From: Wolfgang Bangerth Date: Wed, 30 May 2012 10:34:55 +0000 (+0000) Subject: Fix numerous bugs in GridTools::find_cells_adjacent_to_vertex. X-Git-Tag: v8.0.0~2563 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=68c2d5d387e86d1aa8faea72f45ca1d1f46dcc87;p=dealii.git Fix numerous bugs in GridTools::find_cells_adjacent_to_vertex. git-svn-id: https://svn.dealii.org/trunk@25567 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/news/changes.h b/deal.II/doc/news/changes.h index ac33954c44..68f51af953 100644 --- a/deal.II/doc/news/changes.h +++ b/deal.II/doc/news/changes.h @@ -210,7 +210,7 @@ enabled due to a missing include file in file
  • Fixed: Bug in 3d with hanging nodes in GridTools::find_cells_adjacent_to_vertex() that caused find_active_cell_around_point() to fail in those cases.
    -(Timo Heister, 2012/05/29) +(Timo Heister, Wolfgang Bangerth 2012/05/30)
  • New: The GridIn::read_unv function can now read meshes generated by the Salome framework, see http://www.salome-platform.org/ . diff --git a/deal.II/include/deal.II/grid/grid_tools.h b/deal.II/include/deal.II/grid/grid_tools.h index 7c2a421796..31d9e344c3 100644 --- a/deal.II/include/deal.II/grid/grid_tools.h +++ b/deal.II/include/deal.II/grid/grid_tools.h @@ -276,12 +276,11 @@ namespace GridTools * * For locally refined grids, the * vertex itself might not be a vertex - * of all adjacent cells, but will - * always be located on a face or an - * edge of the adjacent cells returned. - * - * @author Ralf B. Schulz, - * Wolfgang Bangerth, 2006 + * of all adjacent cells that are returned. + * However, it will + * always be either a vertex of a cell of be + * a hanging node located on a face or an + * edge of it. */ template class Container, int spacedim> std::vector::active_cell_iterator> diff --git a/deal.II/source/grid/grid_tools.cc b/deal.II/source/grid/grid_tools.cc index d107d2e9c5..1d8aceb57a 100644 --- a/deal.II/source/grid/grid_tools.cc +++ b/deal.II/source/grid/grid_tools.cc @@ -670,128 +670,113 @@ namespace GridTools Assert(get_tria(container).get_used_vertices()[vertex], ExcVertexNotUsed(vertex)); - // We use a set instead of a vector + // use a set instead of a vector // to ensure that cells are inserted only - // once. A bug in the previous version - // prevented some cases to be - // treated correctly - std::set::active_cell_iterator> adj_cells_set; + // once + std::set::active_cell_iterator> adjacent_cells; typename Container::active_cell_iterator cell = container.begin_active(), endc = container.end(); - // go through all active cells and look - // if the vertex is part of that cell + // go through all active cells and look. if the vertex is part of that cell + // + // in 1d, this is all we need to care about. in 2d/3d we also need to worry + // that the vertex might be a hanging node on a face or edge of a cell; in + // this case, we would want to add those cells as well on whose faces the + // vertex is located but for which it is not a vertex itself. + // + // getting this right is a lot simpler in 2d than in 3d. in 2d, a hanging + // node can only be in the middle of a face and we can query the neighboring + // cell from the current cell. on the other hand, in 3d a hanging node + // vertex can also be on an edge but there can be many other cells on + // this edge and we can not access them from the cell we are currently + // on. + // + // so, in the 3d case, if we run the algorithm as in 2d, we catch all + // those cells for which the vertex we seek is on a *subface*, but we + // miss the case of cells for which the vertex we seek is on a + // sub-edge for which there is no corresponding sub-face (because the + // immediate neighbor behind this face is not refined), see for example + // the bits/find_cells_adjacent_to_vertex_6 testcase. thus, if we + // haven't yet found the vertex for the current cell we also need to + // look at the mid-points of edges for (; cell != endc; ++cell) - for (unsigned v = 0; v < GeometryInfo::vertices_per_cell; v++) - if (cell->vertex_index(v) == vertex) - { - // OK, we found a cell that contains - // the particular vertex. We add it - // to the list. - adj_cells_set.insert(cell); - - // Now we need to make sure that the - // vertex is not a locally refined - // vertex not being part of the - // neighboring cells. So we loop over - // all faces to which this vertex - // belongs, check the level of - // the neighbor, and if it is coarser, - // then check whether the vertex is - // part of that neighbor or not. - for (unsigned vface = 0; vface < dim; vface++) - { - const unsigned face = - GeometryInfo::vertex_to_face[v][vface]; - if (!cell->at_boundary(face)) + { + for (unsigned v = 0; v < GeometryInfo::vertices_per_cell; v++) + if (cell->vertex_index(v) == vertex) + { + // OK, we found a cell that contains + // the given vertex. We add it + // to the list. + adjacent_cells.insert(cell); + + // as explained above, in 2+d we need to check whether + // this vertex is on a face behind which there is a coarser + // neighbor. if this is the case, then we need to also + // add this neighbor + if (dim >= 2) + for (unsigned vface = 0; vface < dim; vface++) { - typename Container::cell_iterator - nb = cell->neighbor(face); - - // Here we - // check - // whether - // the - // neighbor - // is - // coarser. If - // it is, we - // search - // for the - // vertex in - // this - // coarser - // cell and - // only if - // not found - // we will - // add the - // coarser - // cell - // itself - if (nb->level() < cell->level()) + const unsigned int face = + GeometryInfo::vertex_to_face[v][vface]; + + if (!cell->at_boundary(face) + && + (cell->neighbor(face)->level() < cell->level())) { - bool found = false; - for (unsigned v=0; v::vertices_per_cell; v++) - if (nb->vertex_index(v) == vertex) - { - found = true; - break; - } - if (!found) - { - //TODO: it is not - //enough to walk - //over faces to - //the neighbors - //because the - //point may lie - //in a cell that - //only shares an - //edge with cell - //in 3d. Current - //workaround: add - //all neighbors - //of all - //neighbors if - //this vertex is - //a hanging node - //in 3d. [TH] - adj_cells_set.insert(nb); - if (dim==3) - { - for (unsigned faceindex = 0; faceindex < GeometryInfo::faces_per_cell; faceindex++) - { - if (!nb->at_boundary(faceindex) && nb->neighbor(faceindex)->active()) - adj_cells_set.insert(nb->neighbor(faceindex)); - } - } - } - + // there is a coarser cell behind a face to which the + // vertex belongs. the vertex we are looking at is + // then either a vertex of that coarser neighbor, + // or it is a hanging node on one of the faces of + // that cell. in either case, it is adjacent + // to the vertex, so add it to the list as well + // (if the cell was already in the list then + // the std::set makes sure that we get it only once) + adjacent_cells.insert (cell->neighbor(face)); + goto next_cell; } } - } - break; - } + // in any case, we have found a cell, so go to the next cell + goto next_cell; + } - std::vector::active_cell_iterator> - adjacent_cells; + // in 3d also loop over the edges + if (dim >= 3) + { + for (unsigned e=0; e::lines_per_cell; ++e) + if (cell->line(e)->has_children()) + // the only place where this vertex could have been + // hiding is on the mid-edge point of the edge we + // are looking at + if (cell->line(e)->child(0)->vertex_index(1) == vertex) + { + adjacent_cells.insert(cell); + + // jump out of this tangle of nested loops + goto next_cell; + } + } - // We now produce the output vector - // from the set that we assembled above. - typename std::set::active_cell_iterator>::iterator - it = adj_cells_set.begin(), - endit = adj_cells_set.end(); - for(; it != endit; ++it) - adjacent_cells.push_back(*it); + // in more than 3d we would probably have to do the same as + // above also for even lower-dimensional objects + Assert (dim <= 3, ExcNotImplemented()); + // move on to the next cell if we have found the + // vertex on the current one + next_cell: + ; + } - Assert(adjacent_cells.size() > 0, ExcInternalError()); + // if this was an active vertex then there needs to have been + // at least one cell to which it is adjacent! + Assert (adjacent_cells.size() > 0, ExcInternalError()); - return adjacent_cells; + // return the result as a vector, rather than the set we built above + return + std::vector::active_cell_iterator> + (adjacent_cells.begin(), adjacent_cells.end()); } diff --git a/tests/bits/find_cells_adjacent_to_vertex_2.cc b/tests/bits/find_cells_adjacent_to_vertex_2.cc index 0892326250..ac8a4b6a13 100644 --- a/tests/bits/find_cells_adjacent_to_vertex_2.cc +++ b/tests/bits/find_cells_adjacent_to_vertex_2.cc @@ -37,11 +37,8 @@ void check (Triangulation<3> &tria) deallog << "Vertex " << i << " at " << tria.get_vertices()[i] << ": " << cells.size() << " cells" << std::endl; - for(unsigned c=0; c::vertices_per_cell; ++v) - deallog << "<" << cells[c]->vertex(v) << "> "; - deallog << std::endl; - } + for(unsigned c=0; c <0.250000 0.00000 0.00000> <0.00000 0.250000 0.00000> <0.250000 0.250000 0.00000> <0.00000 0.00000 0.250000> <0.250000 0.00000 0.250000> <0.00000 0.250000 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<0.500000 0.250000 0.500000> <0.250000 0.500000 0.500000> <0.500000 0.500000 0.500000> +DEAL:: 2.0 +DEAL:: 2.1 +DEAL:: 2.2 +DEAL:: 2.3 +DEAL:: 2.4 +DEAL:: 2.5 +DEAL:: 2.6 +DEAL:: 2.7 diff --git a/tests/bits/find_cells_adjacent_to_vertex_5.cc b/tests/bits/find_cells_adjacent_to_vertex_5.cc new file mode 100644 index 0000000000..e703772ba1 --- /dev/null +++ b/tests/bits/find_cells_adjacent_to_vertex_5.cc @@ -0,0 +1,103 @@ +// ---------------- find_cells_adjacent_to_vertex_5.cc ------------------ +// $Id$ +// Version: $Name$ +// +// Copyright (C) 2006, 2012 by the deal.II authors and Ralf B. Schulz +// +// This file is subject to QPL and may not be distributed +// without copyright and license information. Please refer +// to the file deal.II/doc/license.html for the text and +// further information on this license. +// +// ---------------- find_cells_adjacent_to_vertex_5.cc ------------------ + + +// similar to the _3 test: a mesh where 8 2d cells meet at one +// point. we then extrude this mesh into the z-direction +// +// this test does not use any local refinement + +#include "../tests.h" +#include +#include +#include +#include +#include + +#include + + +void check (Triangulation<3> &tria) +{ + for(unsigned i=0; i::active_cell_iterator> + cells = GridTools::find_cells_adjacent_to_vertex(tria, i); + + deallog << "Vertex " << i << " at " + << tria.get_vertices()[i] << ": " + << cells.size() << " cells" << std::endl; + + for(unsigned c=0; c > vertices; + vertices.push_back (Point(0,0,0)); + + for (unsigned int i=0; i<16; ++i) + vertices.push_back (Point(std::cos(i*2*numbers::PI/16), + std::sin(i*2*numbers::PI/16), + 0)); + + // then extrude the mesh into + // z-direction + for (unsigned int i=0; i<17; ++i) + vertices.push_back (Point(vertices[i][0], + vertices[i][1], + 1)); + + // now create the 8 cells + std::vector > cells; + for (unsigned int c=0; c<8; ++c) + { + CellData d; + d.vertices[0] = 0; + d.vertices[1] = 1+2*c; + d.vertices[2] = 1+((2*c+2) % 16); + d.vertices[3] = 1+2*c+1; + + for (unsigned int v=4; v<8; ++v) + d.vertices[v] = d.vertices[v-4]+17; + + cells.push_back(d); + } + + Triangulation coarse_grid; + coarse_grid.create_triangulation (vertices, cells, + SubCellData()); + check (coarse_grid); + } + catch (const std::exception &exc) + { + // we shouldn't get here... + deallog << "Caught an error..." << std::endl; + deallog << exc.what() << std::endl; + } +} diff --git a/tests/bits/find_cells_adjacent_to_vertex_5/cmp/generic b/tests/bits/find_cells_adjacent_to_vertex_5/cmp/generic new file mode 100644 index 0000000000..ae9afddd46 --- /dev/null +++ b/tests/bits/find_cells_adjacent_to_vertex_5/cmp/generic @@ -0,0 +1,99 @@ + +DEAL::Vertex 0 at 0.00000 0.00000 0.00000: 8 cells +DEAL:: 0.0 +DEAL:: 0.1 +DEAL:: 0.2 +DEAL:: 0.3 +DEAL:: 0.4 +DEAL:: 0.5 +DEAL:: 0.6 +DEAL:: 0.7 +DEAL::Vertex 1 at 1.00000 0.00000 0.00000: 2 cells +DEAL:: 0.0 +DEAL:: 0.7 +DEAL::Vertex 2 at 0.923880 0.382683 0.00000: 1 cells +DEAL:: 0.0 +DEAL::Vertex 3 at 0.707107 0.707107 0.00000: 2 cells +DEAL:: 0.0 +DEAL:: 0.1 +DEAL::Vertex 4 at 0.382683 0.923880 0.00000: 1 cells +DEAL:: 0.1 +DEAL::Vertex 5 at 6.12323e-17 1.00000 0.00000: 2 cells +DEAL:: 0.1 +DEAL:: 0.2 +DEAL::Vertex 6 at -0.382683 0.923880 0.00000: 1 cells +DEAL:: 0.2 +DEAL::Vertex 7 at -0.707107 0.707107 0.00000: 2 cells +DEAL:: 0.2 +DEAL:: 0.3 +DEAL::Vertex 8 at -0.923880 0.382683 0.00000: 1 cells +DEAL:: 0.3 +DEAL::Vertex 9 at -1.00000 1.22465e-16 0.00000: 2 cells +DEAL:: 0.3 +DEAL:: 0.4 +DEAL::Vertex 10 at -0.923880 -0.382683 0.00000: 1 cells +DEAL:: 0.4 +DEAL::Vertex 11 at -0.707107 -0.707107 0.00000: 2 cells +DEAL:: 0.4 +DEAL:: 0.5 +DEAL::Vertex 12 at -0.382683 -0.923880 0.00000: 1 cells +DEAL:: 0.5 +DEAL::Vertex 13 at -1.83697e-16 -1.00000 0.00000: 2 cells +DEAL:: 0.5 +DEAL:: 0.6 +DEAL::Vertex 14 at 0.382683 -0.923880 0.00000: 1 cells +DEAL:: 0.6 +DEAL::Vertex 15 at 0.707107 -0.707107 0.00000: 2 cells +DEAL:: 0.6 +DEAL:: 0.7 +DEAL::Vertex 16 at 0.923880 -0.382683 0.00000: 1 cells +DEAL:: 0.7 +DEAL::Vertex 17 at 0.00000 0.00000 1.00000: 8 cells +DEAL:: 0.0 +DEAL:: 0.1 +DEAL:: 0.2 +DEAL:: 0.3 +DEAL:: 0.4 +DEAL:: 0.5 +DEAL:: 0.6 +DEAL:: 0.7 +DEAL::Vertex 18 at 1.00000 0.00000 1.00000: 2 cells +DEAL:: 0.0 +DEAL:: 0.7 +DEAL::Vertex 19 at 0.923880 0.382683 1.00000: 1 cells +DEAL:: 0.0 +DEAL::Vertex 20 at 0.707107 0.707107 1.00000: 2 cells +DEAL:: 0.0 +DEAL:: 0.1 +DEAL::Vertex 21 at 0.382683 0.923880 1.00000: 1 cells +DEAL:: 0.1 +DEAL::Vertex 22 at 6.12323e-17 1.00000 1.00000: 2 cells +DEAL:: 0.1 +DEAL:: 0.2 +DEAL::Vertex 23 at -0.382683 0.923880 1.00000: 1 cells +DEAL:: 0.2 +DEAL::Vertex 24 at -0.707107 0.707107 1.00000: 2 cells +DEAL:: 0.2 +DEAL:: 0.3 +DEAL::Vertex 25 at -0.923880 0.382683 1.00000: 1 cells +DEAL:: 0.3 +DEAL::Vertex 26 at -1.00000 1.22465e-16 1.00000: 2 cells +DEAL:: 0.3 +DEAL:: 0.4 +DEAL::Vertex 27 at -0.923880 -0.382683 1.00000: 1 cells +DEAL:: 0.4 +DEAL::Vertex 28 at -0.707107 -0.707107 1.00000: 2 cells +DEAL:: 0.4 +DEAL:: 0.5 +DEAL::Vertex 29 at -0.382683 -0.923880 1.00000: 1 cells +DEAL:: 0.5 +DEAL::Vertex 30 at -1.83697e-16 -1.00000 1.00000: 2 cells +DEAL:: 0.5 +DEAL:: 0.6 +DEAL::Vertex 31 at 0.382683 -0.923880 1.00000: 1 cells +DEAL:: 0.6 +DEAL::Vertex 32 at 0.707107 -0.707107 1.00000: 2 cells +DEAL:: 0.6 +DEAL:: 0.7 +DEAL::Vertex 33 at 0.923880 -0.382683 1.00000: 1 cells +DEAL:: 0.7 diff --git a/tests/bits/find_cells_adjacent_to_vertex_6.cc b/tests/bits/find_cells_adjacent_to_vertex_6.cc new file mode 100644 index 0000000000..5eb4a64eaa --- /dev/null +++ b/tests/bits/find_cells_adjacent_to_vertex_6.cc @@ -0,0 +1,113 @@ +// ---------------- find_cells_adjacent_to_vertex_6.cc ------------------ +// $Id$ +// Version: $Name$ +// +// Copyright (C) 2006, 2012 by the deal.II authors and Ralf B. Schulz +// +// This file is subject to QPL and may not be distributed +// without copyright and license information. Please refer +// to the file deal.II/doc/license.html for the text and +// further information on this license. +// +// ---------------- find_cells_adjacent_to_vertex_6.cc ------------------ + + +// similar to the _3 test: a mesh where 8 2d cells meet at one +// point. we then extrude this mesh into the z-direction +// +// this test then refines one cell. this creates a number of +// interesting problems in that the vertex in the middle of the +// original edge along the axis of the domain is a vertex of 2 cells, +// but is also adjacent to all 7 of the remaining level-0 cells even +// though only two of those are neighbors of the two small cells of +// which the vertex is a part of. + +#include "../tests.h" +#include +#include +#include +#include +#include + +#include + + +void check (Triangulation<3> &tria) +{ + for(unsigned i=0; i::active_cell_iterator> + cells = GridTools::find_cells_adjacent_to_vertex(tria, i); + + deallog << "Vertex " << i << " at " + << tria.get_vertices()[i] << ": " + << cells.size() << " cells" << std::endl; + + for(unsigned c=0; c > vertices; + vertices.push_back (Point(0,0,0)); + + for (unsigned int i=0; i<16; ++i) + vertices.push_back (Point(std::cos(i*2*numbers::PI/16), + std::sin(i*2*numbers::PI/16), + 0)); + + // then extrude the mesh into + // z-direction + for (unsigned int i=0; i<17; ++i) + vertices.push_back (Point(vertices[i][0], + vertices[i][1], + 1)); + + // now create the 8 cells + std::vector > cells; + for (unsigned int c=0; c<8; ++c) + { + CellData d; + d.vertices[0] = 0; + d.vertices[1] = 1+2*c; + d.vertices[2] = 1+((2*c+2) % 16); + d.vertices[3] = 1+2*c+1; + + for (unsigned int v=4; v<8; ++v) + d.vertices[v] = d.vertices[v-4]+17; + + cells.push_back(d); + } + + Triangulation coarse_grid; + coarse_grid.create_triangulation (vertices, cells, + SubCellData()); + + // now also refine one cell + coarse_grid.begin_active()->set_refine_flag(); + coarse_grid.execute_coarsening_and_refinement(); + + check (coarse_grid); + } + catch (const std::exception &exc) + { + // we shouldn't get here... + deallog << "Caught an error..." << std::endl; + deallog << exc.what() << std::endl; + } +} diff --git a/tests/bits/find_cells_adjacent_to_vertex_6/cmp/generic b/tests/bits/find_cells_adjacent_to_vertex_6/cmp/generic new file mode 100644 index 0000000000..df705ec5fc --- /dev/null +++ b/tests/bits/find_cells_adjacent_to_vertex_6/cmp/generic @@ -0,0 +1,189 @@ + +DEAL::Vertex 0 at 0.00000 0.00000 0.00000: 8 cells +DEAL:: 0.1 +DEAL:: 0.2 +DEAL:: 0.3 +DEAL:: 0.4 +DEAL:: 0.5 +DEAL:: 0.6 +DEAL:: 0.7 +DEAL:: 1.0 +DEAL::Vertex 1 at 1.00000 0.00000 0.00000: 2 cells +DEAL:: 0.7 +DEAL:: 1.1 +DEAL::Vertex 2 at 0.923880 0.382683 0.00000: 1 cells +DEAL:: 1.3 +DEAL::Vertex 3 at 0.707107 0.707107 0.00000: 2 cells +DEAL:: 0.1 +DEAL:: 1.2 +DEAL::Vertex 4 at 0.382683 0.923880 0.00000: 1 cells +DEAL:: 0.1 +DEAL::Vertex 5 at 6.12323e-17 1.00000 0.00000: 2 cells +DEAL:: 0.1 +DEAL:: 0.2 +DEAL::Vertex 6 at -0.382683 0.923880 0.00000: 1 cells +DEAL:: 0.2 +DEAL::Vertex 7 at -0.707107 0.707107 0.00000: 2 cells +DEAL:: 0.2 +DEAL:: 0.3 +DEAL::Vertex 8 at -0.923880 0.382683 0.00000: 1 cells +DEAL:: 0.3 +DEAL::Vertex 9 at -1.00000 1.22465e-16 0.00000: 2 cells +DEAL:: 0.3 +DEAL:: 0.4 +DEAL::Vertex 10 at -0.923880 -0.382683 0.00000: 1 cells +DEAL:: 0.4 +DEAL::Vertex 11 at -0.707107 -0.707107 0.00000: 2 cells +DEAL:: 0.4 +DEAL:: 0.5 +DEAL::Vertex 12 at -0.382683 -0.923880 0.00000: 1 cells +DEAL:: 0.5 +DEAL::Vertex 13 at -1.83697e-16 -1.00000 0.00000: 2 cells +DEAL:: 0.5 +DEAL:: 0.6 +DEAL::Vertex 14 at 0.382683 -0.923880 0.00000: 1 cells +DEAL:: 0.6 +DEAL::Vertex 15 at 0.707107 -0.707107 0.00000: 2 cells +DEAL:: 0.6 +DEAL:: 0.7 +DEAL::Vertex 16 at 0.923880 -0.382683 0.00000: 1 cells +DEAL:: 0.7 +DEAL::Vertex 17 at 0.00000 0.00000 1.00000: 8 cells +DEAL:: 0.1 +DEAL:: 0.2 +DEAL:: 0.3 +DEAL:: 0.4 +DEAL:: 0.5 +DEAL:: 0.6 +DEAL:: 0.7 +DEAL:: 1.4 +DEAL::Vertex 18 at 1.00000 0.00000 1.00000: 2 cells +DEAL:: 0.7 +DEAL:: 1.5 +DEAL::Vertex 19 at 0.923880 0.382683 1.00000: 1 cells +DEAL:: 1.7 +DEAL::Vertex 20 at 0.707107 0.707107 1.00000: 2 cells +DEAL:: 0.1 +DEAL:: 1.6 +DEAL::Vertex 21 at 0.382683 0.923880 1.00000: 1 cells +DEAL:: 0.1 +DEAL::Vertex 22 at 6.12323e-17 1.00000 1.00000: 2 cells +DEAL:: 0.1 +DEAL:: 0.2 +DEAL::Vertex 23 at -0.382683 0.923880 1.00000: 1 cells +DEAL:: 0.2 +DEAL::Vertex 24 at -0.707107 0.707107 1.00000: 2 cells +DEAL:: 0.2 +DEAL:: 0.3 +DEAL::Vertex 25 at -0.923880 0.382683 1.00000: 1 cells +DEAL:: 0.3 +DEAL::Vertex 26 at -1.00000 1.22465e-16 1.00000: 2 cells +DEAL:: 0.3 +DEAL:: 0.4 +DEAL::Vertex 27 at -0.923880 -0.382683 1.00000: 1 cells +DEAL:: 0.4 +DEAL::Vertex 28 at -0.707107 -0.707107 1.00000: 2 cells +DEAL:: 0.4 +DEAL:: 0.5 +DEAL::Vertex 29 at -0.382683 -0.923880 1.00000: 1 cells +DEAL:: 0.5 +DEAL::Vertex 30 at -1.83697e-16 -1.00000 1.00000: 2 cells +DEAL:: 0.5 +DEAL:: 0.6 +DEAL::Vertex 31 at 0.382683 -0.923880 1.00000: 1 cells +DEAL:: 0.6 +DEAL::Vertex 32 at 0.707107 -0.707107 1.00000: 2 cells +DEAL:: 0.6 +DEAL:: 0.7 +DEAL::Vertex 33 at 0.923880 -0.382683 1.00000: 1 cells +DEAL:: 0.7 +DEAL::Vertex 34 at 0.500000 0.00000 0.00000: 3 cells +DEAL:: 0.7 +DEAL:: 1.0 +DEAL:: 1.1 +DEAL::Vertex 35 at 0.353553 0.353553 0.00000: 3 cells +DEAL:: 0.1 +DEAL:: 1.0 +DEAL:: 1.2 +DEAL::Vertex 36 at 0.00000 0.00000 0.500000: 9 cells +DEAL:: 0.1 +DEAL:: 0.2 +DEAL:: 0.3 +DEAL:: 0.4 +DEAL:: 0.5 +DEAL:: 0.6 +DEAL:: 0.7 +DEAL:: 1.0 +DEAL:: 1.4 +DEAL::Vertex 37 at 0.961940 0.191342 0.00000: 2 cells +DEAL:: 1.1 +DEAL:: 1.3 +DEAL::Vertex 38 at 1.00000 0.00000 0.500000: 3 cells +DEAL:: 0.7 +DEAL:: 1.1 +DEAL:: 1.5 +DEAL::Vertex 39 at 0.923880 0.382683 0.500000: 2 cells +DEAL:: 1.3 +DEAL:: 1.7 +DEAL::Vertex 40 at 0.815493 0.544895 0.00000: 2 cells +DEAL:: 1.2 +DEAL:: 1.3 +DEAL::Vertex 41 at 0.707107 0.707107 0.500000: 3 cells +DEAL:: 0.1 +DEAL:: 1.2 +DEAL:: 1.6 +DEAL::Vertex 42 at 0.500000 0.00000 1.00000: 3 cells +DEAL:: 0.7 +DEAL:: 1.4 +DEAL:: 1.5 +DEAL::Vertex 43 at 0.353553 0.353553 1.00000: 3 cells +DEAL:: 0.1 +DEAL:: 1.4 +DEAL:: 1.6 +DEAL::Vertex 44 at 0.961940 0.191342 1.00000: 2 cells +DEAL:: 1.5 +DEAL:: 1.7 +DEAL::Vertex 45 at 0.815493 0.544895 1.00000: 2 cells +DEAL:: 1.6 +DEAL:: 1.7 +DEAL::Vertex 46 at 0.500000 0.00000 0.500000: 5 cells +DEAL:: 0.7 +DEAL:: 1.0 +DEAL:: 1.1 +DEAL:: 1.4 +DEAL:: 1.5 +DEAL::Vertex 47 at 0.657747 0.272448 0.00000: 4 cells +DEAL:: 1.0 +DEAL:: 1.1 +DEAL:: 1.2 +DEAL:: 1.3 +DEAL::Vertex 48 at 0.353553 0.353553 0.500000: 5 cells +DEAL:: 0.1 +DEAL:: 1.0 +DEAL:: 1.2 +DEAL:: 1.4 +DEAL:: 1.6 +DEAL::Vertex 49 at 0.961940 0.191342 0.500000: 4 cells +DEAL:: 1.1 +DEAL:: 1.3 +DEAL:: 1.5 +DEAL:: 1.7 +DEAL::Vertex 50 at 0.815493 0.544895 0.500000: 4 cells +DEAL:: 1.2 +DEAL:: 1.3 +DEAL:: 1.6 +DEAL:: 1.7 +DEAL::Vertex 51 at 0.657747 0.272448 1.00000: 4 cells +DEAL:: 1.4 +DEAL:: 1.5 +DEAL:: 1.6 +DEAL:: 1.7 +DEAL::Vertex 52 at 0.657747 0.272448 0.500000: 8 cells +DEAL:: 1.0 +DEAL:: 1.1 +DEAL:: 1.2 +DEAL:: 1.3 +DEAL:: 1.4 +DEAL:: 1.5 +DEAL:: 1.6 +DEAL:: 1.7