From 75c1053c33fa010c13f9e8b0ab23a48449eb5212 Mon Sep 17 00:00:00 2001
From: Luca Heltai <luca.heltai@sissa.it>
Date: Thu, 18 May 2017 15:38:27 +0200
Subject: [PATCH] Implemented regularize corner cells

---
 doc/doxygen/images/regularize_mesh_01.png  | Bin 0 -> 4559 bytes
 doc/doxygen/images/regularize_mesh_02.png  | Bin 0 -> 5348 bytes
 doc/doxygen/images/regularize_mesh_03.png  | Bin 0 -> 4635 bytes
 doc/news/changes/minor/20170518LucaHeltai  |   5 +
 include/deal.II/grid/grid_tools.h          |  93 ++++
 source/grid/grid_tools.cc                  | 307 ++++++++++++
 source/grid/grid_tools.inst.in             |   3 +
 tests/grid/grid_tools_regularize_01.cc     |  50 ++
 tests/grid/grid_tools_regularize_01.output |  35 ++
 tests/grid/grid_tools_regularize_02.cc     |  55 +++
 tests/grid/grid_tools_regularize_02.output | 520 +++++++++++++++++++++
 11 files changed, 1068 insertions(+)
 create mode 100644 doc/doxygen/images/regularize_mesh_01.png
 create mode 100644 doc/doxygen/images/regularize_mesh_02.png
 create mode 100644 doc/doxygen/images/regularize_mesh_03.png
 create mode 100644 doc/news/changes/minor/20170518LucaHeltai
 create mode 100644 tests/grid/grid_tools_regularize_01.cc
 create mode 100644 tests/grid/grid_tools_regularize_01.output
 create mode 100644 tests/grid/grid_tools_regularize_02.cc
 create mode 100644 tests/grid/grid_tools_regularize_02.output

diff --git a/doc/doxygen/images/regularize_mesh_01.png b/doc/doxygen/images/regularize_mesh_01.png
new file mode 100644
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diff --git a/doc/news/changes/minor/20170518LucaHeltai b/doc/news/changes/minor/20170518LucaHeltai
new file mode 100644
index 0000000000..30f83a2bca
--- /dev/null
+++ b/doc/news/changes/minor/20170518LucaHeltai
@@ -0,0 +1,5 @@
+New: Added a GridTools::regularize_corner_cells function that 
+detects if the boundary cells of a mesh at corner positions 
+(with dim adjacent faces on the boundary) need to be split into 
+cells with smaller angles.
+<br> (Luca Heltai, Martin Kronbichler, 2017/05/18)
diff --git a/include/deal.II/grid/grid_tools.h b/include/deal.II/grid/grid_tools.h
index 7b90b8672e..37198c9744 100644
--- a/include/deal.II/grid/grid_tools.h
+++ b/include/deal.II/grid/grid_tools.h
@@ -461,6 +461,99 @@ namespace GridTools
                       const double max_ratio = 1.6180339887,
                       const unsigned int max_iterations = 5);
 
+  /**
+   * Analyze the boundary cells of a mesh, and if one cell is found at
+   * a corner position (with dim adjacent faces on the boundary), and its
+   * dim-dimensional angle fraction exceeds @p limit_angle_fraction,
+   * refine globally once, and replace the children of such cell
+   * with children where the corner is no longer offending the given angle
+   * fraction.
+   *
+   * If no boundary cells exist with two adjacent faces on the boundary, then
+   * the triangulation is left untouched. If instead we do have cells with dim
+   * adjacent faces on the boundary, then the fraction between the dim-dimensional
+   * solid angle and dim*pi/2 is checked against the parameter @p limit_angle_fraction.
+   * If it is higher, the grid is refined once, and the children of the
+   * offending cell are replaced with some cells that instead respect the limit. After
+   * this process the triangulation is flattened, and all Manifold objects are restored
+   * as they were in the original triangulation.
+   *
+   * An example is given by the following mesh, obtained by attaching a SphericalManifold
+   * to a mesh generated using GridGenerator::hyper_cube:
+   *
+   * @code
+   * const SphericalManifold<dim> m0;
+   * Triangulation<dim> tria;
+   * GridGenerator::hyper_cube(tria,-1,1);
+   * tria.set_all_manifold_ids_on_boundary(0);
+   * tria.set_manifold(0, m0);
+   * tria.refine_global(4);
+   * @endcode
+   *
+   * <p ALIGN="center">
+   * @image html regularize_mesh_01.png
+   * </p>
+   *
+   * The four cells that were originally the corners of a square will give you some troubles
+   * during computations, as the jacobian of the transformation from the reference cell to
+   * those cells will go to zero, affecting the error constants of the finite element estimates.
+   *
+   * Those cells have a corner with an angle that is very close to 180 degrees, i.e., an angle
+   * fraction very close to one.
+   *
+   * The same code, adding a call to regularize_corner_cells:
+   * @code
+   * const SphericalManifold<dim> m0;
+   * Triangulation<dim> tria;
+   * GridGenerator::hyper_cube(tria,-1,1);
+   * tria.set_all_manifold_ids_on_boundary(0);
+   * tria.set_manifold(0, m0);
+   * GridTools::regularize_corner_cells(tria);
+   * tria.refine_global(2);
+   * @endcode
+   * generates a mesh that has a much better behaviour w.r.t. the jacobian of the Mapping:
+   *
+   * <p ALIGN="center">
+   * @image html regularize_mesh_02.png
+   * </p>
+   *
+   * This mesh is very similar to the one obtained by GridGenerator::hyper_ball. However, using
+   * GridTools::regularize_corner_cells one has the freedom to choose when to apply the
+   * regularization, i.e., one could in principle first refine a few times, and then call the
+   * regularize_corner_cells function:
+   *
+   * @code
+   * const SphericalManifold<dim> m0;
+   * Triangulation<dim> tria;
+   * GridGenerator::hyper_cube(tria,-1,1);
+   * tria.set_all_manifold_ids_on_boundary(0);
+   * tria.set_manifold(0, m0);
+   * tria.refine_global(2);
+   * GridTools::regularize_corner_cells(tria);
+   * tria.refine_global(1);
+   * @endcode
+   *
+   * This generates the following mesh:
+   *
+   * <p ALIGN="center">
+   * @image html regularize_mesh_03.png
+   * </p>
+   *
+   * The function is currently implemented only for dim = 2 and
+   * will throw an exception if called with dim = 3.
+   *
+   * @param[in,out] tria Triangulation to regularize.
+   *
+   * @param[in] limit_angle_fraction Maximum ratio of angle or solid
+   * angle that is allowed for a corner element in the mesh.
+   *
+   * @author Luca Heltai, Martin Kronbichler, 2017
+   */
+  template <int dim, int spacedim>
+  void
+  regularize_corner_cells(Triangulation<dim,spacedim> &tria,
+                          const double limit_angle_fraction=.75);
+
   /*@}*/
   /**
    * @name Finding cells and vertices of a triangulation
diff --git a/source/grid/grid_tools.cc b/source/grid/grid_tools.cc
index d4e54d2de6..b9616c22de 100644
--- a/source/grid/grid_tools.cc
+++ b/source/grid/grid_tools.cc
@@ -35,6 +35,7 @@
 #include <deal.II/grid/tria_boundary.h>
 #include <deal.II/grid/grid_generator.h>
 #include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_reordering.h>
 #include <deal.II/dofs/dof_handler.h>
 #include <deal.II/dofs/dof_accessor.h>
 #include <deal.II/dofs/dof_tools.h>
@@ -4451,6 +4452,312 @@ next_cell:
       }
   }
 
+
+  template<int dim, int spacedim>
+  void regularize_corner_cells (Triangulation<dim,spacedim> &tria,
+                                const double limit_angle_fraction)
+  {
+    if (dim == 1)
+      return; // Nothing to do
+
+    // Check that we don't have hanging nodes
+    AssertThrow(!tria.has_hanging_nodes(), ExcMessage("The input Triangulation cannot "
+                                                      "have hanging nodes."));
+
+
+    bool has_cells_with_more_than_dim_faces_on_boundary = true;
+    bool has_cells_with_dim_faces_on_boundary = false;
+
+    unsigned int refinement_cycles = 0;
+
+    while (has_cells_with_more_than_dim_faces_on_boundary)
+      {
+        has_cells_with_more_than_dim_faces_on_boundary = false;
+
+        for (auto cell: tria.active_cell_iterators())
+          {
+            unsigned int boundary_face_counter = 0;
+            for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
+              if (cell->face(f)->at_boundary())
+                boundary_face_counter++;
+            if (boundary_face_counter > dim)
+              {
+                has_cells_with_more_than_dim_faces_on_boundary = true;
+                break;
+              }
+            else if (boundary_face_counter == dim)
+              has_cells_with_dim_faces_on_boundary = true;
+          }
+        if (has_cells_with_more_than_dim_faces_on_boundary)
+          {
+            tria.refine_global(1);
+            refinement_cycles++;
+          }
+      }
+
+    if (has_cells_with_dim_faces_on_boundary)
+      {
+        tria.refine_global(1);
+        refinement_cycles++;
+      }
+    else
+      {
+        while (refinement_cycles>0)
+          {
+            for (auto cell: tria.active_cell_iterators())
+              cell->set_coarsen_flag();
+            tria.execute_coarsening_and_refinement();
+            refinement_cycles--;
+          }
+        return;
+      }
+
+    std::vector<bool> cells_to_remove(tria.n_active_cells(), false);
+    std::vector<Point<spacedim> > vertices = tria.get_vertices();
+
+    std::vector<bool> faces_to_remove(tria.n_raw_faces(),false);
+
+    std::vector<CellData<dim> > cells_to_add;
+    SubCellData                 subcelldata_to_add;
+
+    // Trick compiler for dimension independent things
+    const unsigned int
+    v0 = 0, v1 = 1,
+    v2 = (dim > 1 ? 2:0), v3 = (dim > 1 ? 3:0),
+    v4 = (dim > 2 ? 4:0), v5 = (dim > 2 ? 5:0),
+    v6 = (dim > 2 ? 6:0), v7 = (dim > 2 ? 7:0);
+
+    for (auto cell : tria.active_cell_iterators())
+      {
+        double angle_fraction = 0;
+        unsigned int vertex_at_corner = numbers::invalid_unsigned_int;
+
+        if (dim == 2)
+          {
+            Tensor<1,spacedim> p0;
+            p0[spacedim > 1 ? 1 : 0] = 1;
+            Tensor<1,spacedim> p1;
+            p1[0] = 1;
+
+            if (cell->face(v0)->at_boundary() && cell->face(v3)->at_boundary())
+              {
+                p0 = cell->vertex(v0) -  cell->vertex(v2);
+                p1 = cell->vertex(v3) -  cell->vertex(v2);
+                vertex_at_corner = v2;
+              }
+            else  if (cell->face(v3)->at_boundary() && cell->face(v1)->at_boundary())
+              {
+                p0 = cell->vertex(v2) -  cell->vertex(v3);
+                p1 = cell->vertex(v1) -  cell->vertex(v3);
+                vertex_at_corner = v3;
+              }
+            else  if (cell->face(1)->at_boundary() && cell->face(2)->at_boundary())
+              {
+                p0 = cell->vertex(v0) -  cell->vertex(v1);
+                p1 = cell->vertex(v3) -  cell->vertex(v1);
+                vertex_at_corner = v1;
+              }
+            else  if (cell->face(2)->at_boundary() && cell->face(0)->at_boundary())
+              {
+                p0 = cell->vertex(v2) -  cell->vertex(v0);
+                p1 = cell->vertex(v1) -  cell->vertex(v0);
+                vertex_at_corner = v0;
+              }
+            p0 /= p0.norm();
+            p1 /= p1.norm();
+            angle_fraction = std::acos(p0*p1)/numbers::PI;
+
+          }
+        else
+          {
+            Assert(false, ExcNotImplemented());
+          }
+
+        if (angle_fraction > limit_angle_fraction)
+          {
+
+            auto flags_removal = [&](unsigned int f1, unsigned int f2,
+                                     unsigned int n1, unsigned int n2) -> void
+            {
+              cells_to_remove[cell->active_cell_index()] = true;
+              cells_to_remove[cell->neighbor(n1)->active_cell_index()] = true;
+              cells_to_remove[cell->neighbor(n2)->active_cell_index()] = true;
+
+              faces_to_remove[cell->face(f1)->index()] = true;
+              faces_to_remove[cell->face(f2)->index()] = true;
+
+              faces_to_remove[cell->neighbor(n1)->face(f1)->index()] = true;
+              faces_to_remove[cell->neighbor(n2)->face(f2)->index()] = true;
+            };
+
+            auto cell_creation = [&](
+                                   const unsigned int vv0,
+                                   const unsigned int vv1,
+                                   const unsigned int f0,
+                                   const unsigned int f1,
+
+                                   const unsigned int n0,
+                                   const unsigned int v0n0,
+                                   const unsigned int v1n0,
+
+                                   const unsigned int n1,
+                                   const unsigned int v0n1,
+                                   const unsigned int v1n1)
+            {
+              CellData<dim> c1, c2;
+              CellData<1> l1, l2;
+
+              c1.vertices[v0] = cell->vertex_index(vv0);
+              c1.vertices[v1] = cell->vertex_index(vv1);
+              c1.vertices[v2] = cell->neighbor(n0)->vertex_index(v0n0);
+              c1.vertices[v3] = cell->neighbor(n0)->vertex_index(v1n0);
+
+              c1.manifold_id = cell->manifold_id();
+              c1.material_id = cell->material_id();
+
+              c2.vertices[v0] = cell->vertex_index(vv0);
+              c2.vertices[v1] = cell->neighbor(n1)->vertex_index(v0n1);
+              c2.vertices[v2] = cell->vertex_index(vv1);
+              c2.vertices[v3] = cell->neighbor(n1)->vertex_index(v1n1);
+
+              c2.manifold_id = cell->manifold_id();
+              c2.material_id = cell->material_id();
+
+              l1.vertices[0] = cell->vertex_index(vv0);
+              l1.vertices[1] = cell->neighbor(n0)->vertex_index(v0n0);
+
+              l1.boundary_id = cell->line(f0)->boundary_id();
+              l1.manifold_id = cell->line(f0)->manifold_id();
+              subcelldata_to_add.boundary_lines.push_back(l1);
+
+              l2.vertices[0] = cell->vertex_index(vv0);
+              l2.vertices[1] = cell->neighbor(n1)->vertex_index(v0n1);
+
+              l2.boundary_id = cell->line(f1)->boundary_id();
+              l2.manifold_id = cell->line(f1)->manifold_id();
+              subcelldata_to_add.boundary_lines.push_back(l2);
+
+              cells_to_add.push_back(c1);
+              cells_to_add.push_back(c2);
+            };
+
+            if (dim == 2)
+              {
+                switch (vertex_at_corner)
+                  {
+                  case 0:
+                    flags_removal(0,2,3,1);
+                    cell_creation(0,3, 0,2, 3,2,3,  1,1,3);
+                    break;
+                  case 1:
+                    flags_removal(1,2,3,0);
+                    cell_creation(1,2, 2,1, 0,0,2, 3,3,2);
+                    break;
+                  case 2:
+                    flags_removal(3,0,1,2);
+                    cell_creation(2,1, 3,0, 1,3,1, 2,0,1);
+                    break;
+                  case 3:
+                    flags_removal(3,1,0,2);
+                    cell_creation(3,0, 1,3, 2,1,0, 0,2,0);
+                    break;
+                  }
+              }
+            else
+              {
+                Assert(false, ExcNotImplemented());
+              }
+          }
+      }
+
+    // if no cells need to be added, then no regularization is necessary. Restore things
+    // as they were before this function was called.
+    if (cells_to_add.size() == 0)
+      {
+        while (refinement_cycles>0)
+          {
+            for (auto cell: tria.active_cell_iterators())
+              cell->set_coarsen_flag();
+            tria.execute_coarsening_and_refinement();
+            refinement_cycles--;
+          }
+        return;
+      }
+
+    // add the cells that were not marked as skipped
+    for (auto cell : tria.active_cell_iterators())
+      {
+        if (cells_to_remove[cell->active_cell_index()] == false)
+          {
+            CellData<dim> c;
+            for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
+              c.vertices[v] = cell->vertex_index(v);
+            c.manifold_id = cell->manifold_id();
+            c.material_id = cell->material_id();
+            cells_to_add.push_back(c);
+          }
+      }
+
+    // Face counter for both dim == 2 and dim == 3
+    typename Triangulation<dim,spacedim>::active_face_iterator
+    face = tria.begin_active_face(),
+    endf = tria.end_face();
+    for (; face != endf; ++face)
+      if ( (face->at_boundary() || face->manifold_id() != numbers::invalid_manifold_id)
+           && faces_to_remove[face->index()] == false)
+        {
+          for (unsigned int l=0; l<GeometryInfo<dim>::lines_per_face; ++l)
+            {
+              CellData<1> line;
+              if (dim == 2)
+                {
+                  for (unsigned int v=0; v<GeometryInfo<1>::vertices_per_cell; ++v)
+                    line.vertices[v] = face->vertex_index(v);
+                  line.boundary_id = face->boundary_id();
+                  line.manifold_id = face->manifold_id();
+                }
+              else
+                {
+                  for (unsigned int v=0; v<GeometryInfo<1>::vertices_per_cell; ++v)
+                    line.vertices[v] = face->line(l)->vertex_index(v);
+                  line.boundary_id = face->line(l)->boundary_id();
+                  line.manifold_id = face->line(l)->manifold_id();
+                }
+              subcelldata_to_add.boundary_lines.push_back(line);
+            }
+          if (dim == 3)
+            {
+              CellData<2> quad;
+              for (unsigned int v=0; v<GeometryInfo<2>::vertices_per_cell; ++v)
+                quad.vertices[v] = face->vertex_index(v);
+              quad.boundary_id = face->boundary_id();
+              quad.manifold_id = face->manifold_id();
+              subcelldata_to_add.boundary_quads.push_back(quad);
+            }
+        }
+    GridTools::delete_unused_vertices(vertices, cells_to_add, subcelldata_to_add);
+    GridReordering<dim,spacedim>::reorder_cells(cells_to_add, true);
+
+    // Save manifolds
+    auto manifold_ids = tria.get_manifold_ids();
+    std::map<types::manifold_id, const Manifold<dim,spacedim>*> manifolds;
+    // Set manifolds in new Triangulation
+    for (auto manifold_id: manifold_ids)
+      if (manifold_id != numbers::invalid_manifold_id)
+        manifolds[manifold_id] = &tria.get_manifold(manifold_id);
+
+    tria.clear();
+
+    tria.create_triangulation(vertices, cells_to_add, subcelldata_to_add);
+
+    // Restore manifolds
+    for (auto manifold_id: manifold_ids)
+      if (manifold_id != numbers::invalid_manifold_id)
+        tria.set_manifold(manifold_id, *manifolds[manifold_id]);
+  }
+
+
+
 } /* namespace GridTools */
 
 
diff --git a/source/grid/grid_tools.inst.in b/source/grid/grid_tools.inst.in
index 1b593ec313..f148328ef1 100644
--- a/source/grid/grid_tools.inst.in
+++ b/source/grid/grid_tools.inst.in
@@ -411,6 +411,9 @@ for (deal_II_dimension : DIMENSIONS ; deal_II_space_dimension : SPACE_DIMENSIONS
     template void copy_material_to_manifold_id<deal_II_dimension, deal_II_space_dimension>
     (Triangulation<deal_II_dimension, deal_II_space_dimension> &, const bool);
 
+    template
+    void regularize_corner_cells
+    (Triangulation<deal_II_dimension,deal_II_space_dimension> &, double);
     \}
 #endif
 }
diff --git a/tests/grid/grid_tools_regularize_01.cc b/tests/grid/grid_tools_regularize_01.cc
new file mode 100644
index 0000000000..743077afad
--- /dev/null
+++ b/tests/grid/grid_tools_regularize_01.cc
@@ -0,0 +1,50 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2001 - 2015 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// GridTools::regularize_corner_cells
+
+#include "../tests.h"
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_out.h>
+
+template <int dim>
+void test ()
+{
+  const SphericalManifold<dim> m0;
+  Triangulation<dim> tria;
+  GridGenerator::hyper_cube(tria,-1,1);
+  tria.set_all_manifold_ids_on_boundary(0);
+  tria.set_manifold(0, m0);
+
+  GridTools::regularize_corner_cells (tria);
+
+  GridOut grid_out;
+  grid_out.write_msh (tria, deallog.get_file_stream());
+}
+
+
+
+int main ()
+{
+  initlog();
+
+  test<2> ();
+
+  return 0;
+}
+
diff --git a/tests/grid/grid_tools_regularize_01.output b/tests/grid/grid_tools_regularize_01.output
new file mode 100644
index 0000000000..214914d755
--- /dev/null
+++ b/tests/grid/grid_tools_regularize_01.output
@@ -0,0 +1,35 @@
+$NOD
+17
+1  -1.00000 -1.00000 0
+2  1.00000 -1.00000 0
+3  -1.00000 1.00000 0
+4  1.00000 1.00000 0
+5  0.00000 -1.41421 0
+6  -1.41421 0.00000 0
+7  1.41421 0.00000 0
+8  0.00000 1.41421 0
+9  0.00000 0.00000 0
+10  0.00000 -0.707107 0
+11  0.00000 0.707107 0
+12  -0.707107 0.00000 0
+13  0.707107 0.00000 0
+14  -0.621135 -0.621135 0
+15  0.621135 -0.621135 0
+16  -0.621135 0.621135 0
+17  0.621135 0.621135 0
+$ENDNOD
+$ELM
+12
+1 3 0 0 4 12 6 1 14 
+2 3 0 0 4 10 14 1 5 
+3 3 0 0 4 10 5 2 15 
+4 3 0 0 4 13 15 2 7 
+5 3 0 0 4 11 8 3 16 
+6 3 0 0 4 12 16 3 6 
+7 3 0 0 4 13 7 4 17 
+8 3 0 0 4 11 17 4 8 
+9 3 0 0 4 9 12 14 10 
+10 3 0 0 4 9 10 15 13 
+11 3 0 0 4 9 11 16 12 
+12 3 0 0 4 9 13 17 11 
+$ENDELM
diff --git a/tests/grid/grid_tools_regularize_02.cc b/tests/grid/grid_tools_regularize_02.cc
new file mode 100644
index 0000000000..03981670f4
--- /dev/null
+++ b/tests/grid/grid_tools_regularize_02.cc
@@ -0,0 +1,55 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2001 - 2015 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// GridTools::regularize_corner_cells on more complicated mesh
+
+#include "../tests.h"
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_out.h>
+
+int main()
+{
+  initlog();
+
+  Point<2> p0(0,0), p1(4,1);
+  Point<2> c0(.1, .5), c1(3.9,.5);
+
+  SphericalManifold<2> m0(c0);
+  SphericalManifold<2> m1(c1);
+
+  Triangulation<2> tria;
+  std::vector<unsigned int> subdivisions(2);
+  subdivisions[0] = 4;
+  subdivisions[1] = 1;
+  GridGenerator::subdivided_hyper_rectangle(tria,subdivisions, p0,p1,true);
+
+  GridTools::copy_boundary_to_manifold_id(tria);
+
+  tria.set_manifold(0, m0);
+  tria.set_manifold(1, m1);
+
+  GridTools::regularize_corner_cells (tria);
+  tria.refine_global(1);
+
+  GridOut grid_out;
+  grid_out.write_msh (tria, deallog.get_file_stream());
+
+  return 0;
+}
+
+
diff --git a/tests/grid/grid_tools_regularize_02.output b/tests/grid/grid_tools_regularize_02.output
new file mode 100644
index 0000000000..5d2bb06537
--- /dev/null
+++ b/tests/grid/grid_tools_regularize_02.output
@@ -0,0 +1,520 @@
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-- 
2.39.5