From a3f52df42978439a5aea1aaa85bd9305ba62de89 Mon Sep 17 00:00:00 2001
From: Peter Munch <peterrmuench@gmail.com>
Date: Mon, 13 Jul 2020 17:48:46 +0200
Subject: [PATCH] Generalize DataOut::write_vtk for simplex mesh

---
 include/deal.II/base/data_out_base.h          |   21 +
 .../numerics/data_out_dof_data.templates.h    |  150 +-
 source/base/data_out_base.cc                  |  245 +-
 source/numerics/data_out.cc                   |   13 +-
 source/simplex/fe_lib.cc                      |    6 +-
 tests/simplex/data_out_write_vtk_01.cc        |  120 +
 ...rite_vtk_01.with_simplex_support=on.output | 3205 +++++++++++++++++
 7 files changed, 3677 insertions(+), 83 deletions(-)
 create mode 100644 tests/simplex/data_out_write_vtk_01.cc
 create mode 100644 tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output

diff --git a/include/deal.II/base/data_out_base.h b/include/deal.II/base/data_out_base.h
index a2f704fdb1..03fcfeff17 100644
--- a/include/deal.II/base/data_out_base.h
+++ b/include/deal.II/base/data_out_base.h
@@ -24,6 +24,8 @@
 #include <deal.II/base/point.h>
 #include <deal.II/base/table.h>
 
+#include <deal.II/grid/reference_cell.h>
+
 #include <deal.II/numerics/data_component_interpretation.h>
 
 // To be able to serialize XDMFEntry
@@ -319,6 +321,11 @@ namespace DataOutBase
      */
     bool points_are_available;
 
+    /**
+     * Reference-cell type of the underlying cell of this patch.
+     */
+    ReferenceCell::Type reference_cell_type;
+
     /**
      * Default constructor. Sets #n_subdivisions to one, #points_are_available
      * to false, and #patch_index to #no_neighbor.
@@ -464,6 +471,11 @@ namespace DataOutBase
      */
     bool points_are_available;
 
+    /**
+     * Reference-cell type of the underlying cell of this patch.
+     */
+    ReferenceCell::Type reference_cell_type;
+
     /**
      * Default constructor. Sets #points_are_available
      * to false, and #patch_index to #no_neighbor.
@@ -1350,6 +1362,15 @@ namespace DataOutBase
                const unsigned int d2,
                const unsigned int d3);
 
+    /**
+     * Record a single deal.II cell without subdivisions (e.g. simplex) in the
+     * internal reordered format.
+     */
+    void
+    write_cell_single(const unsigned int index,
+                      const unsigned int start,
+                      const unsigned int n_points);
+
     /**
      * Filter and record a data set. If there are multiple values at a given
      * vertex and redundant values are being removed, one is arbitrarily
diff --git a/include/deal.II/numerics/data_out_dof_data.templates.h b/include/deal.II/numerics/data_out_dof_data.templates.h
index 602b339512..a477639ea0 100644
--- a/include/deal.II/numerics/data_out_dof_data.templates.h
+++ b/include/deal.II/numerics/data_out_dof_data.templates.h
@@ -46,6 +46,8 @@
 #include <deal.II/numerics/data_out.h>
 #include <deal.II/numerics/data_out_dof_data.h>
 
+#include <deal.II/simplex/fe_lib.h>
+
 #include <memory>
 #include <string>
 #include <utility>
@@ -60,10 +62,10 @@ namespace internal
   {
     template <int dim, int spacedim>
     ParallelDataBase<dim, spacedim>::ParallelDataBase(
-      const unsigned int               n_datasets,
-      const unsigned int               n_subdivisions,
-      const std::vector<unsigned int> &n_postprocessor_outputs,
-      const Mapping<dim, spacedim> &   mapping,
+      const unsigned int                    n_datasets,
+      const unsigned int                    n_subdivisions,
+      const std::vector<unsigned int> &     n_postprocessor_outputs,
+      const dealii::Mapping<dim, spacedim> &mapping,
       const std::vector<
         std::shared_ptr<dealii::hp::FECollection<dim, spacedim>>>
         &               finite_elements,
@@ -101,9 +103,49 @@ namespace internal
       unsigned int n_q_points = 0;
       if (use_face_values == false)
         {
-          dealii::hp::QCollection<dim> quadrature(
-            QIterated<dim>(QTrapez<1>(), n_subdivisions));
-          n_q_points = quadrature[0].size();
+          const bool do_simplex =
+            std::any_of(finite_elements.begin(),
+                        finite_elements.end(),
+                        [](const auto &fe) {
+                          for (unsigned int i = 0; i < fe->size(); ++i)
+                            if ((*fe)[i].reference_cell_type() !=
+                                ReferenceCell::get_hypercube(dim))
+                              return true;
+                          return false;
+                        });
+
+          const bool do_hex =
+            std::any_of(finite_elements.begin(),
+                        finite_elements.end(),
+                        [](const auto &fe) {
+                          for (unsigned int i = 0; i < fe->size(); ++i)
+                            if ((*fe)[i].reference_cell_type() ==
+                                ReferenceCell::get_hypercube(dim))
+                              return true;
+                          return false;
+                        });
+
+          std::unique_ptr<dealii::Quadrature<dim>> quadrature1;
+          std::unique_ptr<dealii::Quadrature<dim>> quadrature2;
+
+          if (do_simplex)
+            {
+              Assert(1 <= n_subdivisions && n_subdivisions <= 2,
+                     ExcNotImplemented());
+              quadrature1.reset(new Quadrature<dim>(
+                Simplex::FE_P<dim, spacedim>(n_subdivisions == 1 ? 1 : 2)
+                  .get_unit_support_points()));
+            }
+
+          if (do_hex)
+            {
+              quadrature2.reset(new Quadrature<dim>(
+                QIterated<dim>(QTrapez<1>(), n_subdivisions)));
+            }
+
+          n_q_points = std::max(do_simplex ? quadrature1->size() : 0,
+                                do_hex ? quadrature2->size() : 1);
+
           x_fe_values.resize(this->finite_elements.size());
           for (unsigned int i = 0; i < this->finite_elements.size(); ++i)
             {
@@ -117,12 +159,25 @@ namespace internal
                     break;
                   }
               if (x_fe_values[i].get() == nullptr)
-                x_fe_values[i] =
-                  std::make_shared<dealii::hp::FEValues<dim, spacedim>>(
-                    this->mapping_collection,
-                    *this->finite_elements[i],
-                    quadrature,
-                    this->update_flags);
+                {
+                  dealii::hp::QCollection<dim> quadrature;
+
+                  for (unsigned int j = 0; j < this->finite_elements[i]->size();
+                       ++j)
+                    if ((*this->finite_elements[i])[j].reference_cell_type() !=
+                        ReferenceCell::get_hypercube(dim))
+                      quadrature.push_back(*quadrature1);
+                    else
+                      quadrature.push_back(*quadrature2);
+
+                  x_fe_values[i] =
+                    std::make_shared<dealii::hp::FEValues<dim, spacedim>>(
+                      this->mapping_collection,
+                      *this->finite_elements[i],
+                      quadrature,
+                      do_simplex ? (update_flags | update_quadrature_points) :
+                                   update_flags);
+                }
             }
         }
       else
@@ -186,9 +241,49 @@ namespace internal
       if (data.x_fe_values.empty() == false)
         {
           Assert(data.x_fe_face_values.empty() == true, ExcInternalError());
-          dealii::hp::QCollection<dim> quadrature(
-            QIterated<dim>(QTrapez<1>(), n_subdivisions));
+
+          const bool do_simplex =
+            std::any_of(finite_elements.begin(),
+                        finite_elements.end(),
+                        [](const auto &fe) {
+                          for (unsigned int i = 0; i < fe->size(); ++i)
+                            if ((*fe)[i].reference_cell_type() !=
+                                ReferenceCell::get_hypercube(dim))
+                              return true;
+                          return false;
+                        });
+
+          const bool do_hex =
+            std::any_of(finite_elements.begin(),
+                        finite_elements.end(),
+                        [](const auto &fe) {
+                          for (unsigned int i = 0; i < fe->size(); ++i)
+                            if ((*fe)[i].reference_cell_type() ==
+                                ReferenceCell::get_hypercube(dim))
+                              return true;
+                          return false;
+                        });
+
+          std::unique_ptr<dealii::Quadrature<dim>> quadrature1;
+          std::unique_ptr<dealii::Quadrature<dim>> quadrature2;
+
+          if (do_simplex)
+            {
+              Assert(1 <= n_subdivisions && n_subdivisions <= 2,
+                     ExcNotImplemented());
+              quadrature1.reset(new Quadrature<dim>(
+                Simplex::FE_P<dim, spacedim>(n_subdivisions == 1 ? 1 : 2)
+                  .get_unit_support_points()));
+            }
+
+          if (do_hex)
+            {
+              quadrature2.reset(new Quadrature<dim>(
+                QIterated<dim>(QTrapez<1>(), n_subdivisions)));
+            }
+
           x_fe_values.resize(this->finite_elements.size());
+
           for (unsigned int i = 0; i < this->finite_elements.size(); ++i)
             {
               // check if there is a finite element that is equal to the present
@@ -201,12 +296,25 @@ namespace internal
                     break;
                   }
               if (x_fe_values[i].get() == nullptr)
-                x_fe_values[i] =
-                  std::make_shared<dealii::hp::FEValues<dim, spacedim>>(
-                    this->mapping_collection,
-                    *this->finite_elements[i],
-                    quadrature,
-                    this->update_flags);
+                {
+                  dealii::hp::QCollection<dim> quadrature;
+
+                  for (unsigned int j = 0; j < this->finite_elements[i]->size();
+                       ++j)
+                    if ((*this->finite_elements[i])[j].reference_cell_type() !=
+                        ReferenceCell::get_hypercube(dim))
+                      quadrature.push_back(*quadrature1);
+                    else
+                      quadrature.push_back(*quadrature2);
+
+                  x_fe_values[i] =
+                    std::make_shared<dealii::hp::FEValues<dim, spacedim>>(
+                      this->mapping_collection,
+                      *this->finite_elements[i],
+                      quadrature,
+                      do_simplex ? (update_flags | update_quadrature_points) :
+                                   update_flags);
+                }
             }
         }
       else
diff --git a/source/base/data_out_base.cc b/source/base/data_out_base.cc
index 8c52f6145e..3d64d59ba6 100644
--- a/source/base/data_out_base.cc
+++ b/source/base/data_out_base.cc
@@ -292,7 +292,9 @@ namespace DataOutBase
                                         (n_data_sets + spacedim) :
                                         n_data_sets,
                                       patch.data.n_rows()));
-          Assert((n_data_sets == 0) ||
+          Assert(patch.reference_cell_type !=
+                     ReferenceCell::get_hypercube(dim) ||
+                   (n_data_sets == 0) ||
                    (patch.data.n_cols() ==
                     Utilities::fixed_power<dim>(n_subdivisions + 1)),
                  ExcInvalidDatasetSize(patch.data.n_cols(),
@@ -487,6 +489,20 @@ namespace DataOutBase
 
 
 
+  void
+  DataOutFilter::write_cell_single(const unsigned int index,
+                                   const unsigned int start,
+                                   const unsigned int n_points)
+  {
+    (void)index;
+    (void)start;
+    (void)n_points;
+
+    Assert(false, ExcNotImplemented());
+  }
+
+
+
   void
   DataOutFilter::write_data_set(const std::string &     name,
                                 const unsigned int      dimension,
@@ -851,6 +867,27 @@ namespace
                         "it."));
     }
 
+    /**
+     * Write dim-dimensional @p index cell with @p n_point vertices and first
+     * vertex at number @p start.
+     *
+     * @note All inheriting classes should implement this function.
+     */
+    void
+    write_cell_single(const unsigned int index,
+                      const unsigned int start,
+                      const unsigned int n_points)
+    {
+      (void)index;
+      (void)start;
+      (void)n_points;
+
+      Assert(false,
+             ExcMessage("The derived class you are using needs to "
+                        "reimplement this function if you want to call "
+                        "it."));
+    }
+
     /**
      * Do whatever is necessary to terminate the list of cells. This function is
      * usually only reimplemented if deal.II is compiled with zlib. The default
@@ -1060,6 +1097,14 @@ namespace
                const unsigned int y_offset,
                const unsigned int z_offset);
 
+    /**
+     * Print vertices [start, start+n_points[
+     */
+    void
+    write_cell_single(const unsigned int index,
+                      const unsigned int start,
+                      const unsigned int n_points);
+
     /**
      * Write a high-order cell type, i.e., a Lagrange cell
      * in the VTK terminology.
@@ -1452,6 +1497,19 @@ namespace
     stream << '\n';
   }
 
+  void
+  VtkStream::write_cell_single(const unsigned int index,
+                               const unsigned int start,
+                               const unsigned int n_points)
+  {
+    (void)index;
+
+    stream << '\t' << n_points;
+    for (unsigned int i = 0; i < n_points; ++i)
+      stream << '\t' << start + i;
+    stream << '\n';
+  }
+
   template <int dim>
   void
   VtkStream::write_high_order_cell(const unsigned int,
@@ -1612,6 +1670,7 @@ namespace DataOutBase
     : patch_index(no_neighbor)
     , n_subdivisions(1)
     , points_are_available(false)
+    , reference_cell_type(ReferenceCell::get_hypercube(dim))
   // all the other data has a constructor of its own, except for the "neighbors"
   // field, which we set to invalid values.
   {
@@ -1689,6 +1748,7 @@ namespace DataOutBase
     std::swap(n_subdivisions, other_patch.n_subdivisions);
     data.swap(other_patch.data);
     std::swap(points_are_available, other_patch.points_are_available);
+    std::swap(reference_cell_type, other_patch.reference_cell_type);
   }
 
 
@@ -1712,6 +1772,7 @@ namespace DataOutBase
   Patch<0, spacedim>::Patch()
     : patch_index(no_neighbor)
     , points_are_available(false)
+    , reference_cell_type(ReferenceCell::get_hypercube(0))
   {
     Assert(spacedim <= 3, ExcNotImplemented());
   }
@@ -2371,19 +2432,39 @@ namespace DataOutBase
 
     for (const auto &patch : patches)
       {
-        const unsigned int n_subdivisions = patch.n_subdivisions;
-        const unsigned int n              = n_subdivisions + 1;
-        // Length of loops in all dimensions. If a dimension is not used, a loop
-        // of length one will do the job.
-        const unsigned int n1 = (dim > 0) ? n : 1;
-        const unsigned int n2 = (dim > 1) ? n : 1;
-        const unsigned int n3 = (dim > 2) ? n : 1;
+        // special treatment of simplices since they are not subdivided, such
+        // that no new nodes have to be created, but the precomputed ones can be
+        // used
+        if (patch.reference_cell_type != ReferenceCell::get_hypercube(dim))
+          {
+            Point<spacedim> node;
+
+            for (unsigned int point_no = 0; point_no < patch.data.n_cols();
+                 ++point_no)
+              {
+                for (unsigned int d = 0; d < spacedim; ++d)
+                  node[d] =
+                    patch.data(patch.data.size(0) - spacedim + d, point_no);
+
+                out.write_point(count++, node);
+              }
+          }
+        else
+          {
+            const unsigned int n_subdivisions = patch.n_subdivisions;
+            const unsigned int n              = n_subdivisions + 1;
+            // Length of loops in all dimensions. If a dimension is not used, a
+            // loop of length one will do the job.
+            const unsigned int n1 = (dim > 0) ? n : 1;
+            const unsigned int n2 = (dim > 1) ? n : 1;
+            const unsigned int n3 = (dim > 2) ? n : 1;
 
-        for (unsigned int i3 = 0; i3 < n3; ++i3)
-          for (unsigned int i2 = 0; i2 < n2; ++i2)
-            for (unsigned int i1 = 0; i1 < n1; ++i1)
-              out.write_point(count++,
-                              compute_node(patch, i1, i2, i3, n_subdivisions));
+            for (unsigned int i3 = 0; i3 < n3; ++i3)
+              for (unsigned int i2 = 0; i2 < n2; ++i2)
+                for (unsigned int i1 = 0; i1 < n1; ++i1)
+                  out.write_point(
+                    count++, compute_node(patch, i1, i2, i3, n_subdivisions));
+          }
       }
     out.flush_points();
   }
@@ -2397,28 +2478,39 @@ namespace DataOutBase
     unsigned int first_vertex_of_patch = 0;
     for (const auto &patch : patches)
       {
-        const unsigned int n_subdivisions = patch.n_subdivisions;
-        const unsigned int n              = n_subdivisions + 1;
-        // Length of loops in all dimensons
-        const unsigned int n1 = (dim > 0) ? n_subdivisions : 1;
-        const unsigned int n2 = (dim > 1) ? n_subdivisions : 1;
-        const unsigned int n3 = (dim > 2) ? n_subdivisions : 1;
-        // Offsets of outer loops
-        const unsigned int d1 = 1;
-        const unsigned int d2 = n;
-        const unsigned int d3 = n * n;
-        for (unsigned int i3 = 0; i3 < n3; ++i3)
-          for (unsigned int i2 = 0; i2 < n2; ++i2)
-            for (unsigned int i1 = 0; i1 < n1; ++i1)
-              {
-                const unsigned int offset =
-                  first_vertex_of_patch + i3 * d3 + i2 * d2 + i1 * d1;
-                // First write line in x direction
-                out.template write_cell<dim>(count++, offset, d1, d2, d3);
-              }
-        // finally update the number of the first vertex of this patch
-        first_vertex_of_patch +=
-          Utilities::fixed_power<dim>(n_subdivisions + 1);
+        // special treatment of simplices since they are not subdivided
+        if (patch.reference_cell_type != ReferenceCell::get_hypercube(dim))
+          {
+            out.write_cell_single(count++,
+                                  first_vertex_of_patch,
+                                  patch.data.n_cols());
+            first_vertex_of_patch += patch.data.n_cols();
+          }
+        else
+          {
+            const unsigned int n_subdivisions = patch.n_subdivisions;
+            const unsigned int n              = n_subdivisions + 1;
+            // Length of loops in all dimensons
+            const unsigned int n1 = (dim > 0) ? n_subdivisions : 1;
+            const unsigned int n2 = (dim > 1) ? n_subdivisions : 1;
+            const unsigned int n3 = (dim > 2) ? n_subdivisions : 1;
+            // Offsets of outer loops
+            const unsigned int d1 = 1;
+            const unsigned int d2 = n;
+            const unsigned int d3 = n * n;
+            for (unsigned int i3 = 0; i3 < n3; ++i3)
+              for (unsigned int i2 = 0; i2 < n2; ++i2)
+                for (unsigned int i1 = 0; i1 < n1; ++i1)
+                  {
+                    const unsigned int offset =
+                      first_vertex_of_patch + i3 * d3 + i2 * d2 + i1 * d1;
+                    // First write line in x direction
+                    out.template write_cell<dim>(count++, offset, d1, d2, d3);
+                  }
+            // finally update the number of the first vertex of this patch
+            first_vertex_of_patch +=
+              Utilities::fixed_power<dim>(n_subdivisions + 1);
+          }
       }
 
     out.flush_cells();
@@ -4836,18 +4928,39 @@ namespace DataOutBase
     }
 
     // first count the number of cells and cells for later use
-    unsigned int n_nodes;
-    unsigned int n_cells;
-    compute_sizes<dim, spacedim>(patches, n_nodes, n_cells);
+    unsigned int n_nodes            = 0;
+    unsigned int n_cells            = 0;
+    unsigned int n_points_an_n_cell = 0;
 
-    // If a user set to output high order cells, we treat n_subdivisions
-    // as a cell order and adjust variables accordingly, otherwise
-    // each patch is written as a linear cell.
-    unsigned int n_points_per_cell = GeometryInfo<dim>::vertices_per_cell;
-    if (flags.write_higher_order_cells)
+    // compute_sizes<dim, spacedim>(patches, n_nodes, n_cells);
+
+    for (const auto &patch : patches)
       {
-        n_cells           = patches.size();
-        n_points_per_cell = n_nodes / n_cells;
+        // special treatment of simplices since they are not subdivided
+        if (patch.reference_cell_type != ReferenceCell::get_hypercube(dim))
+          {
+            n_nodes += patch.data.n_cols();
+            n_cells += 1;
+            n_points_an_n_cell += patch.data.n_cols() + 1;
+          }
+        else
+          {
+            n_nodes += Utilities::fixed_power<dim>(patch.n_subdivisions + 1);
+
+            if (flags.write_higher_order_cells)
+              {
+                n_cells += 1;
+                n_points_an_n_cell +=
+                  1 + Utilities::fixed_power<dim>(patch.n_subdivisions + 1);
+              }
+            else
+              {
+                n_cells += Utilities::fixed_power<dim>(patch.n_subdivisions);
+                n_points_an_n_cell +=
+                  Utilities::fixed_power<dim>(patch.n_subdivisions) *
+                  (1 + GeometryInfo<dim>::vertices_per_cell);
+              }
+          }
       }
 
     // in gmv format the vertex coordinates and the data have an order that is a
@@ -4879,8 +4992,7 @@ namespace DataOutBase
     out << '\n';
     /////////////////////////////////
     // now for the cells
-    out << "CELLS " << n_cells << ' ' << n_cells * (n_points_per_cell + 1)
-        << '\n';
+    out << "CELLS " << n_cells << ' ' << n_points_an_n_cell << '\n';
     if (flags.write_higher_order_cells)
       write_high_order_cells(patches, vtk_out);
     else
@@ -4890,12 +5002,39 @@ namespace DataOutBase
     // simple
     out << "CELL_TYPES " << n_cells << '\n';
 
-    // need to distinguish between linear and high order cells
-    const unsigned int vtk_cell_id = flags.write_higher_order_cells ?
-                                       vtk_lagrange_cell_type[dim] :
-                                       vtk_cell_type[dim];
-    for (unsigned int i = 0; i < n_cells; ++i)
-      out << ' ' << vtk_cell_id;
+    // need to distinguish between linear cells, simplex cells (linear or
+    // quadratic), and  high order cells
+    for (const auto &patch : patches)
+      {
+        std::pair<unsigned int, unsigned int> vtk_cell_id = {-1, -1};
+
+        if (flags.write_higher_order_cells &&
+            patch.reference_cell_type == ReferenceCell::get_hypercube(dim))
+          vtk_cell_id = {vtk_lagrange_cell_type[dim], 1};
+        else if (patch.reference_cell_type == ReferenceCell::Type::Tri &&
+                 patch.data.n_cols() == 3)
+          vtk_cell_id = {5, 1};
+        else if (patch.reference_cell_type == ReferenceCell::Type::Tri &&
+                 patch.data.n_cols() == 6)
+          vtk_cell_id = {22, 1};
+        else if (patch.reference_cell_type == ReferenceCell::Type::Tet &&
+                 patch.data.n_cols() == 4)
+          vtk_cell_id = {10, 1};
+        else if (patch.reference_cell_type == ReferenceCell::Type::Tet &&
+                 patch.data.n_cols() == 10)
+          vtk_cell_id = {24, 1};
+        else if (patch.reference_cell_type == ReferenceCell::get_hypercube(dim))
+          vtk_cell_id = {vtk_cell_type[dim],
+                         Utilities::pow(patch.n_subdivisions, dim)};
+        else
+          {
+            Assert(false, ExcNotImplemented());
+          }
+
+        for (unsigned int i = 0; i < vtk_cell_id.second; ++i)
+          out << ' ' << vtk_cell_id.first;
+      }
+
     out << '\n';
     ///////////////////////////////////////
     // data output.
diff --git a/source/numerics/data_out.cc b/source/numerics/data_out.cc
index d78b22e2de..2a28a0f04a 100644
--- a/source/numerics/data_out.cc
+++ b/source/numerics/data_out.cc
@@ -97,7 +97,8 @@ DataOut<dim, DoFHandlerType>::build_one_patch(
   ::dealii::DataOutBase::Patch<DoFHandlerType::dimension,
                                DoFHandlerType::space_dimension>
     patch;
-  patch.n_subdivisions = n_subdivisions;
+  patch.n_subdivisions      = n_subdivisions;
+  patch.reference_cell_type = cell_and_index->first->reference_cell_type();
 
   // initialize FEValues
   scratch_data.reinit_all_fe_values(this->dof_data, cell_and_index->first);
@@ -108,8 +109,7 @@ DataOut<dim, DoFHandlerType>::build_one_patch(
   // set the vertices of the patch. if the mapping does not preserve locations
   // (e.g. MappingQEulerian), we need to compute the offset of the vertex for
   // the graphical output. Otherwise, we can just use the vertex info.
-  for (const unsigned int vertex :
-       GeometryInfo<DoFHandlerType::dimension>::vertex_indices())
+  for (const unsigned int vertex : cell_and_index->first->vertex_indices())
     if (fe_patch_values.get_mapping().preserves_vertex_locations())
       patch.vertices[vertex] = cell_and_index->first->vertex(vertex);
     else
@@ -133,7 +133,9 @@ DataOut<dim, DoFHandlerType>::build_one_patch(
   if (curved_cell_region == curved_inner_cells ||
       (curved_cell_region == curved_boundary &&
        (cell_and_index->first->at_boundary() ||
-        (DoFHandlerType::dimension != DoFHandlerType::space_dimension))))
+        (DoFHandlerType::dimension != DoFHandlerType::space_dimension))) ||
+      (cell_and_index->first->reference_cell_type() !=
+       ReferenceCell::get_hypercube(dim)))
     {
       Assert(patch.space_dim == DoFHandlerType::space_dimension,
              ExcInternalError());
@@ -1009,8 +1011,7 @@ DataOut<dim, DoFHandlerType>::build_one_patch(
     }
 
 
-  for (const unsigned int f :
-       GeometryInfo<DoFHandlerType::dimension>::face_indices())
+  for (const unsigned int f : cell_and_index->first->face_indices())
     {
       // let's look up whether the neighbor behind that face is noted in the
       // table of cells which we treat. this can only happen if the neighbor
diff --git a/source/simplex/fe_lib.cc b/source/simplex/fe_lib.cc
index 75af427581..a4b0d0282f 100644
--- a/source/simplex/fe_lib.cc
+++ b/source/simplex/fe_lib.cc
@@ -115,9 +115,9 @@ namespace Simplex
       {
         if (degree == 1)
           {
+            this->unit_support_points.emplace_back(0.0, 0.0);
             this->unit_support_points.emplace_back(1.0, 0.0);
             this->unit_support_points.emplace_back(0.0, 1.0);
-            this->unit_support_points.emplace_back(0.0, 0.0);
 
             // TODO
             this->unit_face_support_points.emplace_back(0.0);
@@ -125,12 +125,12 @@ namespace Simplex
           }
         else if (degree == 2)
           {
+            this->unit_support_points.emplace_back(0.0, 0.0);
             this->unit_support_points.emplace_back(1.0, 0.0);
             this->unit_support_points.emplace_back(0.0, 1.0);
-            this->unit_support_points.emplace_back(0.0, 0.0);
+            this->unit_support_points.emplace_back(0.5, 0.0);
             this->unit_support_points.emplace_back(0.5, 0.5);
             this->unit_support_points.emplace_back(0.0, 0.5);
-            this->unit_support_points.emplace_back(0.5, 0.0);
 
             // TODO
             this->unit_face_support_points.emplace_back(0.0);
diff --git a/tests/simplex/data_out_write_vtk_01.cc b/tests/simplex/data_out_write_vtk_01.cc
new file mode 100644
index 0000000000..027654e519
--- /dev/null
+++ b/tests/simplex/data_out_write_vtk_01.cc
@@ -0,0 +1,120 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+
+// Test DataOut::write_vtk() for simplex meshes.
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/mapping_fe.h>
+
+#include <deal.II/grid/grid_in.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <deal.II/simplex/fe_lib.h>
+#include <deal.II/simplex/grid_generator.h>
+
+#include "../tests.h"
+
+using namespace dealii;
+
+template <int dim>
+class RightHandSideFunction : public Function<dim>
+{
+public:
+  RightHandSideFunction(const unsigned int n_components)
+    : Function<dim>(n_components)
+  {}
+
+  virtual double
+  value(const Point<dim> &p, const unsigned int component = 0) const
+  {
+    return p[component % dim] * p[component % dim];
+  }
+};
+
+template <int dim, int spacedim = dim>
+void
+test(const FiniteElement<dim, spacedim> &fe, const unsigned int n_components)
+{
+  Triangulation<dim, spacedim> tria;
+  Simplex::GridGenerator::subdivided_hyper_cube(tria, dim == 2 ? 4 : 2);
+
+  DoFHandler<dim> dof_handler(tria);
+
+  dof_handler.distribute_dofs(fe);
+
+  Vector<double> solution(dof_handler.n_dofs());
+
+  MappingFE<dim> mapping(Simplex::FE_P<dim>(1));
+
+  VectorTools::interpolate(mapping,
+                           dof_handler,
+                           RightHandSideFunction<dim>(n_components),
+                           solution);
+
+  static unsigned int counter = 0;
+
+  for (unsigned int n_subdivisions = 1; n_subdivisions <= 2; ++n_subdivisions)
+    {
+      DataOut<dim> data_out;
+
+      data_out.attach_dof_handler(dof_handler);
+      data_out.add_data_vector(solution, "solution");
+
+
+      data_out.build_patches(mapping, n_subdivisions);
+
+#if false
+  std::ofstream output("test." + std::to_string(dim) + "." + std::to_string(counter++) + ".vtk");
+  data_out.write_vtk(output);
+#else
+      data_out.write_vtk(deallog.get_file_stream());
+#endif
+    }
+}
+
+int
+main()
+{
+  initlog();
+
+  {
+    const unsigned int dim = 2;
+    test<dim>(Simplex::FE_P<dim>(2) /*=degree*/, 1);
+    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/), dim), dim);
+    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/),
+                            dim,
+                            Simplex::FE_P<dim>(1 /*=degree*/),
+                            1),
+              dim + 1);
+  }
+  {
+    const unsigned int dim = 3;
+    test<dim>(Simplex::FE_P<dim>(2) /*=degree*/, 1);
+    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/), dim), dim);
+    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/),
+                            dim,
+                            Simplex::FE_P<dim>(1 /*=degree*/),
+                            1),
+              dim + 1);
+  }
+}
diff --git a/tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output b/tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output
new file mode 100644
index 0000000000..9545765567
--- /dev/null
+++ b/tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output
@@ -0,0 +1,3205 @@
+
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