C++ MeshEditor::init_vertices_global方法代码示例

//-----------------------------------------------------------------------------
void dolfin::p_refine(Mesh& refined_mesh, const Mesh& mesh)
{
  MeshEditor editor;
  if (mesh.geometry().degree() != 1)
  {
    dolfin_error("refine.cpp",
                 "increase polynomial degree of mesh",
                 "Currently only linear -> quadratic is supported");
  }

  const CellType::Type cell_type = mesh.type().cell_type();

  if (cell_type != CellType::Type::triangle
      and cell_type != CellType::Type::tetrahedron
      and cell_type != CellType::Type::interval)
  {
    dolfin_error("refine.cpp",
                 "increase polynomial degree of mesh",
                 "Unsupported cell type");
  }

  const std::size_t tdim = mesh.topology().dim();
  const std::size_t gdim = mesh.geometry().dim();

  editor.open(refined_mesh, cell_type, tdim, gdim, 2);

  // Copy over mesh
  editor.init_vertices_global(mesh.num_entities(0), mesh.num_entities_global(0));
  for (VertexIterator v(mesh); !v.end(); ++v)
    editor.add_vertex(v->index(), v->point());

  editor.init_cells_global(mesh.num_entities(tdim), mesh.num_entities_global(tdim));
  std::vector<std::size_t> verts(tdim + 1);
  for (CellIterator c(mesh); !c.end(); ++c)
  {
    std::copy(c->entities(0), c->entities(0) + tdim + 1, verts.begin());
    editor.add_cell(c->index(), verts);
  }

  // Initialise edges
  editor.init_entities();

  // Add points at centres of edges
  for (EdgeIterator e(refined_mesh); !e.end(); ++e)
    editor.add_entity_point(1, 0, e->index(), e->midpoint());

  editor.close();
}

//-----------------------------------------------------------------------------
UnitTriangleMesh::UnitTriangleMesh() : Mesh()
{
  // Receive mesh according to parallel policy
  if (MPI::is_receiver(this->mpi_comm()))
  {
    MeshPartitioning::build_distributed_mesh(*this);
    return;
  }

  // Open mesh for editing
  MeshEditor editor;
  editor.open(*this, CellType::triangle, 2, 2);

  // Create vertices
  editor.init_vertices_global(3, 3);
  std::vector<double> x(2);
  x[0] = 0.0; x[1] = 0.0;
  editor.add_vertex(0, x);
  x[0] = 1.0; x[1] = 0.0;
  editor.add_vertex(1, x);
  x[0] = 0.0; x[1] = 1.0;
  editor.add_vertex(2, x);

  // Create cells
  editor.init_cells_global(1, 1);
  std::vector<std::size_t> cell_data(3);
  cell_data[0] = 0; cell_data[1] = 1; cell_data[2] = 2;
  editor.add_cell(0, cell_data);

  // Close mesh editor
  editor.close();

  // Broadcast mesh according to parallel policy
  if (MPI::is_broadcaster(this->mpi_comm()))
  {
    MeshPartitioning::build_distributed_mesh(*this);
    return;
  }
}

//-----------------------------------------------------------------------------
UnitDiscMesh::UnitDiscMesh(MPI_Comm comm, std::size_t n,
                           std::size_t degree, std::size_t gdim)
  : Mesh(comm)
{
  dolfin_assert(n > 0);
  dolfin_assert(gdim == 2 or gdim == 3);
  dolfin_assert(degree == 1 or degree == 2);

  MeshEditor editor;
  editor.open(*this, 2, gdim, degree);
  editor.init_vertices_global(1 + 3*n*(n + 1),
                              1 + 3*n*(n + 1));

  std::size_t c = 0;
  editor.add_vertex(c, Point(0,0,0));
  ++c;

  for (std::size_t i = 1; i <= n; ++i)
    for (std::size_t j = 0; j < 6*i; ++j)
    {
      double r = (double)i/(double)n;
      double th = 2*M_PI*(double)j/(double)(6*i);
      double x = r*cos(th);
      double y = r*sin(th);
      editor.add_vertex(c, Point(x, y, 0));
      ++c;
    }

  editor.init_cells(6*n*n);

  c = 0;
  std::size_t base_i = 0;
  std::size_t row_i = 1;
  for (std::size_t i = 1; i <= n; ++i)
  {
    std::size_t base_m = base_i;
    base_i = 1 + 3*i*(i - 1);
    std::size_t row_m = row_i;
    row_i = 6*i;

    for (std::size_t k = 0; k != 6; ++k)
      for (std::size_t j = 0; j < (i*2 - 1); ++j)
      {
        std::size_t i0, i1, i2;
        if (j%2 == 0)
        {
          i0 = base_i + (k*i + j/2)%row_i;
          i1 = base_i + (k*i + j/2 + 1)%row_i;
          i2 = base_m + (k*(i-1) + j/2)%row_m;
        }
        else
        {
          i0 = base_m + (k*(i-1) + j/2)%row_m;
          i1 = base_m + (k*(i-1) + j/2 + 1)%row_m;
          i2 = base_i + (k*i + j/2 + 1)%row_i;
        }

        editor.add_cell(c, i0, i1, i2);
        ++c;
      }
  }

  // Initialise entities required for this degree polynomial mesh
  // and allocate space for the point coordinate data

  if (degree == 2)
  {
    editor.init_entities();

    for (EdgeIterator e(*this); !e.end(); ++e)
    {
      Point v0 = Vertex(*this, e->entities(0)[0]).point();
      Point v1 = Vertex(*this, e->entities(0)[1]).point();
      Point pt = e->midpoint();

      if (std::abs(v0.norm() - 1.0) < 1e-6 and
          std::abs(v1.norm() - 1.0) < 1e-6)
        pt *= v0.norm()/pt.norm();

      // Add Edge-based point
      editor.add_entity_point(1, 0, e->index(), pt);
    }
  }

  editor.close();
}

//.........这里部分代码省略.........
              boundary.topology().shared_entities(0)[local_boundary_index]
                = other_processes;

              // FIXME: More sophisticated ownership determination
              if (min_process < owner)
                owner = min_process;
            }
            const std::size_t global_mesh_index
              = mesh.topology().global_indices(0)[local_mesh_index];
            global_index_owner[global_mesh_index] = owner;

            // Update counts
            if (owner == my_rank)
              num_owned_vertices++;
            num_boundary_vertices++;
          }
        }

        // Count boundary cells (facets of the mesh)
        num_boundary_cells++;
      }
    }
  }

  // Initiate boundary topology
  /*
  boundary.topology().init(0, num_boundary_vertices,
                           MPI::sum(mesh.mpi_comm(), num_owned_vertices));
  boundary.topology().init(D - 1, num_boundary_cells,
                           MPI::sum(mesh.mpi_comm(), num_boundary_cells));
  */

  // Specify number of vertices and cells
  editor.init_vertices_global(num_boundary_vertices,
                              MPI::sum(mesh.mpi_comm(), num_owned_vertices));
  editor.init_cells_global(num_boundary_cells, MPI::sum(mesh.mpi_comm(),
                                                        num_boundary_cells));

  // Write vertex map
  MeshFunction<std::size_t>& vertex_map = boundary.entity_map(0);
  if (num_boundary_vertices > 0)
  {
    vertex_map.init(reference_to_no_delete_pointer(boundary), 0,
                    num_boundary_vertices);
  }
  std::map<std::size_t, std::size_t>::const_iterator it;
  for (it = boundary_vertices.begin(); it != boundary_vertices.end(); ++it)
    vertex_map[it->second] = it->first;

  // Get vertex ownership distribution, and find index to start global
  // numbering from
  std::vector<std::size_t> ownership_distribution(num_processes);
  MPI::all_gather(mesh.mpi_comm(), num_owned_vertices, ownership_distribution);
  std::size_t start_index = 0;
  for (std::size_t j = 0; j < my_rank; j++)
    start_index += ownership_distribution[j];

  // Set global indices of owned vertices, request global indices for
  // vertices owned elsewhere
  std::map<std::size_t, std::size_t> global_indices;
  std::vector<std::vector<std::size_t>> request_global_indices(num_processes);

  std::size_t current_index = start_index;
  for (std::size_t local_boundary_index = 0;
       local_boundary_index<num_boundary_vertices; local_boundary_index++)
  {

//.........这里部分代码省略.........
      vert2remove_idx = edge_vertex[1];
  }
  else
  {
    // No vertices to remove, cannot coarsen
    cout << "all vertices forbidden" << endl;
    editor.close();
    return false;
  }

  Vertex vertex_to_remove(mesh, vert2remove_idx);

  // Remove cells around edge
  num_cells_to_remove = 0;
  for (CellIterator cn(shortest_edge); !cn.end(); ++cn)
  {
    cell_to_remove[cn->index()] = true;
    num_cells_to_remove++;

    // Update cell map
    old2new_cell[cn->index()] = -1;
  }

  // Regenerate cells around vertex
  for (CellIterator cn(vertex_to_remove); !cn.end(); ++cn)
  {
    cell_to_regenerate[cn->index()] = true;

    // Update cell map (will be filled in with correct index)
    old2new_cell[cn->index()] = -1;
  }

  // Specify number of vertices and cells
  editor.init_vertices_global(num_vertices - 1, num_vertices - 1);
  editor.init_cells_global(num_cells - num_cells_to_remove,
                           num_cells - num_cells_to_remove);

  cout << "Number of cells in old mesh: " << num_cells << "; to remove: " <<
    num_cells_to_remove << endl;

  // Add old vertices
  std::size_t vertex = 0;
  for(VertexIterator v(mesh); !v.end(); ++v)
  {
    if(vertex_to_remove.index() == v->index())
      old2new_vertex[v->index()] = -1;
    else
    {
      //cout << "adding old vertex at: " << v->point() << endl;
      old2new_vertex[v->index()] = vertex;
      editor.add_vertex(vertex, v->point());
      vertex++;
    }
  }

  // Add old unrefined cells
  std::size_t cv_idx;
  std::size_t current_cell = 0;
  std::vector<std::size_t> cell_vertices(cell_type.num_entities(0));
  for (CellIterator c(mesh); !c.end(); ++c)
  {
    if (cell_to_remove[*c] == false && cell_to_regenerate[*c] == false)
    {
      cv_idx = 0;
      for (VertexIterator v(*c); !v.end(); ++v)
        cell_vertices[cv_idx++] = old2new_vertex[v->index()];

//-----------------------------------------------------------------------------
void UniformMeshRefinement::refine(Mesh& refined_mesh,
                                   const Mesh& mesh)
{
  not_working_in_parallel("UniformMeshRefinement::refine");

  log(TRACE, "Refining simplicial mesh uniformly.");

  // Check that refined_mesh and mesh are not the same
  if (&refined_mesh == &mesh)
  {
    dolfin_error("UniformMeshRefinement.cpp",
                 "refine mesh",
                 "Refined_mesh and mesh point to the same object");
  }

  // Generate cell - edge connectivity if not generated
  mesh.init(mesh.topology().dim(), 1);

  // Generate edge - vertex connectivity if not generated
  mesh.init(1, 0);

  // Mesh needs to be ordered (so we can pick right combination of vertices/edges)
  if (!mesh.ordered())
    dolfin_error("UniformMeshRefinement.cpp",
                 "refine mesh",
                 "Mesh is not ordered according to the UFC numbering convention, consider calling mesh.order()");

  // Get cell type
  const CellType& cell_type = mesh.type();

  // Open new mesh for editing
  MeshEditor editor;
  editor.open(refined_mesh, cell_type.cell_type(),
              mesh.topology().dim(), mesh.geometry().dim());

  // Get size of mesh
  const std::size_t num_vertices = mesh.size(0);
  const std::size_t num_edges = mesh.size(1);
  const std::size_t num_cells = mesh.size(mesh.topology().dim());

  // Specify number of vertices and cells
  editor.init_vertices_global(num_vertices + num_edges, num_vertices + num_edges);
  editor.init_cells_global(ipow(2, mesh.topology().dim())*num_cells,
                           ipow(2, mesh.topology().dim())*num_cells);

  // Add old vertices
  std::size_t vertex = 0;
  for (VertexIterator v(mesh); !v.end(); ++v)
  {
    editor.add_vertex(vertex, v->point());
    vertex++;
  }

  // Add new vertices
  for (EdgeIterator e(mesh); !e.end(); ++e)
  {
    editor.add_vertex(vertex, e->midpoint());
    vertex++;
  }

  // Add cells
  std::size_t current_cell = 0;
  for (CellIterator c(mesh); !c.end(); ++c)
    cell_type.refine_cell(*c, editor, current_cell);

  // Close editor
  editor.close();

  // Make sure that mesh is ordered after refinement
  //refined_mesh.order();
}

//-----------------------------------------------------------------------------
void IntervalMesh::build(std::size_t nx, double a, double b)
{
  // Receive mesh according to parallel policy
  if (MPI::is_receiver(this->mpi_comm()))
  {
    MeshPartitioning::build_distributed_mesh(*this);
    return;
  }

  if (std::abs(a - b) < DOLFIN_EPS)
  {
    dolfin_error("Interval.cpp",
                 "create interval",
                 "Length of interval is zero. Consider checking your dimensions");
  }

  if (b < a)
  {
    dolfin_error("Interval.cpp",
                 "create interval",
                 "Length of interval is negative. Consider checking the order of your arguments");
  }

  if (nx < 1)
  {
    dolfin_error("Interval.cpp",
                 "create interval",
                 "Number of points on interval is (%d), it must be at least 1", nx);
  }

  rename("mesh", "Mesh of the interval (a, b)");

  // Open mesh for editing
  MeshEditor editor;
  editor.open(*this, CellType::interval, 1, 1);

  // Create vertices and cells:
  editor.init_vertices_global((nx+1), (nx+1));
  editor.init_cells_global(nx, nx);

  // Create main vertices:
  for (std::size_t ix = 0; ix <= nx; ix++)
  {
    const std::vector<double>
      x(1, a + (static_cast<double>(ix)*(b - a)/static_cast<double>(nx)));
    editor.add_vertex(ix, x);
  }

  // Create intervals
  for (std::size_t ix = 0; ix < nx; ix++)
  {
    std::vector<std::size_t> cell(2);
    cell[0] = ix; cell[1] = ix + 1;
    editor.add_cell(ix, cell);
  }

  // Close mesh editor
  editor.close();

  // Broadcast mesh according to parallel policy
  if (MPI::is_broadcaster(this->mpi_comm()))
  {
    std::cout << "Building mesh (dist 0a)" << std::endl;
    MeshPartitioning::build_distributed_mesh(*this);
    std::cout << "Building mesh (dist 1a)" << std::endl;
    return;
  }
}

//-----------------------------------------------------------------------------
UnitHexMesh::UnitHexMesh(MPI_Comm comm, std::size_t nx, std::size_t ny,
                         std::size_t nz) : Mesh(comm)
{
  // Receive mesh according to parallel policy
  if (MPI::is_receiver(this->mpi_comm()))
  {
    MeshPartitioning::build_distributed_mesh(*this);
    return;
  }

  MeshEditor editor;
  editor.open(*this, CellType::hexahedron, 3, 3);

  // Create vertices and cells:
  editor.init_vertices_global((nx + 1)*(ny + 1)*(nz + 1),
                              (nx + 1)*(ny + 1)*(nz + 1));
  editor.init_cells_global(nx*ny*nz, nx*ny*nz);

  // Storage for vertices
  std::vector<double> x(3);

  const double a = 0.0;
  const double b = 1.0;
  const double c = 0.0;
  const double d = 1.0;
  const double e = 0.0;
  const double f = 1.0;

  // Create main vertices:
  std::size_t vertex = 0;
  for (std::size_t iz = 0; iz <= nz; iz++)
  {
    x[2] = e + ((static_cast<double>(iz))*(f - e)/static_cast<double>(nz));
    for (std::size_t iy = 0; iy <= ny; iy++)
    {
      x[1] = c + ((static_cast<double>(iy))*(d - c)/static_cast<double>(ny));
      for (std::size_t ix = 0; ix <= nx; ix++)
      {
        x[0] = a + ((static_cast<double>(ix))*(b - a)/static_cast<double>(nx));
        editor.add_vertex(vertex, x);
        vertex++;
      }
    }
  }

  // Create cuboids
  std::size_t cell = 0;
  std::vector<std::size_t> v(8);
  for (std::size_t iz = 0; iz < nz; iz++)
    for (std::size_t iy = 0; iy < ny; iy++)
      for (std::size_t ix = 0; ix < nx; ix++)
      {
        v[0] = (iz*(ny + 1) + iy)*(nx + 1) + ix;
        v[1] = v[0] + 1;
        v[2] = v[0] + (nx + 1);
        v[3] = v[1] + (nx + 1);
        v[4] = v[0] + (nx + 1)*(ny + 1);
        v[5] = v[1] + (nx + 1)*(ny + 1);
        v[6] = v[2] + (nx + 1)*(ny + 1);
        v[7] = v[3] + (nx + 1)*(ny + 1);
        editor.add_cell(cell, v);
        ++cell;
      }

  // Close mesh editor
  editor.close();

  // Broadcast mesh according to parallel policy
  if (MPI::is_broadcaster(this->mpi_comm()))
  {
    MeshPartitioning::build_distributed_mesh(*this);
    return;
  }


}

//-----------------------------------------------------------------------------
void XMLMesh::read_mesh(Mesh& mesh, const pugi::xml_node mesh_node)
{
  // Get cell type and geometric dimension
  const std::string cell_type_str = mesh_node.attribute("celltype").value();
  const std::size_t gdim = mesh_node.attribute("dim").as_uint();

  // Get topological dimension
  boost::scoped_ptr<CellType> cell_type(CellType::create(cell_type_str));
  const std::size_t tdim = cell_type->dim();

  // Create mesh for editing
  MeshEditor editor;
  editor.open(mesh, cell_type_str, tdim, gdim);

  // Get vertices xml node
  pugi::xml_node xml_vertices = mesh_node.child("vertices");
  dolfin_assert(xml_vertices);

  // Get number of vertices and init editor
  const std::size_t num_vertices = xml_vertices.attribute("size").as_uint();
  editor.init_vertices_global(num_vertices, num_vertices);

  // Iterate over vertices and add to mesh
  Point p;
  for (pugi::xml_node_iterator it = xml_vertices.begin();
       it != xml_vertices.end(); ++it)
  {
    const std::size_t index = it->attribute("index").as_uint();
    p[0] = it->attribute("x").as_double();
    p[1] = it->attribute("y").as_double();
    p[2] = it->attribute("z").as_double();
    editor.add_vertex(index, p);
  }

  // Get cells node
  pugi::xml_node xml_cells = mesh_node.child("cells");
  dolfin_assert(xml_cells);

  // Get number of cells and init editor
  const std::size_t num_cells = xml_cells.attribute("size").as_uint();
  editor.init_cells_global(num_cells, num_cells);

  // Create list of vertex index attribute names
  const unsigned int num_vertices_per_cell = cell_type->num_vertices(tdim);
  std::vector<std::string> v_str(num_vertices_per_cell);
  for (std::size_t i = 0; i < num_vertices_per_cell; ++i)
    v_str[i] = "v" + boost::lexical_cast<std::string, unsigned int>(i);

  // Iterate over cells and add to mesh
  std::vector<std::size_t> v(num_vertices_per_cell);
  for (pugi::xml_node_iterator it = xml_cells.begin(); it != xml_cells.end();
       ++it)
  {
    const std::size_t index = it->attribute("index").as_uint();
    for (unsigned int i = 0; i < num_vertices_per_cell; ++i)
      v[i] = it->attribute(v_str[i].c_str()).as_uint();
    editor.add_cell(index, v);
  }

  // Close mesh editor
  editor.close();
}

//-----------------------------------------------------------------------------
dolfin::Mesh MeshRenumbering::renumber_by_color(const Mesh& mesh,
                                 const std::vector<std::size_t> coloring_type)
{
  // Start timer
  Timer timer("Renumber mesh by color");

  // Get some some mesh
  const std::size_t tdim = mesh.topology().dim();
  const std::size_t gdim = mesh.geometry().dim();
  const std::size_t num_local_vertices  = mesh.size(0);
  const std::size_t num_global_vertices = mesh.size_global(0);
  const std::size_t num_local_cells     = mesh.size(tdim);
  const std::size_t num_global_cells    = mesh.size_global(tdim);

  // Check that requested coloring is a cell coloring
  if (coloring_type[0] != tdim)
  {
    dolfin_error("MeshRenumbering.cpp",
                 "renumber mesh by color",
                 "Coloring is not a cell coloring: only cell colorings are supported");
  }

  // Compute renumbering
  std::vector<double> new_coordinates;
  std::vector<std::size_t> new_connections;
  MeshRenumbering::compute_renumbering(mesh, coloring_type, new_coordinates,
                                       new_connections);

  // Create new mesh
  Mesh new_mesh;

  // Create mesh editor
  MeshEditor editor;
  editor.open(new_mesh, mesh.type().cell_type(), tdim, gdim);
  editor.init_cells_global(num_local_cells, num_global_cells);
  editor.init_vertices_global(num_local_vertices, num_global_vertices);

  // Add vertices
  dolfin_assert(new_coordinates.size() == num_local_vertices*gdim);
  for (std::size_t i = 0; i < num_local_vertices; ++i)
  {
    std::vector<double> x(gdim);
    for (std::size_t j = 0; j < gdim; ++j)
      x[j] = new_coordinates[i*gdim + j];
    editor.add_vertex(i, x);
  }

  cout << "Done adding vertices" << endl;

  // Add cells
  dolfin_assert(new_coordinates.size() == num_local_vertices*gdim);
  const std::size_t vertices_per_cell = mesh.type().num_entities(0);
  for (std::size_t i = 0; i < num_local_cells; ++i)
  {
    std::vector<std::size_t> c(vertices_per_cell);
    std::copy(new_connections.begin() + i*vertices_per_cell,
              new_connections.begin() + i*vertices_per_cell + vertices_per_cell,
              c.begin());
    editor.add_cell(i, c);
  }

  editor.close();

  cout << "Close editor" << endl;

  // Initialise coloring data
  typedef std::map<std::vector<std::size_t>, std::pair<std::vector<std::size_t>,
           std::vector<std::vector<std::size_t>>>>::const_iterator
    ConstMeshColoringData;

  // Get old coloring
  ConstMeshColoringData mesh_coloring
    = mesh.topology().coloring.find(coloring_type);
  if (mesh_coloring == mesh.topology().coloring.end())
  {
    dolfin_error("MeshRenumbering.cpp",
                 "renumber mesh by color",
                 "Requested mesh coloring has not been computed");
  }

  // Get old coloring data
  const std::vector<std::size_t>& colors = mesh_coloring->second.first;
  const std::vector<std::vector<std::size_t>>&
    entities_of_color = mesh_coloring->second.second;
  dolfin_assert(colors.size() == num_local_cells);
  dolfin_assert(!entities_of_color.empty());
  const std::size_t num_colors = entities_of_color.size();

  // New coloring data
  dolfin_assert(new_mesh.topology().coloring.empty());
  std::vector<std::size_t> new_colors(colors.size());
  std::vector<std::vector<std::size_t>> new_entities_of_color(num_colors);

  std::size_t current_cell = 0;
  for (std::size_t color = 0; color < num_colors; color++)
  {
    // Get the array of cell indices of current color
    const std::vector<std::size_t>& colored_cells = entities_of_color[color];
    std::vector<std::size_t>& new_colored_cells = new_entities_of_color[color];
//.........这里部分代码省略.........

//-----------------------------------------------------------------------------
void RectangleMesh::build(const Point& p0, const Point& p1,
                          std::size_t nx, std::size_t ny,
                          std::string diagonal)
{
  // Receive mesh according to parallel policy
  if (MPI::is_receiver(this->mpi_comm()))
  {
    MeshPartitioning::build_distributed_mesh(*this);
    return;
  }

  // Check options
  if (diagonal != "left" && diagonal != "right" && diagonal != "right/left"
          && diagonal != "left/right" && diagonal != "crossed")
  {
    dolfin_error("RectangleMesh.cpp",
                 "create rectangle",
                 "Unknown mesh diagonal definition: allowed options are \"left\", \"right\", \"left/right\", \"right/left\" and \"crossed\"");
  }

  // Extract minimum and maximum coordinates
  const double x0 = std::min(p0.x(), p1.x());
  const double x1 = std::max(p0.x(), p1.x());
  const double y0 = std::min(p0.y(), p1.y());
  const double y1 = std::max(p0.y(), p1.y());

  const double a = x0;
  const double b = x1;
  const double c = y0;
  const double d = y1;

  if (std::abs(x0 - x1) < DOLFIN_EPS || std::abs(y0 - y1) < DOLFIN_EPS)
  {
    dolfin_error("Rectangle.cpp",
                 "create rectangle",
                 "Rectangle seems to have zero width, height or depth. Consider checking your dimensions");
  }

  if (nx < 1 || ny < 1)
  {
    dolfin_error("RectangleMesh.cpp",
                 "create rectangle",
                 "Rectangle has non-positive number of vertices in some dimension: number of vertices must be at least 1 in each dimension");
  }

  rename("mesh", "Mesh of the unit square (a,b) x (c,d)");
  // Open mesh for editing
  MeshEditor editor;
  editor.open(*this, CellType::triangle, 2, 2);

  // Create vertices and cells:
  if (diagonal == "crossed")
  {
    editor.init_vertices_global((nx + 1)*(ny + 1) + nx*ny,
                                  (nx + 1)*(ny + 1) + nx*ny);
    editor.init_cells_global(4*nx*ny, 4*nx*ny);
  }
  else
  {
    editor.init_vertices_global((nx + 1)*(ny + 1), (nx + 1)*(ny + 1));
    editor.init_cells_global(2*nx*ny, 2*nx*ny);
  }

  // Storage for vertices
  std::vector<double> x(2);

  // Create main vertices:
  std::size_t vertex = 0;
  for (std::size_t iy = 0; iy <= ny; iy++)
  {
    x[1] = c + ((static_cast<double>(iy))*(d - c)/static_cast<double>(ny));
    for (std::size_t ix = 0; ix <= nx; ix++)
    {
      x[0] = a + ((static_cast<double>(ix))*(b - a)/static_cast<double>(nx));
      editor.add_vertex(vertex, x);
      vertex++;
    }
  }

  // Create midpoint vertices if the mesh type is crossed
  if (diagonal == "crossed")
  {
    for (std::size_t iy = 0; iy < ny; iy++)
    {
      x[1] = c +(static_cast<double>(iy) + 0.5)*(d - c)/static_cast<double>(ny);
      for (std::size_t ix = 0; ix < nx; ix++)
      {
        x[0] = a + (static_cast<double>(ix) + 0.5)*(b - a)/static_cast<double>(nx);
        editor.add_vertex(vertex, x);
        vertex++;
      }
    }
  }

  // Create triangles
  std::size_t cell = 0;
  if (diagonal == "crossed")
  {
    boost::multi_array<std::size_t, 2> cells(boost::extents[4][3]);
//.........这里部分代码省略.........

//-----------------------------------------------------------------------------
void SubMesh::init(const Mesh& mesh,
                   const std::vector<std::size_t>& sub_domains,
                   std::size_t sub_domain)
{
  // Open mesh for editing
  MeshEditor editor;
  const std::size_t D = mesh.topology().dim();
  editor.open(*this, mesh.type().cell_type(), D,
              mesh.geometry().dim());

  // Build set of cells that are in sub-mesh
  std::vector<bool> parent_cell_in_subdomain(mesh.num_cells(), false);
  std::set<std::size_t> submesh_cells;
  for (CellIterator cell(mesh); !cell.end(); ++cell)
  {
    if (sub_domains[cell->index()] == sub_domain)
    {
      parent_cell_in_subdomain[cell->index()] = true;
      submesh_cells.insert(cell->index());
    }
  }

  // Map from parent vertex index to submesh vertex index
  std::map<std::size_t, std::size_t> parent_to_submesh_vertex_indices;

  // Map from submesh cell to parent cell
  std::vector<std::size_t> submesh_cell_parent_indices;
  submesh_cell_parent_indices.reserve(submesh_cells.size());

  // Vector from parent cell index to submesh cell index
  std::vector<std::size_t> parent_to_submesh_cell_indices(mesh.num_cells(), 0);

  // Add sub-mesh cells
  editor.init_cells_global(submesh_cells.size(), submesh_cells.size());
  std::size_t current_cell = 0;
  std::size_t current_vertex = 0;
  for (std::set<std::size_t>::iterator cell_it = submesh_cells.begin();
       cell_it != submesh_cells.end(); ++cell_it)
  {
    // Data structure to hold new vertex indices for cell
    std::vector<std::size_t> cell_vertices;

    // Create cell
    Cell cell(mesh, *cell_it);

    // Iterate over cell vertices
    for (VertexIterator vertex(cell); !vertex.end(); ++vertex)
    {
      const std::size_t parent_vertex_index = vertex->index();

      // Look for parent vertex in map
      std::map<std::size_t, std::size_t>::iterator vertex_it
        = parent_to_submesh_vertex_indices.find(parent_vertex_index);

      // If vertex has been inserted, get new index, otherwise
      // increment and insert
      std::size_t submesh_vertex_index = 0;
      if (vertex_it != parent_to_submesh_vertex_indices.end())
        submesh_vertex_index = vertex_it->second;
      else
      {
        submesh_vertex_index = current_vertex++;
        parent_to_submesh_vertex_indices[parent_vertex_index]
          = submesh_vertex_index;
      }

      // Add vertex to list of cell vertices (new indexing)
      cell_vertices.push_back(submesh_vertex_index);
    }

    // Add parent cell index to list
    submesh_cell_parent_indices.push_back(cell.index());

    // Store parent cell -> submesh cell indices
    parent_to_submesh_cell_indices[cell.index()] = current_cell;

    // Add cell to mesh
    editor.add_cell(current_cell++, cell_vertices);
  }

  // Vector to hold submesh vertex -> parent vertex
  std::vector<std::size_t> parent_vertex_indices;
  parent_vertex_indices.resize(parent_to_submesh_vertex_indices.size());

  // Initialise mesh editor
  editor.init_vertices_global(parent_to_submesh_vertex_indices.size(),
                              parent_to_submesh_vertex_indices.size());

  // Add vertices
  for (std::map<std::size_t, std::size_t>::iterator it
         = parent_to_submesh_vertex_indices.begin();
       it != parent_to_submesh_vertex_indices.end(); ++it)
  {
    Vertex vertex(mesh, it->first);
    if (MPI::size(mesh.mpi_comm()) > 1)
      error("SubMesh::init not working in parallel");

    // FIXME: Get global vertex index
    editor.add_vertex(it->second, vertex.point());
//.........这里部分代码省略.........