centers:
+DEAL::0.647149053 0.440449363 2.05690007
+DEAL::0.831469612 0.555570233 2.00758252
+DEAL::0.815881065 0.341233990 2.01292390
+DEAL::0.638772917 0.638772917 2.05155870
+DEAL::0.739309332 0.498009798 1.35482753
+DEAL::0.739309332 0.498009798 2.70965506
+DEAL::
+DEAL::Face centers:
+DEAL::0.325328493 0.462828493 0.716311131
+DEAL::0.440449363 0.647149053 0.705696826
+DEAL::0.502105188 0.502105188 0.698005305
+DEAL::0.258335105 0.599884130 0.724002653
+DEAL::0.382888928 0.554988773 4.66840596e-16
+DEAL::0.382888928 0.554988773 1.42200796
+DEAL::
+DEAL::Face centers:
+DEAL::0.440449363 0.647149053 0.705696826
+DEAL::0.555570233 0.831469612 0.695082521
+DEAL::0.638772917 0.638772917 0.683852899
+DEAL::0.341233990 0.815881065 0.716926449
+DEAL::0.498009798 0.739309332 6.04635250e-15
+DEAL::0.498009798 0.739309332 1.40077935
+DEAL::
+DEAL::Face centers:
+DEAL::0.108442831 0.520942831 0.738770377
+DEAL::0.151766577 0.750864056 0.735232275
+DEAL::0.258335105 0.599884130 0.724002653
+DEAL::-2.26573725e-12 0.662500000 0.750000000
+DEAL::0.130104704 0.635903443 8.50827542e-16
+DEAL::0.130104704 0.635903443 1.47400265
+DEAL::
+DEAL::Face centers:
+DEAL::0.151766577 0.750864056 0.735232275
+DEAL::0.195090322 0.980785280 0.731694174
+DEAL::0.341233990 0.815881065 0.716926449
+DEAL::-1.10370101e-12 0.887500000 0.750000000
+DEAL::0.173428449 0.865824668 -6.19424954e-16
+DEAL::0.173428449 0.865824668 1.46692645
+DEAL::
+DEAL::Face centers:
+DEAL::0.325328493 0.462828493 2.14893339
+DEAL::0.440449363 0.647149053 2.11709048
+DEAL::0.502105188 0.502105188 2.09401592
+DEAL::0.258335105 0.599884130 2.17200796
+DEAL::0.382888928 0.554988773 1.42200796
+DEAL::0.382888928 0.554988773 2.84401592
+DEAL::
+DEAL::Face centers:
+DEAL::0.440449363 0.647149053 2.11709048
+DEAL::0.555570233 0.831469612 2.08524756
+DEAL::0.638772917 0.638772917 2.05155870
+DEAL::0.341233990 0.815881065 2.15077935
+DEAL::0.498009798 0.739309332 1.40077935
+DEAL::0.498009798 0.739309332 2.80155870
+DEAL::
+DEAL::Face centers:
+DEAL::0.108442831 0.520942831 2.21631113
+DEAL::0.151766577 0.750864056 2.20569683
+DEAL::0.258335105 0.599884130 2.17200796
+DEAL::-1.55226695e-12 0.662500000 2.25000000
+DEAL::0.130104704 0.635903443 1.47400265
+DEAL::0.130104704 0.635903443 2.94800531
+DEAL::
+DEAL::Face centers:
+DEAL::0.151766577 0.750864056 2.20569683
+DEAL::0.195090322 0.980785280 2.19508252
+DEAL::0.341233990 0.815881065 2.15077935
+DEAL::-1.60935195e-12 0.887500000 2.25000000
+DEAL::0.173428449 0.865824668 1.46692645
+DEAL::0.173428449 0.865824668 2.93385290
+DEAL::
+DEAL::Face centers:
+DEAL::-0.108442831 0.520942831 0.738770377
+DEAL::-0.151766577 0.750864056 0.735232275
+DEAL::-2.26573725e-12 0.662500000 0.750000000
+DEAL::-0.258335105 0.599884130 0.724002653
+DEAL::-0.130104704 0.635903443 0.00000000
+DEAL::-0.130104704 0.635903443 1.47400265
+DEAL::
+DEAL::Face centers:
+DEAL::-0.151766577 0.750864056 0.735232275
+DEAL::-0.195090322 0.980785280 0.731694174
+DEAL::-1.10370101e-12 0.887500000 0.750000000
+DEAL::-0.341233990 0.815881065 0.716926449
+DEAL::-0.173428449 0.865824668 -8.36325190e-17
+DEAL::-0.173428449 0.865824668 1.46692645
+DEAL::
+DEAL::Face centers:
+DEAL::-0.325328493 0.462828493 0.716311131
+DEAL::-0.440449363 0.647149053 0.705696826
+DEAL::-0.258335105 0.599884130 0.724002653
+DEAL::-0.502105188 0.502105188 0.698005305
+DEAL::-0.382888928 0.554988773 -1.58579428e-15
+DEAL::-0.382888928 0.554988773 1.42200796
+DEAL::
+DEAL::Face centers:
+DEAL::-0.440449363 0.647149053 0.705696826
+DEAL::-0.555570233 0.831469612 0.695082521
+DEAL::-0.341233990 0.815881065 0.716926449
+DEAL::-0.638772917 0.638772917 0.683852899
+DEAL::-0.498009798 0.739309332 -2.72526873e-15
+DEAL::-0.498009798 0.739309332 1.40077935
+DEAL::
+DEAL::Face centers:
+DEAL::-0.108442831 0.520942831 2.21631113
+DEAL::-0.151766577 0.750864056 2.20569683
+DEAL::-1.55226695e-12 0.662500000 2.25000000
+DEAL::-0.258335105 0.599884130 2.17200796
+DEAL::-0.130104704 0.635903443 1.47400265
+DEAL::-0.130104704 0.635903443 2.94800531
+DEAL::
+DEAL::Face centers:
+DEAL::-0.151766577 0.750864056 2.20569683
+DEAL::-0.195090322 0.980785280 2.19508252
+DEAL::-1.60935195e-12 0.887500000 2.25000000
+DEAL::-0.341233990 0.815881065 2.15077935
+DEAL::-0.173428449 0.865824668 1.46692645
+DEAL::-0.173428449 0.865824668 2.93385290
+DEAL::
+DEAL::Face centers:
+DEAL::-0.325328493 0.462828493 2.14893339
+DEAL::-0.440449363 0.647149053 2.11709048
+DEAL::-0.258335105 0.599884130 2.17200796
+DEAL::-0.502105188 0.502105188 2.09401592
+DEAL::-0.382888928 0.554988773 1.42200796
+DEAL::-0.382888928 0.554988773 2.84401592
+DEAL::
+DEAL::Face centers:
+DEAL::-0.440449363 0.647149053 2.11709048
+DEAL::-0.555570233 0.831469612 2.08524756
+DEAL::-0.341233990 0.815881065 2.15077935
+DEAL::-0.638772917 0.638772917 2.05155870
+DEAL::-0.498009798 0.739309332 1.40077935
+DEAL::-0.498009798 0.739309332 2.80155870
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 0.325328493 0.702072540
+DEAL::-0.647149053 0.440449363 0.685633357
+DEAL::-0.502105188 0.502105188 0.698005305
+DEAL::-0.599884130 0.258335105 0.689700592
+DEAL::-0.554988773 0.382888928 0.00000000
+DEAL::-0.554988773 0.382888928 1.38770590
+DEAL::
+DEAL::Face centers:
+DEAL::-0.647149053 0.440449363 0.685633357
+DEAL::-0.831469612 0.555570233 0.669194174
+DEAL::-0.638772917 0.638772917 0.683852899
+DEAL::-0.815881065 0.341233990 0.670974632
+DEAL::-0.739309332 0.498009798 2.23654328e-14
+DEAL::-0.739309332 0.498009798 1.35482753
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 0.108442831 0.696054604
+DEAL::-0.750864056 0.151766577 0.675041867
+DEAL::-0.599884130 0.258335105 0.689700592
+DEAL::-0.662500000 -2.19575242e-12 0.681395879
+DEAL::-0.635903443 0.130104704 7.28623094e-15
+DEAL::-0.635903443 0.130104704 1.37109647
+DEAL::
+DEAL::Face centers:
+DEAL::-0.750864056 0.151766577 0.675041867
+DEAL::-0.980785280 0.195090322 0.654029131
+DEAL::-0.815881065 0.341233990 0.670974632
+DEAL::-0.887500000 -1.08762905e-12 0.658096366
+DEAL::-0.865824668 0.173428449 -3.27215932e-15
+DEAL::-0.865824668 0.173428449 1.32907100
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 0.325328493 2.10621762
+DEAL::-0.647149053 0.440449363 2.05690007
+DEAL::-0.502105188 0.502105188 2.09401592
+DEAL::-0.599884130 0.258335105 2.06910178
+DEAL::-0.554988773 0.382888928 1.38770590
+DEAL::-0.554988773 0.382888928 2.77541179
+DEAL::
+DEAL::Face centers:
+DEAL::-0.647149053 0.440449363 2.05690007
+DEAL::-0.831469612 0.555570233 2.00758252
+DEAL::-0.638772917 0.638772917 2.05155870
+DEAL::-0.815881065 0.341233990 2.01292390
+DEAL::-0.739309332 0.498009798 1.35482753
+DEAL::-0.739309332 0.498009798 2.70965506
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 0.108442831 2.08816381
+DEAL::-0.750864056 0.151766577 2.02512560
+DEAL::-0.599884130 0.258335105 2.06910178
+DEAL::-0.662500000 -1.58503801e-12 2.04418764
+DEAL::-0.635903443 0.130104704 1.37109647
+DEAL::-0.635903443 0.130104704 2.74219294
+DEAL::
+DEAL::Face centers:
+DEAL::-0.750864056 0.151766577 2.02512560
+DEAL::-0.980785280 0.195090322 1.96208739
+DEAL::-0.815881065 0.341233990 2.01292390
+DEAL::-0.887500000 -1.46301296e-12 1.97428910
+DEAL::-0.865824668 0.173428449 1.32907100
+DEAL::-0.865824668 0.173428449 2.65814200
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 -0.108442831 0.696054604
+DEAL::-0.750864056 -0.151766577 0.675041867
+DEAL::-0.662500000 -2.19575242e-12 0.681395879
+DEAL::-0.599884130 -0.258335105 0.689700592
+DEAL::-0.635903443 -0.130104704 -5.10608442e-15
+DEAL::-0.635903443 -0.130104704 1.37109647
+DEAL::
+DEAL::Face centers:
+DEAL::-0.750864056 -0.151766577 0.675041867
+DEAL::-0.980785280 -0.195090322 0.654029131
+DEAL::-0.887500000 -1.08762905e-12 0.658096366
+DEAL::-0.815881065 -0.341233990 0.670974632
+DEAL::-0.865824668 -0.173428449 3.44178996e-14
+DEAL::-0.865824668 -0.173428449 1.32907100
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 -0.325328493 0.702072540
+DEAL::-0.647149053 -0.440449363 0.685633357
+DEAL::-0.599884130 -0.258335105 0.689700592
+DEAL::-0.502105188 -0.502105188 0.698005305
+DEAL::-0.554988773 -0.382888928 7.44490461e-15
+DEAL::-0.554988773 -0.382888928 1.38770590
+DEAL::
+DEAL::Face centers:
+DEAL::-0.647149053 -0.440449363 0.685633357
+DEAL::-0.831469612 -0.555570233 0.669194174
+DEAL::-0.815881065 -0.341233990 0.670974632
+DEAL::-0.638772917 -0.638772917 0.683852899
+DEAL::-0.739309332 -0.498009798 1.96497323e-14
+DEAL::-0.739309332 -0.498009798 1.35482753
+DEAL::
+DEAL::Face centers:
+DEAL::-0.520942831 -0.108442831 2.08816381
+DEAL::-0.750864056 -0.151766577 2.02512560
+DEAL::-0.662500000 -1.58503801e-12 2.04418764
+DEAL::-0.599884130 -0.258335105 2.06910178
+DEAL::-0.635903443 -0.130104704 1.37109647
+DEAL::-0.635903443 -0.130104704 2.74219294
+DEAL::
+DEAL::Face centers:
+DEAL::-0.750864056 -0.151766577 2.02512560
+DEAL::-0.980785280 -0.195090322 1.96208739
+DEAL::-0.887500000 -1.46301296e-12 1.97428910
+DEAL::-0.815881065 -0.341233990 2.01292390
+DEAL::-0.865824668 -0.173428449 1.32907100
+DEAL::-0.865824668 -0.173428449 2.65814200
+DEAL::
+DEAL::Face centers:
+DEAL::-0.462828493 -0.325328493 2.10621762
+DEAL::-0.647149053 -0.440449363 2.05690007
+DEAL::-0.599884130 -0.258335105 2.06910178
+DEAL::-0.502105188 -0.502105188 2.09401592
+DEAL::-0.554988773 -0.382888928 1.38770590
+DEAL::-0.554988773 -0.382888928 2.77541179
+DEAL::
+DEAL::Face centers:
+DEAL::-0.647149053 -0.440449363 2.05690007
+DEAL::-0.831469612 -0.555570233 2.00758252
+DEAL::-0.815881065 -0.341233990 2.01292390
+DEAL::-0.638772917 -0.638772917 2.05155870
+DEAL::-0.739309332 -0.498009798 1.35482753
+DEAL::-0.739309332 -0.498009798 2.70965506
+DEAL::
+DEAL::Face centers:
+DEAL::-0.325328493 -0.462828493 0.716311131
+DEAL::-0.440449363 -0.647149053 0.705696826
+DEAL::-0.502105188 -0.502105188 0.698005305
+DEAL::-0.258335105 -0.599884130 0.724002653
+DEAL::-0.382888928 -0.554988773 2.22725196e-16
+DEAL::-0.382888928 -0.554988773 1.42200796
+DEAL::
+DEAL::Face centers:
+DEAL::-0.440449363 -0.647149053 0.705696826
+DEAL::-0.555570233 -0.831469612 0.695082521
+DEAL::-0.638772917 -0.638772917 0.683852899
+DEAL::-0.341233990 -0.815881065 0.716926449
+DEAL::-0.498009798 -0.739309332 2.89647496e-15
+DEAL::-0.498009798 -0.739309332 1.40077935
+DEAL::
+DEAL::Face centers:
+DEAL::-0.108442831 -0.520942831 0.738770377
+DEAL::-0.151766577 -0.750864056 0.735232275
+DEAL::-0.258335105 -0.599884130 0.724002653
+DEAL::2.26589083e-12 -0.662500000 0.750000000
+DEAL::-0.130104704 -0.635903443 7.02273168e-16
+DEAL::-0.130104704 -0.635903443 1.47400265
+DEAL::
+DEAL::Face centers:
+DEAL::-0.151766577 -0.750864056 0.735232275
+DEAL::-0.195090322 -0.980785280 0.731694174
+DEAL::-0.341233990 -0.815881065 0.716926449
+DEAL::1.10396962e-12 -0.887500000 0.750000000
+DEAL::-0.173428449 -0.865824668 -7.86428573e-16
+DEAL::-0.173428449 -0.865824668 1.46692645
+DEAL::
+DEAL::Face centers:
+DEAL::-0.325328493 -0.462828493 2.14893339
+DEAL::-0.440449363 -0.647149053 2.11709048
+DEAL::-0.502105188 -0.502105188 2.09401592
+DEAL::-0.258335105 -0.599884130 2.17200796
+DEAL::-0.382888928 -0.554988773 1.42200796
+DEAL::-0.382888928 -0.554988773 2.84401592
+DEAL::
+DEAL::Face centers:
+DEAL::-0.440449363 -0.647149053 2.11709048
+DEAL::-0.555570233 -0.831469612 2.08524756
+DEAL::-0.638772917 -0.638772917 2.05155870
+DEAL::-0.341233990 -0.815881065 2.15077935
+DEAL::-0.498009798 -0.739309332 1.40077935
+DEAL::-0.498009798 -0.739309332 2.80155870
+DEAL::
+DEAL::Face centers:
+DEAL::-0.108442831 -0.520942831 2.21631113
+DEAL::-0.151766577 -0.750864056 2.20569683
+DEAL::-0.258335105 -0.599884130 2.17200796
+DEAL::1.55226787e-12 -0.662500000 2.25000000
+DEAL::-0.130104704 -0.635903443 1.47400265
+DEAL::-0.130104704 -0.635903443 2.94800531
+DEAL::
+DEAL::Face centers:
+DEAL::-0.151766577 -0.750864056 2.20569683
+DEAL::-0.195090322 -0.980785280 2.19508252
+DEAL::-0.341233990 -0.815881065 2.15077935
+DEAL::1.60940487e-12 -0.887500000 2.25000000
+DEAL::-0.173428449 -0.865824668 1.46692645
+DEAL::-0.173428449 -0.865824668 2.93385290
+DEAL::
+DEAL::Face centers:
+DEAL::0.108442831 -0.520942831 0.738770377
+DEAL::0.151766577 -0.750864056 0.735232275
+DEAL::2.26589083e-12 -0.662500000 0.750000000
+DEAL::0.258335105 -0.599884130 0.724002653
+DEAL::0.130104704 -0.635903443 0.00000000
+DEAL::0.130104704 -0.635903443 1.47400265
+DEAL::
+DEAL::Face centers:
+DEAL::0.151766577 -0.750864056 0.735232275
+DEAL::0.195090322 -0.980785280 0.731694174
+DEAL::1.10396962e-12 -0.887500000 0.750000000
+DEAL::0.341233990 -0.815881065 0.716926449
+DEAL::0.173428449 -0.865824668 -8.38681001e-17
+DEAL::0.173428449 -0.865824668 1.46692645
+DEAL::
+DEAL::Face centers:
+DEAL::0.325328493 -0.462828493 0.716311131
+DEAL::0.440449363 -0.647149053 0.705696826
+DEAL::0.258335105 -0.599884130 0.724002653
+DEAL::0.502105188 -0.502105188 0.698005305
+DEAL::0.382888928 -0.554988773 -1.58586887e-15
+DEAL::0.382888928 -0.554988773 1.42200796
+DEAL::
+DEAL::Face centers:
+DEAL::0.440449363 -0.647149053 0.705696826
+DEAL::0.555570233 -0.831469612 0.695082521
+DEAL::0.341233990 -0.815881065 0.716926449
+DEAL::0.638772917 -0.638772917 0.683852899
+DEAL::0.498009798 -0.739309332 -2.58707084e-15
+DEAL::0.498009798 -0.739309332 1.40077935
+DEAL::
+DEAL::Face centers:
+DEAL::0.108442831 -0.520942831 2.21631113
+DEAL::0.151766577 -0.750864056 2.20569683
+DEAL::1.55226787e-12 -0.662500000 2.25000000
+DEAL::0.258335105 -0.599884130 2.17200796
+DEAL::0.130104704 -0.635903443 1.47400265
+DEAL::0.130104704 -0.635903443 2.94800531
+DEAL::
+DEAL::Face centers:
+DEAL::0.151766577 -0.750864056 2.20569683
+DEAL::0.195090322 -0.980785280 2.19508252
+DEAL::1.60940487e-12 -0.887500000 2.25000000
+DEAL::0.341233990 -0.815881065 2.15077935
+DEAL::0.173428449 -0.865824668 1.46692645
+DEAL::0.173428449 -0.865824668 2.93385290
+DEAL::
+DEAL::Face centers:
+DEAL::0.325328493 -0.462828493 2.14893339
+DEAL::0.440449363 -0.647149053 2.11709048
+DEAL::0.258335105 -0.599884130 2.17200796
+DEAL::0.502105188 -0.502105188 2.09401592
+DEAL::0.382888928 -0.554988773 1.42200796
+DEAL::0.382888928 -0.554988773 2.84401592
+DEAL::
+DEAL::Face centers:
+DEAL::0.440449363 -0.647149053 2.11709048
+DEAL::0.555570233 -0.831469612 2.08524756
+DEAL::0.341233990 -0.815881065 2.15077935
+DEAL::0.638772917 -0.638772917 2.05155870
+DEAL::0.498009798 -0.739309332 1.40077935
+DEAL::0.498009798 -0.739309332 2.80155870
+DEAL::
+DEAL::Face centers:
+DEAL::0.462828493 -0.325328493 0.702072540
+DEAL::0.647149053 -0.440449363 0.685633357
+DEAL::0.502105188 -0.502105188 0.698005305
+DEAL::0.599884130 -0.258335105 0.689700592
+DEAL::0.554988773 -0.382888928 0.00000000
+DEAL::0.554988773 -0.382888928 1.38770590
+DEAL::
+DEAL::Face centers:
+DEAL::0.647149053 -0.440449363 0.685633357
+DEAL::0.831469612 -0.555570233 0.669194174
+DEAL::0.638772917 -0.638772917 0.683852899
+DEAL::0.815881065 -0.341233990 0.670974632
+DEAL::0.739309332 -0.498009798 2.23518464e-14
+DEAL::0.739309332 -0.498009798 1.35482753
+DEAL::
+DEAL::Face centers:
+DEAL::0.520942831 -0.108442831 0.696054604
+DEAL::0.750864056 -0.151766577 0.675041867
+DEAL::0.599884130 -0.258335105 0.689700592
+DEAL::0.662500000 2.19576823e-12 0.681395879
+DEAL::0.635903443 -0.130104704 7.28177805e-15
+DEAL::0.635903443 -0.130104704 1.37109647
+DEAL::
+DEAL::Face centers:
+DEAL::0.750864056 -0.151766577 0.675041867
+DEAL::0.980785280 -0.195090322 0.654029131
+DEAL::0.815881065 -0.341233990 0.670974632
+DEAL::0.887500000 1.08765619e-12 0.658096366
+DEAL::0.865824668 -0.173428449 -3.27700010e-15
+DEAL::0.865824668 -0.173428449 1.32907100
+DEAL::
+DEAL::Face centers:
+DEAL::0.462828493 -0.325328493 2.10621762
+DEAL::0.647149053 -0.440449363 2.05690007
+DEAL::0.502105188 -0.502105188 2.09401592
+DEAL::0.599884130 -0.258335105 2.06910178
+DEAL::0.554988773 -0.382888928 1.38770590
+DEAL::0.554988773 -0.382888928 2.77541179
+DEAL::
+DEAL::Face centers:
+DEAL::0.647149053 -0.440449363 2.05690007
+DEAL::0.831469612 -0.555570233 2.00758252
+DEAL::0.638772917 -0.638772917 2.05155870
+DEAL::0.815881065 -0.341233990 2.01292390
+DEAL::0.739309332 -0.498009798 1.35482753
+DEAL::0.739309332 -0.498009798 2.70965506
+DEAL::
+DEAL::Face centers:
+DEAL::0.520942831 -0.108442831 2.08816381
+DEAL::0.750864056 -0.151766577 2.02512560
+DEAL::0.599884130 -0.258335105 2.06910178
+DEAL::0.662500000 1.58504737e-12 2.04418764
+DEAL::0.635903443 -0.130104704 1.37109647
+DEAL::0.635903443 -0.130104704 2.74219294
+DEAL::
+DEAL::Face centers:
+DEAL::0.750864056 -0.151766577 2.02512560
+DEAL::0.980785280 -0.195090322 1.96208739
+DEAL::0.815881065 -0.341233990 2.01292390
+DEAL::0.887500000 1.46303299e-12 1.97428910
+DEAL::0.865824668 -0.173428449 1.32907100
+DEAL::0.865824668 -0.173428449 2.65814200
+DEAL::

diff --git a/tests/manifold/transfinite_manifold_09.cc b/tests/manifold/transfinite_manifold_09.cc
new file mode 100644 (file)
index 0000000..56c135b
--- /dev/null
+++ b/tests/manifold/transfinite_manifold_09.cc
@@ -0,0 +1,82 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 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.
+//
+// ---------------------------------------------------------------------
+
+
+// This test verifies that the transfinite interpolation works on a distorted
+// cylinder with some given coordinates
+
+#include <deal.II/grid/grid_reordering.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/tria.h>
+
+#include "../tests.h"
+
+
+int
+main()
+{
+  initlog();
+  deallog << std::setprecision(9);
+
+  const double       radius = 1.;
+  const double       length = 3.;
+  constexpr int      dim    = 3;
+  Triangulation<dim> tria;
+
+  // position of auxiliary point to achieve an angle of 120 degrees in corner
+  // of inner cell
+  std::vector<Point<3>> vertices{
+    {1.6666666666666663, 0., -0.69035593728849154},
+    {2.4033740890369071, 0., 0.046351485081748842},
+    {2., 0., -0.82842712474618985},
+    {2.7222718241315023, 0., -0.10615530061468759},
+    {1.5548344933395739, 0.44817247098067337, -0.64403353438675115},
+    {2.2998293798138509, 0.44396471873216636, 0.073847495332288168},
+    {1.9264041086678665, 0.53755670408577649, -0.79794270842148385},
+    {2.6272400227990982, 0.52932727817817915, -0.10032762350281543}};
+
+  std::vector<CellData<3>> cell_data(1);
+  for (unsigned int v = 0; v < 8; ++v)
+    cell_data[0].vertices[v] = v;
+
+  SubCellData subcell_data;
+  tria.create_triangulation(vertices, cell_data, subcell_data);
+
+  // set cylindrical manifold on face 3
+  tria.set_all_manifold_ids(1);
+  tria.begin_active()->face(3)->set_all_manifold_ids(2);
+
+  // attach 3 cylindrical manifolds to mesh
+  tria.set_manifold(
+    2,
+    CylindricalManifold<dim>(Point<dim>{std::sqrt(0.5), 0., std::sqrt(0.5)},
+                             Point<dim>()));
+  TransfiniteInterpolationManifold<dim> transfinite;
+  transfinite.initialize(tria);
+  tria.set_manifold(1, transfinite);
+
+  deallog << "Cell center " << tria.begin_active()->center(true, true)
+          << std::endl;
+
+  tria.refine_global();
+  for (auto &cell : tria.active_cell_iterators())
+    {
+      deallog << "Face centers:" << std::endl;
+      for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
+        deallog << cell->face(f)->center(true) << std::endl;
+      deallog << std::endl;
+    }
+}

diff --git a/tests/manifold/transfinite_manifold_09.output b/tests/manifold/transfinite_manifold_09.output
new file mode 100644 (file)
index 0000000..5b1781c
--- /dev/null
+++ b/tests/manifold/transfinite_manifold_09.output
@@ -0,0 +1,66 @@
+
+DEAL::Cell center 2.15645306 0.246102405 -0.387255898
+DEAL::Face centers:
+DEAL::1.72686639 0.118021667 -0.716717669
+DEAL::2.09348518 0.117360966 -0.352666356
+DEAL::1.82340345 0.111780133 -0.495775131
+DEAL::1.99694814 0.123602502 -0.573608919
+DEAL::1.93327463 5.82867088e-16 -0.541599103
+DEAL::1.88545778 0.235227227 -0.526165775
+DEAL::
+DEAL::Face centers:
+DEAL::2.09348518 0.117360966 -0.352666356
+DEAL::2.46010386 0.116700256 0.0113850583
+DEAL::2.19279309 0.111254164 -0.129774718
+DEAL::2.36079598 0.122807060 -0.211506604
+DEAL::2.29982389 2.44249065e-15 -0.175049842
+DEAL::2.25217134 0.233909456 -0.164637645
+DEAL::
+DEAL::Face centers:
+DEAL::1.90318191 0.129978764 -0.792602334
+DEAL::2.26425899 0.129048601 -0.432449218
+DEAL::1.99694814 0.123602502 -0.573608919
+DEAL::2.17049284 0.135424870 -0.651442708
+DEAL::2.09813685 8.57647287e-15 -0.612439147
+DEAL::2.06444662 0.258561147 -0.607754968
+DEAL::
+DEAL::Face centers:
+DEAL::2.26425899 0.129048601 -0.432449218
+DEAL::2.62533577 0.128118408 -0.0722958004
+DEAL::2.36079598 0.122807060 -0.211506604
+DEAL::2.52879886 0.134359956 -0.293238489
+DEAL::2.46107721 3.58046925e-15 -0.249498785
+DEAL::2.42373612 0.256711711 -0.250464804
+DEAL::
+DEAL::Face centers:
+DEAL::1.67571475 0.353436728 -0.695521133
+DEAL::2.04254855 0.351469274 -0.336541670
+DEAL::1.76852329 0.335340400 -0.474967228
+DEAL::1.94974023 0.369565666 -0.557095797
+DEAL::1.88545778 0.235227227 -0.526165775
+DEAL::1.83121627 0.469215465 -0.504307774
+DEAL::
+DEAL::Face centers:
+DEAL::2.04254855 0.351469274 -0.336541670
+DEAL::2.40938146 0.349501562 0.0224386816
+DEAL::2.13998480 0.333762493 -0.113673414
+DEAL::2.31194543 0.367208407 -0.200429796
+DEAL::2.25217134 0.233909456 -0.164637645
+DEAL::2.19819384 0.466608879 -0.147900503
+DEAL::
+DEAL::Face centers:
+DEAL::1.86155918 0.388051477 -0.775335130
+DEAL::2.21913756 0.385304928 -0.420984367
+DEAL::1.94974023 0.369565666 -0.557095797
+DEAL::2.13095717 0.403790933 -0.639224365
+DEAL::2.06444662 0.258561147 -0.607754968
+DEAL::2.01148237 0.513405328 -0.583796769
+DEAL::
+DEAL::Face centers:
+DEAL::2.21913756 0.385304928 -0.420984367
+DEAL::2.57671328 0.382557607 -0.0666309407
+DEAL::2.31194543 0.367208407 -0.200429796
+DEAL::2.48390607 0.400654321 -0.287186177
+DEAL::2.42373612 0.256711711 -0.250464804
+DEAL::2.36742019 0.509793323 -0.232455984
+DEAL::

diff --git a/tests/manifold/transfinite_manifold_10.cc b/tests/manifold/transfinite_manifold_10.cc
new file mode 100644 (file)
index 0000000..ca79261
--- /dev/null
+++ b/tests/manifold/transfinite_manifold_10.cc
@@ -0,0 +1,176 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 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.
+//
+// ---------------------------------------------------------------------
+
+
+// This test verifies that the transfinite interpolation works on a torus
+
+#include <deal.II/base/std_cxx14/memory.h>
+
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/tria.h>
+
+#include "../tests.h"
+
+
+class InnerTorusManifold : public ChartManifold<3, 3, 3>
+{
+public:
+  static const unsigned int dim      = 3;
+  static const unsigned int spacedim = 3;
+  static const unsigned int chartdim = 3;
+
+  InnerTorusManifold()
+    : ChartManifold<dim, spacedim>(Tensor<1, 3>({0., 0., 2 * numbers::PI}))
+  {}
+
+  virtual std::unique_ptr<Manifold<dim, spacedim>>
+  clone() const override
+  {
+    return std_cxx14::make_unique<InnerTorusManifold>();
+  }
+
+  virtual Point<chartdim>
+  pull_back(const Point<spacedim> &space_point) const override
+  {
+    const double phi    = std::atan2(space_point[2], space_point[0]);
+    const double radius = std::sqrt(space_point[0] * space_point[0] +
+                                    space_point[2] * space_point[2]);
+    return Point<3>(radius, space_point[1], phi);
+  }
+
+  virtual Point<spacedim>
+  push_forward(const Point<chartdim> &chart_point) const override
+  {
+    return Point<3>(chart_point[0] * std::cos(chart_point[2]),
+                    chart_point[1],
+                    chart_point[0] * std::sin(chart_point[2]));
+  }
+};
+
+
+
+int
+main()
+{
+  initlog();
+  deallog << std::setprecision(9);
+
+  const unsigned int dim = 3;
+  Triangulation<dim> tria;
+
+  const double       R       = 2;
+  const double       r       = 0.5;
+  const unsigned int n_cells = 3;
+
+  // the first 8 vertices are in the x-y-plane
+  Point<3> const        p = Point<3>(R, 0.0, 0.0);
+  double const          a = 1. / (1 + std::sqrt(2.0));
+  std::vector<Point<3>> vertices(8 * n_cells);
+  vertices[0] = p + Point<3>(-1, -1, 0) * (r / std::sqrt(2.0)),
+  vertices[1] = p + Point<3>(+1, -1, 0) * (r / std::sqrt(2.0)),
+  vertices[2] = p + Point<3>(-1, -1, 0) * (r / std::sqrt(2.0) * a),
+  vertices[3] = p + Point<3>(+1, -1, 0) * (r / std::sqrt(2.0) * a),
+  vertices[4] = p + Point<3>(-1, +1, 0) * (r / std::sqrt(2.0) * a),
+  vertices[5] = p + Point<3>(+1, +1, 0) * (r / std::sqrt(2.0) * a),
+  vertices[6] = p + Point<3>(-1, +1, 0) * (r / std::sqrt(2.0)),
+  vertices[7] = p + Point<3>(+1, +1, 0) * (r / std::sqrt(2.0));
+
+  // create remaining vertices by rotating around positive y-axis
+  double phi_cell = 2.0 * numbers::PI / n_cells;
+  for (unsigned int c = 1; c < n_cells; ++c)
+    {
+      for (unsigned int v = 0; v < 8; ++v)
+        {
+          double const r_2d      = vertices[v][0];
+          vertices[8 * c + v][0] = r_2d * std::cos(phi_cell * c);
+          vertices[8 * c + v][1] = vertices[v][1];
+          vertices[8 * c + v][2] = r_2d * std::sin(phi_cell * c);
+        }
+    }
+
+  // cell connectivity
+  std::vector<CellData<3>> cells(5 * n_cells);
+  for (unsigned int c = 0; c < n_cells; ++c)
+    {
+      for (unsigned int j = 0; j < 2; ++j)
+        {
+          unsigned int offset = (8 * (c + j)) % (8 * n_cells);
+          // cell 0 in x-y-plane
+          cells[5 * c].vertices[0 + j * 4] = offset + 0;
+          cells[5 * c].vertices[1 + j * 4] = offset + 1;
+          cells[5 * c].vertices[2 + j * 4] = offset + 2;
+          cells[5 * c].vertices[3 + j * 4] = offset + 3;
+          // cell 1 in x-y-plane
+          cells[5 * c + 1].vertices[0 + j * 4] = offset + 2;
+          cells[5 * c + 1].vertices[1 + j * 4] = offset + 3;
+          cells[5 * c + 1].vertices[2 + j * 4] = offset + 4;
+          cells[5 * c + 1].vertices[3 + j * 4] = offset + 5;
+          // cell 2 in x-y-plane
+          cells[5 * c + 2].vertices[0 + j * 4] = offset + 4;
+          cells[5 * c + 2].vertices[1 + j * 4] = offset + 5;
+          cells[5 * c + 2].vertices[2 + j * 4] = offset + 6;
+          cells[5 * c + 2].vertices[3 + j * 4] = offset + 7;
+          // cell 3 in x-y-plane
+          cells[5 * c + 3].vertices[0 + j * 4] = offset + 0;
+          cells[5 * c + 3].vertices[1 + j * 4] = offset + 2;
+          cells[5 * c + 3].vertices[2 + j * 4] = offset + 6;
+          cells[5 * c + 3].vertices[3 + j * 4] = offset + 4;
+          // cell 4 in x-y-plane
+          cells[5 * c + 4].vertices[0 + j * 4] = offset + 3;
+          cells[5 * c + 4].vertices[1 + j * 4] = offset + 1;
+          cells[5 * c + 4].vertices[2 + j * 4] = offset + 5;
+          cells[5 * c + 4].vertices[3 + j * 4] = offset + 7;
+        }
+
+      cells[5 * c].material_id     = 0;
+      cells[5 * c + 1].material_id = 0;
+      cells[5 * c + 2].material_id = 0;
+      cells[5 * c + 3].material_id = 0;
+      cells[5 * c + 4].material_id = 0;
+    }
+
+  tria.create_triangulation(vertices, cells, SubCellData());
+
+  tria.set_all_manifold_ids(0);
+
+  for (auto &cell : tria.cell_iterators())
+    {
+      bool cell_at_boundary = false;
+      for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
+        if (cell->at_boundary(f))
+          cell_at_boundary = true;
+      if (cell_at_boundary == false)
+        cell->set_all_manifold_ids(2);
+    }
+  tria.set_all_manifold_ids_on_boundary(1);
+  tria.set_manifold(1, TorusManifold<dim>(2, 0.5));
+  tria.set_manifold(2, InnerTorusManifold());
+  TransfiniteInterpolationManifold<dim> transfinite;
+  transfinite.initialize(tria);
+  tria.set_manifold(0, transfinite);
+
+  for (unsigned int cycle = 0; cycle < 2; ++cycle)
+    {
+      tria.refine_global(1);
+      deallog << "Cycle " << cycle << std::endl;
+      deallog << "Number of active cells: " << tria.n_active_cells()
+              << std::endl;
+      deallog << "Vertices: " << std::endl;
+      for (auto &v : tria.get_vertices())
+        deallog << v << std::endl;
+      deallog << std::endl;
+    }
+  return 0;
+}

diff --git a/tests/manifold/transfinite_manifold_10.output b/tests/manifold/transfinite_manifold_10.output
new file mode 100644 (file)
index 0000000..fe9af30
--- /dev/null
+++ b/tests/manifold/transfinite_manifold_10.output
@@ -0,0 +1,1227 @@
+
+DEAL::Cycle 0
+DEAL::Number of active cells: 120
+DEAL::Vertices: 
+DEAL::1.64644661 -0.353553391 0.00000000
+DEAL::2.35355339 -0.353553391 0.00000000
+DEAL::1.85355339 -0.146446609 0.00000000
+DEAL::2.14644661 -0.146446609 0.00000000
+DEAL::1.85355339 0.146446609 0.00000000
+DEAL::2.14644661 0.146446609 0.00000000
+DEAL::1.64644661 0.353553391 0.00000000
+DEAL::2.35355339 0.353553391 0.00000000
+DEAL::-0.823223305 -0.353553391 1.42586459
+DEAL::-1.17677670 -0.353553391 2.03823703
+DEAL::-0.926776695 -0.146446609 1.60522432
+DEAL::-1.07322330 -0.146446609 1.85887729
+DEAL::-0.926776695 0.146446609 1.60522432
+DEAL::-1.07322330 0.146446609 1.85887729
+DEAL::-0.823223305 0.353553391 1.42586459
+DEAL::-1.17677670 0.353553391 2.03823703
+DEAL::-0.823223305 -0.353553391 -1.42586459
+DEAL::-1.17677670 -0.353553391 -2.03823703
+DEAL::-0.926776695 -0.146446609 -1.60522432
+DEAL::-1.07322330 -0.146446609 -1.85887729
+DEAL::-0.926776695 0.146446609 -1.60522432
+DEAL::-1.07322330 0.146446609 -1.85887729
+DEAL::-0.823223305 0.353553391 -1.42586459
+DEAL::-1.17677670 0.353553391 -2.03823703
+DEAL::2.00000000 -0.500000000 0.00000000
+DEAL::1.75000000 -0.250000000 -2.52976221e-14
+DEAL::1.50000000 6.12323400e-17 0.00000000
+DEAL::0.823223305 -0.353553391 1.42586459
+DEAL::2.25000000 -0.250000000 4.30090529e-15
+DEAL::2.50000000 0.00000000 0.00000000
+DEAL::1.17677670 -0.353553391 2.03823703
+DEAL::2.00000000 -0.146446609 0.00000000
+DEAL::1.85355339 0.00000000 0.00000000
+DEAL::0.926776695 -0.146446609 1.60522432
+DEAL::2.14644661 0.00000000 0.00000000
+DEAL::1.07322330 -0.146446609 1.85887729
+DEAL::2.00000000 0.146446609 0.00000000
+DEAL::1.75000000 0.250000000 -3.53725085e-15
+DEAL::0.926776695 0.146446609 1.60522432
+DEAL::2.25000000 0.250000000 4.30096961e-15
+DEAL::1.07322330 0.146446609 1.85887729
+DEAL::2.00000000 0.500000000 0.00000000
+DEAL::0.823223305 0.353553391 1.42586459
+DEAL::1.17677670 0.353553391 2.03823703
+DEAL::-1.00000000 -0.500000000 1.73205081
+DEAL::-0.875000000 -0.250000000 1.51554446
+DEAL::-0.750000000 6.12323400e-17 1.29903811
+DEAL::-1.64644661 -0.353553391 1.66396990e-15
+DEAL::-1.12500000 -0.250000000 1.94855716
+DEAL::-1.25000000 0.00000000 2.16506351
+DEAL::-2.35355339 -0.353553391 2.37860249e-15
+DEAL::-1.00000000 -0.146446609 1.73205081
+DEAL::-0.926776695 0.00000000 1.60522432
+DEAL::-1.85355339 -0.146446609 1.87328094e-15
+DEAL::-1.07322330 0.00000000 1.85887729
+DEAL::-2.14644661 -0.146446609 2.16929145e-15
+DEAL::-1.00000000 0.146446609 1.73205081
+DEAL::-0.875000000 0.250000000 1.51554446
+DEAL::-1.85355339 0.146446609 1.87328094e-15
+DEAL::-1.12500000 0.250000000 1.94855716
+DEAL::-2.14644661 0.146446609 2.16929145e-15
+DEAL::-1.00000000 0.500000000 1.73205081
+DEAL::-1.64644661 0.353553391 1.66396990e-15
+DEAL::-2.35355339 0.353553391 2.37860249e-15
+DEAL::0.823223305 -0.353553391 -1.42586459
+DEAL::-1.00000000 -0.500000000 -1.73205081
+DEAL::-0.875000000 -0.250000000 -1.51554446
+DEAL::-0.750000000 6.12323400e-17 -1.29903811
+DEAL::1.17677670 -0.353553391 -2.03823703
+DEAL::-1.12500000 -0.250000000 -1.94855716
+DEAL::-1.25000000 0.00000000 -2.16506351
+DEAL::0.926776695 -0.146446609 -1.60522432
+DEAL::-1.00000000 -0.146446609 -1.73205081
+DEAL::-0.926776695 0.00000000 -1.60522432
+DEAL::1.07322330 -0.146446609 -1.85887729
+DEAL::-1.07322330 0.00000000 -1.85887729
+DEAL::0.926776695 0.146446609 -1.60522432
+DEAL::-1.00000000 0.146446609 -1.73205081
+DEAL::-0.875000000 0.250000000 -1.51554446
+DEAL::1.07322330 0.146446609 -1.85887729
+DEAL::-1.12500000 0.250000000 -1.94855716
+DEAL::0.823223305 0.353553391 -1.42586459
+DEAL::-1.00000000 0.500000000 -1.73205081
+DEAL::1.17677670 0.353553391 -2.03823703
+DEAL::1.00000000 -0.500000000 1.73205081
+DEAL::2.00000000 -0.323223305 1.44931457e-14
+DEAL::1.67677670 -5.97921627e-13 -4.50889981e-14
+DEAL::0.875000000 -0.250000000 1.51554446
+DEAL::0.750000000 2.83276945e-16 1.29903811
+DEAL::1.12500000 -0.250000000 1.94855716
+DEAL::1.25000000 -1.22464680e-16 2.16506351
+DEAL::1.00000000 -0.146446609 1.73205081
+DEAL::2.00000000 0.00000000 0.00000000
+DEAL::0.926776695 0.00000000 1.60522432
+DEAL::2.32322330 -7.22743012e-14 -2.63246240e-15
+DEAL::1.07322330 0.00000000 1.85887729
+DEAL::1.00000000 0.146446609 1.73205081
+DEAL::2.00000000 0.323223305 -2.26621556e-15
+DEAL::0.875000000 0.250000000 1.51554446
+DEAL::1.12500000 0.250000000 1.94855716
+DEAL::1.00000000 0.500000000 1.73205081
+DEAL::-2.00000000 -0.500000000 2.02128620e-15
+DEAL::-1.00000000 -0.323223305 1.73205081
+DEAL::-0.838388348 2.26821425e-13 1.45213121
+DEAL::-1.75000000 -0.250000000 2.14313190e-16
+DEAL::-1.50000000 6.12323400e-17 1.51596465e-15
+DEAL::-2.25000000 -0.250000000 1.22659542e-14
+DEAL::-2.50000000 -1.22464680e-16 2.52660775e-15
+DEAL::-2.00000000 -0.146446609 2.02128620e-15
+DEAL::-1.00000000 0.00000000 1.73205081
+DEAL::-1.85355339 0.00000000 1.87328094e-15
+DEAL::-1.16161165 -7.32041130e-14 2.01197040
+DEAL::-2.14644661 0.00000000 2.16929145e-15
+DEAL::-2.00000000 0.146446609 2.02128620e-15
+DEAL::-1.00000000 0.323223305 1.73205081
+DEAL::-1.75000000 0.250000000 -1.33999904e-15
+DEAL::-2.25000000 0.250000000 -6.73185741e-13
+DEAL::-2.00000000 0.500000000 2.02128620e-15
+DEAL::0.875000000 -0.250000000 -1.51554446
+DEAL::0.750000000 6.12323400e-17 -1.29903811
+DEAL::1.00000000 -0.500000000 -1.73205081
+DEAL::-1.00000000 -0.323223305 -1.73205081
+DEAL::-0.838388348 1.87831780e-13 -1.45213121
+DEAL::1.12500000 -0.250000000 -1.94855716
+DEAL::1.25000000 -1.22464680e-16 -2.16506351
+DEAL::0.926776695 0.00000000 -1.60522432
+DEAL::1.00000000 -0.146446609 -1.73205081
+DEAL::-1.00000000 0.00000000 -1.73205081
+DEAL::1.07322330 0.00000000 -1.85887729
+DEAL::-1.16161165 -6.37533395e-14 -2.01197040
+DEAL::0.875000000 0.250000000 -1.51554446
+DEAL::1.00000000 0.146446609 -1.73205081
+DEAL::-1.00000000 0.323223305 -1.73205081
+DEAL::1.12500000 0.250000000 -1.94855716
+DEAL::1.00000000 0.500000000 -1.73205081
+DEAL::1.00000000 -0.323223305 1.73205081
+DEAL::1.00000000 0.00000000 1.73205081
+DEAL::1.00000000 0.323223305 1.73205081
+DEAL::0.838388348 -8.19801709e-14 1.45213121
+DEAL::1.16161165 -2.32163213e-14 2.01197040
+DEAL::-2.00000000 -0.323223305 -9.03492694e-14
+DEAL::-2.00000000 0.00000000 7.35035672e-15
+DEAL::-2.00000000 0.323223305 1.31695335e-13
+DEAL::-1.67677670 -7.93711468e-14 -1.28393095e-15
+DEAL::-2.32322330 -2.32440769e-14 2.84512798e-16
+DEAL::1.00000000 -0.323223305 -1.73205081
+DEAL::1.00000000 0.00000000 -1.73205081
+DEAL::1.00000000 0.323223305 -1.73205081
+DEAL::0.838388348 -7.79764291e-14 -1.45213121
+DEAL::1.16161165 -2.32440769e-14 -2.01197040
+DEAL::
+DEAL::Cycle 1
+DEAL::Number of active cells: 960
+DEAL::Vertices: 
+DEAL::1.64644661 -0.353553391 0.00000000
+DEAL::2.35355339 -0.353553391 0.00000000
+DEAL::1.85355339 -0.146446609 0.00000000
+DEAL::2.14644661 -0.146446609 0.00000000
+DEAL::1.85355339 0.146446609 0.00000000
+DEAL::2.14644661 0.146446609 0.00000000
+DEAL::1.64644661 0.353553391 0.00000000
+DEAL::2.35355339 0.353553391 0.00000000
+DEAL::-0.823223305 -0.353553391 1.42586459
+DEAL::-1.17677670 -0.353553391 2.03823703
+DEAL::-0.926776695 -0.146446609 1.60522432
+DEAL::-1.07322330 -0.146446609 1.85887729
+DEAL::-0.926776695 0.146446609 1.60522432
+DEAL::-1.07322330 0.146446609 1.85887729
+DEAL::-0.823223305 0.353553391 1.42586459
+DEAL::-1.17677670 0.353553391 2.03823703
+DEAL::-0.823223305 -0.353553391 -1.42586459
+DEAL::-1.17677670 -0.353553391 -2.03823703
+DEAL::-0.926776695 -0.146446609 -1.60522432
+DEAL::-1.07322330 -0.146446609 -1.85887729
+DEAL::-0.926776695 0.146446609 -1.60522432
+DEAL::-1.07322330 0.146446609 -1.85887729
+DEAL::-0.823223305 0.353553391 -1.42586459
+DEAL::-1.17677670 0.353553391 -2.03823703
+DEAL::2.00000000 -0.500000000 0.00000000
+DEAL::1.75000000 -0.250000000 -2.52976221e-14
+DEAL::1.50000000 6.12323400e-17 0.00000000
+DEAL::0.823223305 -0.353553391 1.42586459
+DEAL::2.25000000 -0.250000000 4.30090529e-15
+DEAL::2.50000000 0.00000000 0.00000000
+DEAL::1.17677670 -0.353553391 2.03823703
+DEAL::2.00000000 -0.146446609 0.00000000
+DEAL::1.85355339 0.00000000 0.00000000
+DEAL::0.926776695 -0.146446609 1.60522432
+DEAL::2.14644661 0.00000000 0.00000000
+DEAL::1.07322330 -0.146446609 1.85887729
+DEAL::2.00000000 0.146446609 0.00000000
+DEAL::1.75000000 0.250000000 -3.53725085e-15
+DEAL::0.926776695 0.146446609 1.60522432
+DEAL::2.25000000 0.250000000 4.30096961e-15
+DEAL::1.07322330 0.146446609 1.85887729
+DEAL::2.00000000 0.500000000 0.00000000
+DEAL::0.823223305 0.353553391 1.42586459
+DEAL::1.17677670 0.353553391 2.03823703
+DEAL::-1.00000000 -0.500000000 1.73205081
+DEAL::-0.875000000 -0.250000000 1.51554446
+DEAL::-0.750000000 6.12323400e-17 1.29903811
+DEAL::-1.64644661 -0.353553391 1.66396990e-15
+DEAL::-1.12500000 -0.250000000 1.94855716
+DEAL::-1.25000000 0.00000000 2.16506351
+DEAL::-2.35355339 -0.353553391 2.37860249e-15
+DEAL::-1.00000000 -0.146446609 1.73205081
+DEAL::-0.926776695 0.00000000 1.60522432
+DEAL::-1.85355339 -0.146446609 1.87328094e-15
+DEAL::-1.07322330 0.00000000 1.85887729
+DEAL::-2.14644661 -0.146446609 2.16929145e-15
+DEAL::-1.00000000 0.146446609 1.73205081
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+DEAL::-1.99548984 0.132282510 1.15209659
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+DEAL::-1.84661082 0.304193188 1.06614126
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+DEAL::-2.07322330 -0.0732233047 3.01598493e-15
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+DEAL::-1.66863757 0.00000000 0.963388348
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+DEAL::-1.73205081 -0.0732233047 1.00000000
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+DEAL::1.11265995 -0.102752908 1.92718356
+DEAL::6.76337175e-14 -4.50007186e-14 2.41161165
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+DEAL::1.99548984 0.132282510 1.15209659
+DEAL::1.99548984 -0.132282510 1.15209659
+DEAL::0.887340051 0.102752908 1.53691805
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+DEAL::0.808466761 -0.161812113 1.40030551
+DEAL::1.08085186e-16 8.75182807e-14 1.76516504
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+DEAL::2.06379611 -0.161812113 1.19153324
+DEAL::1.92718356 0.102752908 1.11265995
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+DEAL::-1.40030551 0.161812113 0.808466761
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+DEAL::-1.92718356 -0.102752908 1.11265995
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+DEAL::-2.06379611 0.161812113 1.19153324
+DEAL::-1.92718356 -0.102752908 -1.11265995
+DEAL::-2.06379611 -0.161812113 -1.19153324
+DEAL::-1.92718356 0.102752908 -1.11265995
+DEAL::-2.06379611 0.161812113 -1.19153324
+DEAL::-5.23558607e-15 -0.383066477 -1.83818789
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+DEAL::5.67528134e-13 -0.225319899 -1.89724709
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+DEAL::1.87218421 -0.383066477 -1.08090606
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+DEAL::1.82103744 -0.225319899 -1.05137645
+DEAL::-7.19922906e-15 -0.0732233047 -1.92677670
+DEAL::-7.74641374e-15 -0.0732233047 -2.07322330
+DEAL::-7.19922906e-15 0.0732233047 -1.92677670
+DEAL::-7.74641374e-15 0.0732233047 -2.07322330
+DEAL::1.66863757 -0.0732233047 -0.963388348
+DEAL::1.79546405 -0.0732233047 -1.03661165
+DEAL::1.66863757 0.0732233047 -0.963388348
+DEAL::1.79546405 0.0732233047 -1.03661165
+DEAL::-3.01666664e-12 0.225319899 -1.89724709
+DEAL::-2.48779697e-13 0.225319899 -2.10275291
+DEAL::-1.51379385e-12 0.383066477 -1.83818789
+DEAL::1.22487673e-13 0.383066477 -2.16181211
+DEAL::1.64306418 0.225319899 -0.948623546
+DEAL::1.82103744 0.225319899 -1.05137645
+DEAL::1.59191741 0.383066477 -0.919093943
+DEAL::1.87218421 0.383066477 -1.08090606
+DEAL::-1.89466820e-14 -0.161812113 -1.61693352
+DEAL::2.87219587e-15 -0.102752908 -1.77468010
+DEAL::-1.28127524e-12 0.161812113 -1.61693352
+DEAL::-1.38739924e-12 0.102752908 -1.77468010
+DEAL::1.40030551 -0.161812113 -0.808466761
+DEAL::1.53691805 -0.102752908 -0.887340051
+DEAL::1.40030551 0.161812113 -0.808466761
+DEAL::1.53691805 0.102752908 -0.887340051
+DEAL::-2.37037178e-15 -0.102752908 -2.22531990
+DEAL::-1.61299904e-13 -0.161812113 -2.38306648
+DEAL::3.54417759e-15 0.102752908 -2.22531990
+DEAL::3.73009000e-15 0.161812113 -2.38306648
+DEAL::1.92718356 -0.102752908 -1.11265995
+DEAL::2.06379611 -0.161812113 -1.19153324
+DEAL::1.92718356 0.102752908 -1.11265995
+DEAL::2.06379611 0.161812113 -1.19153324
+DEAL::