From: David Wells Date: Sat, 4 Aug 2018 02:48:21 +0000 (-0400) Subject: Add an option to copy manifold ids in extrude_triangulation. X-Git-Tag: v9.1.0-rc1~826^2~2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=d9fbffcf5d5755b49658261a0d1daeecf1c6f861;p=dealii.git Add an option to copy manifold ids in extrude_triangulation. --- diff --git a/doc/news/changes/major/20180811DavidWells b/doc/news/changes/major/20180811DavidWells new file mode 100644 index 0000000000..7a7ca6ed3d --- /dev/null +++ b/doc/news/changes/major/20180811DavidWells @@ -0,0 +1,4 @@ +Improved: GridGenerator::extrude_triangulation can now optionally extrude manifold +ids. +
+(2018/08/11, David Wells) diff --git a/include/deal.II/grid/grid_generator.h b/include/deal.II/grid/grid_generator.h index 46796992d7..bd277e3592 100644 --- a/include/deal.II/grid/grid_generator.h +++ b/include/deal.II/grid/grid_generator.h @@ -1280,18 +1280,56 @@ namespace GridGenerator * $0$, $1$, and $42$, then the $z = 0$ boundary id of @p result will be $43$ * and the $z = \text{height}$ boundary id will be $44$. * + * This function does not, by default, copy manifold ids. The reason for + * this is that there is no way to set the manifold ids on the lines of the + * resulting Triangulation without more information: for example, if two + * faces of @p input with different manifold ids meet at a shared vertex then + * there is no a priori reason to pick one manifold id or another + * for the lines created in @p result that are parallel to the $z$-axis and + * pass through that point. If @p copy_manifold_ids is true + * then this function sets line manifold ids by picking the one that appears + * first in @p manifold_priorities. For example: if @p + * manifold_priorities is {0, 42, numbers::flat_manifold_id} + * and the line under consideration is adjacent to faces with manifold ids of + * 0 and 42, then that line will have a manifold id + * of 0. The correct ordering is almost always + *
    + *
  1. manifold ids set on the boundary,
    2. + *
  2. manifold ids that describe most of the cells in the Triangulation + * (e.g., numbers::flat_manifold_id), and
    3. + *
  3. any manifold ids corresponding to TransfiniteInterpolationManifold + * manifolds.
    4. + *
+ * + * In particular, since TransfiniteInterpolationManifold interpolates + * between surrounding manifolds, its manifold id should usually not be set + * on lines or faces that are adjacent to cells with different manifold + * ids. The default value for @p manifold_priorities follows this ranking + * (where each category is sorted in ascending order): + *
    + *
  1. manifold ids associated with manifolds that are not + * TransfiniteInterpolationManifold, and
    2. + *
  2. manifold ids associated with any TransfiniteInterpolationManifold + * objects.
    3. + *
+ * Note that numbers::flat_manifold_id (should it be a manifold id of @p + * input) will always be the last entry in the first category. + * * @note The 2d input triangulation @p input must be a coarse mesh that has * no refined cells. * * @note Since @p input and @p output have different spatial dimensions no - * manifold objects are copied (nor are any manifold ids set) by this - * function. + * manifold objects are copied by this function regardless of the value of + * @p copy_manifold_ids. */ void - extrude_triangulation(const Triangulation<2, 2> &input, - const unsigned int n_slices, - const double height, - Triangulation<3, 3> & result); + extrude_triangulation( + const Triangulation<2, 2> & input, + const unsigned int n_slices, + const double height, + Triangulation<3, 3> & result, + const bool copy_manifold_ids = false, + const std::vector &manifold_priorities = {}); /** * Overload of the previous function. Take a 2d Triangulation that is being @@ -1312,9 +1350,12 @@ namespace GridGenerator * @author Weixiong Zheng, 2018 */ void - extrude_triangulation(const Triangulation<2, 2> &input, - const std::vector &slice_coordinates, - Triangulation<3, 3> & result); + extrude_triangulation( + const Triangulation<2, 2> & input, + const std::vector & slice_coordinates, + Triangulation<3, 3> & result, + const bool copy_manifold_ids = false, + const std::vector &manifold_priorities = {}); /** diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc index 672638ff38..fa87331b02 100644 --- a/source/grid/grid_generator.cc +++ b/source/grid/grid_generator.cc @@ -4476,10 +4476,13 @@ namespace GridGenerator void - extrude_triangulation(const Triangulation<2, 2> &input, - const unsigned int n_slices, - const double height, - Triangulation<3, 3> & result) + extrude_triangulation( + const Triangulation<2, 2> & input, + const unsigned int n_slices, + const double height, + Triangulation<3, 3> & result, + const bool copy_manifold_ids, + const std::vector &manifold_priorities) { Assert(input.n_levels() == 1, ExcMessage( @@ -4497,13 +4500,19 @@ namespace GridGenerator std::vector slices_z_values; for (unsigned int i = 0; i < n_slices; ++i) slices_z_values.push_back(i * delta_h); - extrude_triangulation(input, slices_z_values, result); + extrude_triangulation( + input, slices_z_values, result, copy_manifold_ids, manifold_priorities); } + + void - extrude_triangulation(const Triangulation<2, 2> &input, - const std::vector &slice_coordinates, - Triangulation<3, 3> & result) + extrude_triangulation( + const Triangulation<2, 2> & input, + const std::vector & slice_coordinates, + Triangulation<3, 3> & result, + const bool copy_manifold_ids, + const std::vector &manifold_priorities) { Assert(input.n_levels() == 1, ExcMessage( @@ -4516,6 +4525,66 @@ namespace GridGenerator "The number of slices for extrusion must be at least 2.")); Assert(std::is_sorted(slice_coordinates.begin(), slice_coordinates.end()), ExcMessage("Slice z-coordinates should be in ascending order")); + + const auto priorities = [&]() -> std::vector { + // if a non-empty (i.e., not the default) vector is given for + // manifold_priorities then use it (but check its validity in debug + // mode) + if (0 < manifold_priorities.size()) + { +#ifdef DEBUG + // check that the provided manifold_priorities is valid + std::vector sorted_manifold_priorities = + manifold_priorities; + std::sort(sorted_manifold_priorities.begin(), + sorted_manifold_priorities.end()); + Assert(std::unique(sorted_manifold_priorities.begin(), + sorted_manifold_priorities.end()) == + sorted_manifold_priorities.end(), + ExcMessage( + "The given vector of manifold ids may not contain any " + "duplicated entries.")); + std::vector sorted_manifold_ids = + input.get_manifold_ids(); + std::sort(sorted_manifold_ids.begin(), sorted_manifold_ids.end()); + if (sorted_manifold_priorities != sorted_manifold_ids) + { + std::ostringstream message; + message << "The given triangulation has manifold ids {"; + for (const types::manifold_id manifold_id : sorted_manifold_ids) + if (manifold_id != sorted_manifold_ids.back()) + message << manifold_id << ", "; + message << sorted_manifold_ids.back() << "}, but \n" + << " the given vector of manifold ids is {"; + for (const types::manifold_id manifold_id : manifold_priorities) + if (manifold_id != manifold_priorities.back()) + message << manifold_id << ", "; + message + << manifold_priorities.back() << "}.\n" + << " These vectors should contain the same elements.\n"; + const std::string m = message.str(); + Assert(false, ExcMessage(m)); + } +#endif + return manifold_priorities; + } + // otherwise use the default ranking: ascending order, but TFI manifolds + // are at the end. + std::vector default_priorities = + input.get_manifold_ids(); + const auto first_tfi_it = std::partition( + default_priorities.begin(), + default_priorities.end(), + [&input](const types::manifold_id &id) { + return dynamic_cast *>( + &input.get_manifold(id)) == nullptr; + }); + std::sort(default_priorities.begin(), first_tfi_it); + std::sort(first_tfi_it, default_priorities.end()); + + return default_priorities; + }(); + const std::size_t n_slices = slice_coordinates.size(); std::vector> points(n_slices * input.n_vertices()); std::vector> cells; @@ -4523,9 +4592,9 @@ namespace GridGenerator // copy the array of points as many times as there will be slices, // one slice at a time. The z-axis value are defined in slices_coordinates - for (unsigned int slice_n = 0; slice_n < n_slices; ++slice_n) + for (std::size_t slice_n = 0; slice_n < n_slices; ++slice_n) { - for (unsigned int vertex_n = 0; vertex_n < input.n_vertices(); + for (std::size_t vertex_n = 0; vertex_n < input.n_vertices(); ++vertex_n) { const Point<2> vertex = input.get_vertices()[vertex_n]; @@ -4538,7 +4607,7 @@ namespace GridGenerator // time for (const auto &cell : input.active_cell_iterators()) { - for (unsigned int slice_n = 0; slice_n < n_slices - 1; ++slice_n) + for (std::size_t slice_n = 0; slice_n < n_slices - 1; ++slice_n) { CellData<3> this_cell; for (unsigned int vertex_n = 0; @@ -4554,14 +4623,14 @@ namespace GridGenerator } this_cell.material_id = cell->material_id(); + if (copy_manifold_ids) + this_cell.manifold_id = cell->manifold_id(); cells.push_back(this_cell); } } - // next, create face data for all of the outer faces for which the - // boundary indicator will not be equal to zero (where we would - // explicitly set it to something that is already the default -- - // no need to do that) + // Next, create face data for all faces that are orthogonal to the x-y + // plane SubCellData subcell_data; std::vector> &quads = subcell_data.boundary_quads; types::boundary_id max_boundary_id = 0; @@ -4573,20 +4642,44 @@ namespace GridGenerator quad.boundary_id = face->boundary_id(); if (face->at_boundary()) max_boundary_id = std::max(max_boundary_id, quad.boundary_id); - for (unsigned int slice = 0; slice < n_slices - 1; ++slice) + if (copy_manifold_ids) + quad.manifold_id = face->manifold_id(); + for (std::size_t slice_n = 0; slice_n < n_slices - 1; ++slice_n) { quad.vertices[0] = - face->vertex_index(0) + slice * input.n_vertices(); + face->vertex_index(0) + slice_n * input.n_vertices(); quad.vertices[1] = - face->vertex_index(1) + slice * input.n_vertices(); + face->vertex_index(1) + slice_n * input.n_vertices(); quad.vertices[2] = - face->vertex_index(0) + (slice + 1) * input.n_vertices(); + face->vertex_index(0) + (slice_n + 1) * input.n_vertices(); quad.vertices[3] = - face->vertex_index(1) + (slice + 1) * input.n_vertices(); + face->vertex_index(1) + (slice_n + 1) * input.n_vertices(); quads.push_back(quad); } } + // if necessary, create face data for faces parallel to the x-y + // plane. This is only necessary if we need to set manifolds. + if (copy_manifold_ids) + for (const auto &cell : input.active_cell_iterators()) + { + CellData<2> quad; + quad.boundary_id = numbers::internal_face_boundary_id; + quad.manifold_id = cell->manifold_id(); // check is outside loop + for (std::size_t slice_n = 1; slice_n < n_slices - 1; ++slice_n) + { + quad.vertices[0] = + cell->vertex_index(0) + slice_n * input.n_vertices(); + quad.vertices[1] = + cell->vertex_index(1) + slice_n * input.n_vertices(); + quad.vertices[2] = + cell->vertex_index(2) + slice_n * input.n_vertices(); + quad.vertices[3] = + cell->vertex_index(3) + slice_n * input.n_vertices(); + quads.push_back(quad); + } + } + // then mark the bottom and top boundaries of the extruded mesh // with max_boundary_id+1 and max_boundary_id+2. check that this // remains valid @@ -4609,6 +4702,8 @@ namespace GridGenerator quad.vertices[1] = cell->vertex_index(1); quad.vertices[2] = cell->vertex_index(2); quad.vertices[3] = cell->vertex_index(3); + if (copy_manifold_ids) + quad.manifold_id = cell->manifold_id(); quads.push_back(quad); quad.boundary_id = top_boundary_id; @@ -4616,6 +4711,8 @@ namespace GridGenerator vertex_n < GeometryInfo<3>::vertices_per_face; ++vertex_n) quad.vertices[vertex_n] += (n_slices - 1) * input.n_vertices(); + if (copy_manifold_ids) + quad.manifold_id = cell->manifold_id(); quads.push_back(quad); } @@ -4628,6 +4725,16 @@ namespace GridGenerator // as discussed in the edge orientation paper mentioned in the // introduction to the GridReordering class. result.create_triangulation(points, cells, subcell_data); + + for (auto manifold_id_it = priorities.rbegin(); + manifold_id_it != priorities.rend(); + ++manifold_id_it) + for (auto &face : result.active_face_iterators()) + if (face->manifold_id() == *manifold_id_it) + for (unsigned int line_n = 0; + line_n < GeometryInfo<3>::lines_per_face; + ++line_n) + face->line(line_n)->set_manifold_id(*manifold_id_it); } diff --git a/tests/grid/extrude_copy_manifold.cc b/tests/grid/extrude_copy_manifold.cc new file mode 100644 index 0000000000..979b2ee40b --- /dev/null +++ b/tests/grid/extrude_copy_manifold.cc @@ -0,0 +1,141 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2018 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. +// +// --------------------------------------------------------------------- + +// Check that we can correctly copy manifold ids during extrusion. The output +// was manually checked by plotting points in paraview. + + +#include +#include +#include +#include + +#include "../tests.h" + +void +test() +{ + Triangulation<2> triangulation_2; + GridGenerator::hyper_ball(triangulation_2); + for (auto &cell : triangulation_2.active_cell_iterators()) + if (cell->at_boundary()) + { + cell->set_manifold_id(1); + for (unsigned int face_n = 0; face_n < GeometryInfo<2>::faces_per_cell; + ++face_n) + if (!cell->face(face_n)->at_boundary()) + cell->face(face_n)->set_manifold_id(1); + } + for (auto &cell : triangulation_2.active_cell_iterators()) + if (!cell->at_boundary()) + cell->set_all_manifold_ids(numbers::flat_manifold_id); + TransfiniteInterpolationManifold<2> tfi_manifold_2; + tfi_manifold_2.initialize(triangulation_2); + triangulation_2.set_manifold(1, tfi_manifold_2); + + Triangulation<3> triangulation_3; + GridGenerator::extrude_triangulation( + triangulation_2, 3, 1.0, triangulation_3, true); + TransfiniteInterpolationManifold<3> tfi_manifold; + tfi_manifold.initialize(triangulation_3); + CylindricalManifold<3> cylinder_manifold(2); + triangulation_3.set_manifold(0, cylinder_manifold); + triangulation_3.set_manifold(42, tfi_manifold); + triangulation_3.refine_global(1); + + std::map>> line_centers; + std::map>> face_centers; + std::map>> cell_centers; + + for (const auto &cell : triangulation_3.active_cell_iterators()) + { + cell_centers[cell->manifold_id()].push_back(cell->center()); + for (unsigned int face_n = 0; face_n < GeometryInfo<3>::faces_per_cell; + ++face_n) + face_centers[cell->face(face_n)->manifold_id()].push_back( + cell->face(face_n)->center()); + for (unsigned int line_n = 0; line_n < GeometryInfo<3>::lines_per_cell; + ++line_n) + line_centers[cell->line(line_n)->manifold_id()].push_back( + cell->line(line_n)->center()); + } + + deallog << "cell centers:" << std::endl; + for (const std::pair>> &key : + cell_centers) + { + // cell centers are already unique: we only visited each cell once + deallog << "manifold id: " << key.first << std::endl; + for (const Point<3> &point : key.second) + deallog << point[0] << ", " << point[1] << ", " << point[2] + << std::endl; + } + deallog << std::endl; + + // The generated arrays of face and line centers contain duplicates: get rid + // of them by sorting and then std::unique-ing + auto point_comparator = [](const Point<3> &a, const Point<3> &b) { + // just use std::tuple's lexical ordering so that we don't have to think + // too hard + return std::tie(a[0], a[1], a[2]) < std::tie(b[0], b[1], b[2]); + }; + + deallog << "face centers:" << std::endl; + for (std::pair>> &key : + face_centers) + { + deallog << "manifold id: " << key.first << std::endl; + std::sort(key.second.begin(), key.second.end(), point_comparator); + key.second.erase(std::unique(key.second.begin(), key.second.end()), + key.second.end()); + for (const Point<3> &point : key.second) + deallog << point[0] << ", " << point[1] << ", " << point[2] + << std::endl; + } + + deallog << "line centers:" << std::endl; + for (std::pair>> &key : + line_centers) + { + deallog << "manifold id: " << key.first << std::endl; + std::sort(key.second.begin(), key.second.end(), point_comparator); + key.second.erase(std::unique(key.second.begin(), key.second.end()), + key.second.end()); + for (const Point<3> &point : key.second) + deallog << point[0] << ", " << point[1] << ", " << point[2] + << std::endl; + } + + // reenable if we want to look at pictures + if (false) + { + std::ofstream out("out-" + std::to_string(3) + ".vtu"); + GridOut grid_out; + grid_out.write_vtu(triangulation_3, out); + + Triangulation<2, 3> triangulation_23; + GridGenerator::extract_boundary_mesh(triangulation_3, triangulation_23); + std::ofstream out23("out-23.vtu"); + grid_out.write_vtu(triangulation_23, out23); + } +} + + +int +main() +{ + initlog(); + test(); +} diff --git a/tests/grid/extrude_copy_manifold.output b/tests/grid/extrude_copy_manifold.output new file mode 100644 index 0000000000..d7bf109c6c --- /dev/null +++ b/tests/grid/extrude_copy_manifold.output @@ -0,0 +1,689 @@ + +DEAL::cell centers: +DEAL::manifold id: 1 +DEAL::-0.301777, -0.713388, 0.125000 +DEAL::0.301777, -0.713388, 0.125000 +DEAL::-0.198223, -0.433058, 0.125000 +DEAL::0.198223, -0.433058, 0.125000 +DEAL::-0.301777, -0.713388, 0.375000 +DEAL::0.301777, -0.713388, 0.375000 +DEAL::-0.198223, -0.433058, 0.375000 +DEAL::0.198223, -0.433058, 0.375000 +DEAL::-0.301777, -0.713388, 0.625000 +DEAL::0.301777, -0.713388, 0.625000 +DEAL::-0.198223, -0.433058, 0.625000 +DEAL::0.198223, -0.433058, 0.625000 +DEAL::-0.301777, -0.713388, 0.875000 +DEAL::0.301777, -0.713388, 0.875000 +DEAL::-0.198223, -0.433058, 0.875000 +DEAL::0.198223, -0.433058, 0.875000 +DEAL::-0.713388, -0.301777, 0.125000 +DEAL::-0.433058, -0.198223, 0.125000 +DEAL::-0.713388, 0.301777, 0.125000 +DEAL::-0.433058, 0.198223, 0.125000 +DEAL::-0.713388, -0.301777, 0.375000 +DEAL::-0.433058, -0.198223, 0.375000 +DEAL::-0.713388, 0.301777, 0.375000 +DEAL::-0.433058, 0.198223, 0.375000 +DEAL::-0.713388, -0.301777, 0.625000 +DEAL::-0.433058, -0.198223, 0.625000 +DEAL::-0.713388, 0.301777, 0.625000 +DEAL::-0.433058, 0.198223, 0.625000 +DEAL::-0.713388, -0.301777, 0.875000 +DEAL::-0.433058, -0.198223, 0.875000 +DEAL::-0.713388, 0.301777, 0.875000 +DEAL::-0.433058, 0.198223, 0.875000 +DEAL::0.713388, -0.301777, 0.125000 +DEAL::0.713388, 0.301777, 0.125000 +DEAL::0.433058, -0.198223, 0.125000 +DEAL::0.433058, 0.198223, 0.125000 +DEAL::0.713388, -0.301777, 0.375000 +DEAL::0.713388, 0.301777, 0.375000 +DEAL::0.433058, -0.198223, 0.375000 +DEAL::0.433058, 0.198223, 0.375000 +DEAL::0.713388, -0.301777, 0.625000 +DEAL::0.713388, 0.301777, 0.625000 +DEAL::0.433058, -0.198223, 0.625000 +DEAL::0.433058, 0.198223, 0.625000 +DEAL::0.713388, -0.301777, 0.875000 +DEAL::0.713388, 0.301777, 0.875000 +DEAL::0.433058, -0.198223, 0.875000 +DEAL::0.433058, 0.198223, 0.875000 +DEAL::-0.301777, 0.713388, 0.125000 +DEAL::-0.198223, 0.433058, 0.125000 +DEAL::0.301777, 0.713388, 0.125000 +DEAL::0.198223, 0.433058, 0.125000 +DEAL::-0.301777, 0.713388, 0.375000 +DEAL::-0.198223, 0.433058, 0.375000 +DEAL::0.301777, 0.713388, 0.375000 +DEAL::0.198223, 0.433058, 0.375000 +DEAL::-0.301777, 0.713388, 0.625000 +DEAL::-0.198223, 0.433058, 0.625000 +DEAL::0.301777, 0.713388, 0.625000 +DEAL::0.198223, 0.433058, 0.625000 +DEAL::-0.301777, 0.713388, 0.875000 +DEAL::-0.198223, 0.433058, 0.875000 +DEAL::0.301777, 0.713388, 0.875000 +DEAL::0.198223, 0.433058, 0.875000 +DEAL::manifold id: 4294967295 +DEAL::-0.146447, -0.146447, 0.125000 +DEAL::0.146447, -0.146447, 0.125000 +DEAL::-0.146447, 0.146447, 0.125000 +DEAL::0.146447, 0.146447, 0.125000 +DEAL::-0.146447, -0.146447, 0.375000 +DEAL::0.146447, -0.146447, 0.375000 +DEAL::-0.146447, 0.146447, 0.375000 +DEAL::0.146447, 0.146447, 0.375000 +DEAL::-0.146447, -0.146447, 0.625000 +DEAL::0.146447, -0.146447, 0.625000 +DEAL::-0.146447, 0.146447, 0.625000 +DEAL::0.146447, 0.146447, 0.625000 +DEAL::-0.146447, -0.146447, 0.875000 +DEAL::0.146447, -0.146447, 0.875000 +DEAL::-0.146447, 0.146447, 0.875000 +DEAL::0.146447, 0.146447, 0.875000 +DEAL:: +DEAL::face centers: +DEAL::manifold id: 0 +DEAL::-0.853553, -0.353553, 0.125000 +DEAL::-0.853553, -0.353553, 0.375000 +DEAL::-0.853553, -0.353553, 0.625000 +DEAL::-0.853553, -0.353553, 0.875000 +DEAL::-0.853553, 0.353553, 0.125000 +DEAL::-0.853553, 0.353553, 0.375000 +DEAL::-0.853553, 0.353553, 0.625000 +DEAL::-0.853553, 0.353553, 0.875000 +DEAL::-0.353553, -0.853553, 0.125000 +DEAL::-0.353553, -0.853553, 0.625000 +DEAL::-0.353553, -0.853553, 0.375000 +DEAL::-0.353553, -0.853553, 0.875000 +DEAL::-0.353553, 0.853553, 0.375000 +DEAL::-0.353553, 0.853553, 0.875000 +DEAL::-0.353553, 0.853553, 0.125000 +DEAL::-0.353553, 0.853553, 0.625000 +DEAL::0.353553, -0.853553, 0.125000 +DEAL::0.353553, -0.853553, 0.625000 +DEAL::0.353553, -0.853553, 0.375000 +DEAL::0.353553, -0.853553, 0.875000 +DEAL::0.353553, 0.853553, 0.125000 +DEAL::0.353553, 0.853553, 0.375000 +DEAL::0.353553, 0.853553, 0.625000 +DEAL::0.353553, 0.853553, 0.875000 +DEAL::0.853553, -0.353553, 0.375000 +DEAL::0.853553, -0.353553, 0.875000 +DEAL::0.853553, -0.353553, 0.125000 +DEAL::0.853553, -0.353553, 0.625000 +DEAL::0.853553, 0.353553, 0.125000 +DEAL::0.853553, 0.353553, 0.375000 +DEAL::0.853553, 0.353553, 0.625000 +DEAL::0.853553, 0.353553, 0.875000 +DEAL::manifold id: 1 +DEAL::-0.823223, 1.66533e-16, 0.125000 +DEAL::-0.823223, 1.66533e-16, 0.625000 +DEAL::-0.823223, 1.66533e-16, 0.375000 +DEAL::-0.823223, 1.66533e-16, 0.875000 +DEAL::-0.713388, 0.301777, 0.00000 +DEAL::-0.713388, 0.301777, 0.500000 +DEAL::-0.713388, 0.301777, 1.00000 +DEAL::-0.713388, -0.301777, 0.00000 +DEAL::-0.713388, -0.301777, 0.250000 +DEAL::-0.713388, -0.301777, 0.500000 +DEAL::-0.713388, -0.301777, 0.750000 +DEAL::-0.713388, -0.301777, 1.00000 +DEAL::-0.713388, 0.301777, 0.250000 +DEAL::-0.713388, 0.301777, 0.750000 +DEAL::-0.603553, -0.603553, 0.125000 +DEAL::-0.603553, -0.603553, 0.375000 +DEAL::-0.603553, -0.603553, 0.625000 +DEAL::-0.603553, -0.603553, 0.875000 +DEAL::-0.603553, 0.603553, 0.125000 +DEAL::-0.603553, 0.603553, 0.375000 +DEAL::-0.603553, 0.603553, 0.625000 +DEAL::-0.603553, 0.603553, 0.875000 +DEAL::-0.573223, -0.250000, 0.125000 +DEAL::-0.573223, -0.250000, 0.375000 +DEAL::-0.573223, -0.250000, 0.625000 +DEAL::-0.573223, -0.250000, 0.875000 +DEAL::-0.573223, 0.250000, 0.125000 +DEAL::-0.573223, 0.250000, 0.375000 +DEAL::-0.573223, 0.250000, 0.625000 +DEAL::-0.573223, 0.250000, 0.875000 +DEAL::-0.469670, 5.55112e-17, 0.125000 +DEAL::-0.469670, 5.55112e-17, 0.375000 +DEAL::-0.469670, 5.55112e-17, 0.625000 +DEAL::-0.469670, 5.55112e-17, 0.875000 +DEAL::-0.433058, -0.198223, 0.00000 +DEAL::-0.433058, -0.198223, 0.500000 +DEAL::-0.433058, -0.198223, 1.00000 +DEAL::-0.433058, 0.198223, 0.00000 +DEAL::-0.433058, 0.198223, 0.250000 +DEAL::-0.433058, 0.198223, 0.500000 +DEAL::-0.433058, 0.198223, 0.750000 +DEAL::-0.433058, 0.198223, 1.00000 +DEAL::-0.433058, -0.198223, 0.250000 +DEAL::-0.433058, -0.198223, 0.750000 +DEAL::-0.396447, -0.396447, 0.125000 +DEAL::-0.396447, -0.396447, 0.625000 +DEAL::-0.396447, -0.396447, 0.375000 +DEAL::-0.396447, -0.396447, 0.875000 +DEAL::-0.396447, 0.396447, 0.125000 +DEAL::-0.396447, 0.396447, 0.375000 +DEAL::-0.396447, 0.396447, 0.625000 +DEAL::-0.396447, 0.396447, 0.875000 +DEAL::-0.301777, -0.713388, 0.00000 +DEAL::-0.301777, -0.713388, 0.250000 +DEAL::-0.301777, -0.713388, 0.500000 +DEAL::-0.301777, -0.713388, 0.750000 +DEAL::-0.301777, -0.713388, 1.00000 +DEAL::-0.301777, 0.713388, 0.00000 +DEAL::-0.301777, 0.713388, 0.500000 +DEAL::-0.301777, 0.713388, 1.00000 +DEAL::-0.301777, 0.713388, 0.250000 +DEAL::-0.301777, 0.713388, 0.750000 +DEAL::-0.250000, -0.573223, 0.125000 +DEAL::-0.250000, -0.573223, 0.375000 +DEAL::-0.250000, -0.573223, 0.625000 +DEAL::-0.250000, -0.573223, 0.875000 +DEAL::-0.250000, 0.573223, 0.125000 +DEAL::-0.250000, 0.573223, 0.375000 +DEAL::-0.250000, 0.573223, 0.625000 +DEAL::-0.250000, 0.573223, 0.875000 +DEAL::-0.198223, -0.433058, 0.00000 +DEAL::-0.198223, -0.433058, 0.500000 +DEAL::-0.198223, -0.433058, 1.00000 +DEAL::-0.198223, 0.433058, 0.00000 +DEAL::-0.198223, 0.433058, 0.500000 +DEAL::-0.198223, 0.433058, 1.00000 +DEAL::-0.198223, -0.433058, 0.250000 +DEAL::-0.198223, -0.433058, 0.750000 +DEAL::-0.198223, 0.433058, 0.250000 +DEAL::-0.198223, 0.433058, 0.750000 +DEAL::-4.16334e-17, -0.823223, 0.125000 +DEAL::-4.16334e-17, -0.823223, 0.625000 +DEAL::-4.16334e-17, -0.823223, 0.375000 +DEAL::-4.16334e-17, -0.823223, 0.875000 +DEAL::-1.38778e-17, -0.469670, 0.125000 +DEAL::-1.38778e-17, -0.469670, 0.375000 +DEAL::-1.38778e-17, -0.469670, 0.625000 +DEAL::-1.38778e-17, -0.469670, 0.875000 +DEAL::1.11022e-16, 0.469670, 0.125000 +DEAL::1.11022e-16, 0.469670, 0.375000 +DEAL::1.11022e-16, 0.469670, 0.625000 +DEAL::1.11022e-16, 0.469670, 0.875000 +DEAL::3.05311e-16, 0.823223, 0.375000 +DEAL::3.05311e-16, 0.823223, 0.875000 +DEAL::3.05311e-16, 0.823223, 0.125000 +DEAL::3.05311e-16, 0.823223, 0.625000 +DEAL::0.198223, -0.433058, 0.250000 +DEAL::0.198223, -0.433058, 0.750000 +DEAL::0.198223, -0.433058, 0.00000 +DEAL::0.198223, -0.433058, 0.500000 +DEAL::0.198223, -0.433058, 1.00000 +DEAL::0.198223, 0.433058, 0.00000 +DEAL::0.198223, 0.433058, 0.500000 +DEAL::0.198223, 0.433058, 1.00000 +DEAL::0.198223, 0.433058, 0.250000 +DEAL::0.198223, 0.433058, 0.750000 +DEAL::0.250000, -0.573223, 0.125000 +DEAL::0.250000, -0.573223, 0.375000 +DEAL::0.250000, -0.573223, 0.625000 +DEAL::0.250000, -0.573223, 0.875000 +DEAL::0.250000, 0.573223, 0.125000 +DEAL::0.250000, 0.573223, 0.375000 +DEAL::0.250000, 0.573223, 0.625000 +DEAL::0.250000, 0.573223, 0.875000 +DEAL::0.301777, -0.713388, 0.250000 +DEAL::0.301777, -0.713388, 0.750000 +DEAL::0.301777, -0.713388, 0.00000 +DEAL::0.301777, -0.713388, 0.500000 +DEAL::0.301777, -0.713388, 1.00000 +DEAL::0.301777, 0.713388, 0.00000 +DEAL::0.301777, 0.713388, 0.500000 +DEAL::0.301777, 0.713388, 1.00000 +DEAL::0.301777, 0.713388, 0.250000 +DEAL::0.301777, 0.713388, 0.750000 +DEAL::0.396447, -0.396447, 0.375000 +DEAL::0.396447, -0.396447, 0.875000 +DEAL::0.396447, -0.396447, 0.125000 +DEAL::0.396447, -0.396447, 0.625000 +DEAL::0.396447, 0.396447, 0.375000 +DEAL::0.396447, 0.396447, 0.875000 +DEAL::0.396447, 0.396447, 0.125000 +DEAL::0.396447, 0.396447, 0.625000 +DEAL::0.433058, -0.198223, 0.00000 +DEAL::0.433058, -0.198223, 0.500000 +DEAL::0.433058, -0.198223, 1.00000 +DEAL::0.433058, -0.198223, 0.250000 +DEAL::0.433058, -0.198223, 0.750000 +DEAL::0.433058, 0.198223, 0.250000 +DEAL::0.433058, 0.198223, 0.750000 +DEAL::0.433058, 0.198223, 0.00000 +DEAL::0.433058, 0.198223, 0.500000 +DEAL::0.433058, 0.198223, 1.00000 +DEAL::0.469670, -6.93889e-18, 0.125000 +DEAL::0.469670, -6.93889e-18, 0.375000 +DEAL::0.469670, -6.93889e-18, 0.625000 +DEAL::0.469670, -6.93889e-18, 0.875000 +DEAL::0.573223, -0.250000, 0.125000 +DEAL::0.573223, -0.250000, 0.375000 +DEAL::0.573223, -0.250000, 0.625000 +DEAL::0.573223, -0.250000, 0.875000 +DEAL::0.573223, 0.250000, 0.125000 +DEAL::0.573223, 0.250000, 0.375000 +DEAL::0.573223, 0.250000, 0.625000 +DEAL::0.573223, 0.250000, 0.875000 +DEAL::0.603553, -0.603553, 0.125000 +DEAL::0.603553, -0.603553, 0.375000 +DEAL::0.603553, -0.603553, 0.625000 +DEAL::0.603553, -0.603553, 0.875000 +DEAL::0.603553, 0.603553, 0.125000 +DEAL::0.603553, 0.603553, 0.375000 +DEAL::0.603553, 0.603553, 0.625000 +DEAL::0.603553, 0.603553, 0.875000 +DEAL::0.713388, -0.301777, 0.00000 +DEAL::0.713388, -0.301777, 0.250000 +DEAL::0.713388, -0.301777, 0.500000 +DEAL::0.713388, -0.301777, 0.750000 +DEAL::0.713388, -0.301777, 1.00000 +DEAL::0.713388, 0.301777, 0.250000 +DEAL::0.713388, 0.301777, 0.750000 +DEAL::0.713388, 0.301777, 0.00000 +DEAL::0.713388, 0.301777, 0.500000 +DEAL::0.713388, 0.301777, 1.00000 +DEAL::0.823223, -3.46945e-17, 0.375000 +DEAL::0.823223, -3.46945e-17, 0.875000 +DEAL::0.823223, -3.46945e-17, 0.125000 +DEAL::0.823223, -3.46945e-17, 0.625000 +DEAL::manifold id: 4294967295 +DEAL::-0.292893, -0.146447, 0.125000 +DEAL::-0.292893, -0.146447, 0.375000 +DEAL::-0.292893, -0.146447, 0.625000 +DEAL::-0.292893, -0.146447, 0.875000 +DEAL::-0.292893, 0.146447, 0.125000 +DEAL::-0.292893, 0.146447, 0.375000 +DEAL::-0.292893, 0.146447, 0.625000 +DEAL::-0.292893, 0.146447, 0.875000 +DEAL::-0.146447, -0.292893, 0.125000 +DEAL::-0.146447, -0.292893, 0.375000 +DEAL::-0.146447, -0.292893, 0.625000 +DEAL::-0.146447, -0.292893, 0.875000 +DEAL::-0.146447, -0.146447, 0.00000 +DEAL::-0.146447, -0.146447, 0.250000 +DEAL::-0.146447, -0.146447, 0.500000 +DEAL::-0.146447, -0.146447, 0.750000 +DEAL::-0.146447, -0.146447, 1.00000 +DEAL::-0.146447, 0.00000, 0.125000 +DEAL::-0.146447, 0.00000, 0.375000 +DEAL::-0.146447, 0.00000, 0.625000 +DEAL::-0.146447, 0.00000, 0.875000 +DEAL::-0.146447, 0.146447, 0.00000 +DEAL::-0.146447, 0.146447, 0.250000 +DEAL::-0.146447, 0.146447, 0.500000 +DEAL::-0.146447, 0.146447, 0.750000 +DEAL::-0.146447, 0.146447, 1.00000 +DEAL::-0.146447, 0.292893, 0.125000 +DEAL::-0.146447, 0.292893, 0.375000 +DEAL::-0.146447, 0.292893, 0.625000 +DEAL::-0.146447, 0.292893, 0.875000 +DEAL::0.00000, -0.146447, 0.125000 +DEAL::0.00000, -0.146447, 0.375000 +DEAL::0.00000, -0.146447, 0.625000 +DEAL::0.00000, -0.146447, 0.875000 +DEAL::0.00000, 0.146447, 0.125000 +DEAL::0.00000, 0.146447, 0.375000 +DEAL::0.00000, 0.146447, 0.625000 +DEAL::0.00000, 0.146447, 0.875000 +DEAL::0.146447, -0.292893, 0.125000 +DEAL::0.146447, -0.292893, 0.375000 +DEAL::0.146447, -0.292893, 0.625000 +DEAL::0.146447, -0.292893, 0.875000 +DEAL::0.146447, -0.146447, 0.00000 +DEAL::0.146447, -0.146447, 0.250000 +DEAL::0.146447, -0.146447, 0.500000 +DEAL::0.146447, -0.146447, 0.750000 +DEAL::0.146447, -0.146447, 1.00000 +DEAL::0.146447, 0.00000, 0.125000 +DEAL::0.146447, 0.00000, 0.375000 +DEAL::0.146447, 0.00000, 0.625000 +DEAL::0.146447, 0.00000, 0.875000 +DEAL::0.146447, 0.146447, 0.00000 +DEAL::0.146447, 0.146447, 0.250000 +DEAL::0.146447, 0.146447, 0.500000 +DEAL::0.146447, 0.146447, 0.750000 +DEAL::0.146447, 0.146447, 1.00000 +DEAL::0.146447, 0.292893, 0.125000 +DEAL::0.146447, 0.292893, 0.375000 +DEAL::0.146447, 0.292893, 0.625000 +DEAL::0.146447, 0.292893, 0.875000 +DEAL::0.292893, -0.146447, 0.125000 +DEAL::0.292893, -0.146447, 0.375000 +DEAL::0.292893, -0.146447, 0.625000 +DEAL::0.292893, -0.146447, 0.875000 +DEAL::0.292893, 0.146447, 0.125000 +DEAL::0.292893, 0.146447, 0.375000 +DEAL::0.292893, 0.146447, 0.625000 +DEAL::0.292893, 0.146447, 0.875000 +DEAL::line centers: +DEAL::manifold id: 0 +DEAL::-1.00000, 2.22045e-16, 0.125000 +DEAL::-1.00000, 2.22045e-16, 0.375000 +DEAL::-1.00000, 2.22045e-16, 0.625000 +DEAL::-1.00000, 2.22045e-16, 0.875000 +DEAL::-0.853553, -0.353553, 0.00000 +DEAL::-0.853553, -0.353553, 0.500000 +DEAL::-0.853553, -0.353553, 1.00000 +DEAL::-0.853553, 0.353553, 0.00000 +DEAL::-0.853553, 0.353553, 0.500000 +DEAL::-0.853553, 0.353553, 1.00000 +DEAL::-0.853553, -0.353553, 0.250000 +DEAL::-0.853553, -0.353553, 0.750000 +DEAL::-0.853553, 0.353553, 0.250000 +DEAL::-0.853553, 0.353553, 0.750000 +DEAL::-0.707107, -0.707107, 0.125000 +DEAL::-0.707107, -0.707107, 0.375000 +DEAL::-0.707107, -0.707107, 0.625000 +DEAL::-0.707107, -0.707107, 0.875000 +DEAL::-0.707107, 0.707107, 0.125000 +DEAL::-0.707107, 0.707107, 0.375000 +DEAL::-0.707107, 0.707107, 0.625000 +DEAL::-0.707107, 0.707107, 0.875000 +DEAL::-0.353553, -0.853553, 0.00000 +DEAL::-0.353553, -0.853553, 0.500000 +DEAL::-0.353553, -0.853553, 1.00000 +DEAL::-0.353553, -0.853553, 0.250000 +DEAL::-0.353553, -0.853553, 0.750000 +DEAL::-0.353553, 0.853553, 0.00000 +DEAL::-0.353553, 0.853553, 0.500000 +DEAL::-0.353553, 0.853553, 1.00000 +DEAL::-0.353553, 0.853553, 0.250000 +DEAL::-0.353553, 0.853553, 0.750000 +DEAL::-5.55112e-17, -1.00000, 0.125000 +DEAL::-5.55112e-17, -1.00000, 0.375000 +DEAL::-5.55112e-17, -1.00000, 0.625000 +DEAL::-5.55112e-17, -1.00000, 0.875000 +DEAL::3.88578e-16, 1.00000, 0.125000 +DEAL::3.88578e-16, 1.00000, 0.375000 +DEAL::3.88578e-16, 1.00000, 0.625000 +DEAL::3.88578e-16, 1.00000, 0.875000 +DEAL::0.353553, -0.853553, 0.250000 +DEAL::0.353553, -0.853553, 0.750000 +DEAL::0.353553, -0.853553, 0.00000 +DEAL::0.353553, -0.853553, 0.500000 +DEAL::0.353553, -0.853553, 1.00000 +DEAL::0.353553, 0.853553, 0.00000 +DEAL::0.353553, 0.853553, 0.500000 +DEAL::0.353553, 0.853553, 1.00000 +DEAL::0.353553, 0.853553, 0.250000 +DEAL::0.353553, 0.853553, 0.750000 +DEAL::0.707107, -0.707107, 0.125000 +DEAL::0.707107, -0.707107, 0.375000 +DEAL::0.707107, -0.707107, 0.625000 +DEAL::0.707107, -0.707107, 0.875000 +DEAL::0.707107, 0.707107, 0.125000 +DEAL::0.707107, 0.707107, 0.375000 +DEAL::0.707107, 0.707107, 0.625000 +DEAL::0.707107, 0.707107, 0.875000 +DEAL::0.853553, -0.353553, 0.250000 +DEAL::0.853553, -0.353553, 0.750000 +DEAL::0.853553, 0.353553, 0.250000 +DEAL::0.853553, 0.353553, 0.750000 +DEAL::0.853553, -0.353553, 0.00000 +DEAL::0.853553, -0.353553, 0.500000 +DEAL::0.853553, -0.353553, 1.00000 +DEAL::0.853553, 0.353553, 0.00000 +DEAL::0.853553, 0.353553, 0.500000 +DEAL::0.853553, 0.353553, 1.00000 +DEAL::1.00000, -5.55112e-17, 0.125000 +DEAL::1.00000, -5.55112e-17, 0.375000 +DEAL::1.00000, -5.55112e-17, 0.625000 +DEAL::1.00000, -5.55112e-17, 0.875000 +DEAL::manifold id: 1 +DEAL::-0.823223, 1.66533e-16, 0.00000 +DEAL::-0.823223, 1.66533e-16, 0.500000 +DEAL::-0.823223, 1.66533e-16, 1.00000 +DEAL::-0.823223, 1.66533e-16, 0.250000 +DEAL::-0.823223, 1.66533e-16, 0.750000 +DEAL::-0.646447, 1.11022e-16, 0.125000 +DEAL::-0.646447, 1.11022e-16, 0.375000 +DEAL::-0.646447, 1.11022e-16, 0.625000 +DEAL::-0.646447, 1.11022e-16, 0.875000 +DEAL::-0.603553, -0.603553, 0.00000 +DEAL::-0.603553, -0.603553, 0.500000 +DEAL::-0.603553, -0.603553, 1.00000 +DEAL::-0.603553, 0.603553, 0.00000 +DEAL::-0.603553, 0.603553, 0.500000 +DEAL::-0.603553, 0.603553, 1.00000 +DEAL::-0.603553, -0.603553, 0.250000 +DEAL::-0.603553, -0.603553, 0.750000 +DEAL::-0.603553, 0.603553, 0.250000 +DEAL::-0.603553, 0.603553, 0.750000 +DEAL::-0.573223, -0.250000, 0.00000 +DEAL::-0.573223, -0.250000, 0.500000 +DEAL::-0.573223, -0.250000, 1.00000 +DEAL::-0.573223, -0.250000, 0.250000 +DEAL::-0.573223, -0.250000, 0.750000 +DEAL::-0.573223, 0.250000, 0.00000 +DEAL::-0.573223, 0.250000, 0.250000 +DEAL::-0.573223, 0.250000, 0.500000 +DEAL::-0.573223, 0.250000, 0.750000 +DEAL::-0.573223, 0.250000, 1.00000 +DEAL::-0.500000, -0.500000, 0.125000 +DEAL::-0.500000, -0.500000, 0.375000 +DEAL::-0.500000, -0.500000, 0.625000 +DEAL::-0.500000, -0.500000, 0.875000 +DEAL::-0.500000, 0.500000, 0.125000 +DEAL::-0.500000, 0.500000, 0.375000 +DEAL::-0.500000, 0.500000, 0.625000 +DEAL::-0.500000, 0.500000, 0.875000 +DEAL::-0.469670, 5.55112e-17, 0.00000 +DEAL::-0.469670, 5.55112e-17, 0.250000 +DEAL::-0.469670, 5.55112e-17, 0.500000 +DEAL::-0.469670, 5.55112e-17, 0.750000 +DEAL::-0.469670, 5.55112e-17, 1.00000 +DEAL::-0.396447, -0.396447, 0.00000 +DEAL::-0.396447, -0.396447, 0.500000 +DEAL::-0.396447, -0.396447, 1.00000 +DEAL::-0.396447, 0.396447, 0.00000 +DEAL::-0.396447, 0.396447, 0.500000 +DEAL::-0.396447, 0.396447, 1.00000 +DEAL::-0.396447, -0.396447, 0.250000 +DEAL::-0.396447, -0.396447, 0.750000 +DEAL::-0.396447, 0.396447, 0.250000 +DEAL::-0.396447, 0.396447, 0.750000 +DEAL::-0.250000, -0.573223, 0.00000 +DEAL::-0.250000, -0.573223, 0.500000 +DEAL::-0.250000, -0.573223, 1.00000 +DEAL::-0.250000, -0.573223, 0.250000 +DEAL::-0.250000, -0.573223, 0.750000 +DEAL::-0.250000, 0.573223, 0.00000 +DEAL::-0.250000, 0.573223, 0.500000 +DEAL::-0.250000, 0.573223, 1.00000 +DEAL::-0.250000, 0.573223, 0.250000 +DEAL::-0.250000, 0.573223, 0.750000 +DEAL::-4.16334e-17, -0.823223, 0.00000 +DEAL::-4.16334e-17, -0.823223, 0.500000 +DEAL::-4.16334e-17, -0.823223, 1.00000 +DEAL::-4.16334e-17, -0.823223, 0.250000 +DEAL::-4.16334e-17, -0.823223, 0.750000 +DEAL::-2.77556e-17, -0.646447, 0.125000 +DEAL::-2.77556e-17, -0.646447, 0.375000 +DEAL::-2.77556e-17, -0.646447, 0.625000 +DEAL::-2.77556e-17, -0.646447, 0.875000 +DEAL::-1.38778e-17, -0.469670, 0.00000 +DEAL::-1.38778e-17, -0.469670, 0.250000 +DEAL::-1.38778e-17, -0.469670, 0.500000 +DEAL::-1.38778e-17, -0.469670, 0.750000 +DEAL::-1.38778e-17, -0.469670, 1.00000 +DEAL::5.55112e-17, 0.469670, 0.00000 +DEAL::5.55112e-17, 0.469670, 0.500000 +DEAL::5.55112e-17, 0.469670, 1.00000 +DEAL::1.38778e-16, 0.823223, 0.00000 +DEAL::1.38778e-16, 0.823223, 0.500000 +DEAL::1.38778e-16, 0.823223, 1.00000 +DEAL::1.66533e-16, 0.469670, 0.250000 +DEAL::1.66533e-16, 0.469670, 0.750000 +DEAL::2.22045e-16, 0.646447, 0.125000 +DEAL::2.22045e-16, 0.646447, 0.375000 +DEAL::2.22045e-16, 0.646447, 0.625000 +DEAL::2.22045e-16, 0.646447, 0.875000 +DEAL::4.71845e-16, 0.823223, 0.250000 +DEAL::4.71845e-16, 0.823223, 0.750000 +DEAL::0.250000, -0.573223, 0.250000 +DEAL::0.250000, -0.573223, 0.750000 +DEAL::0.250000, -0.573223, 0.00000 +DEAL::0.250000, -0.573223, 0.500000 +DEAL::0.250000, -0.573223, 1.00000 +DEAL::0.250000, 0.573223, 0.00000 +DEAL::0.250000, 0.573223, 0.500000 +DEAL::0.250000, 0.573223, 1.00000 +DEAL::0.250000, 0.573223, 0.250000 +DEAL::0.250000, 0.573223, 0.750000 +DEAL::0.396447, -0.396447, 0.250000 +DEAL::0.396447, -0.396447, 0.750000 +DEAL::0.396447, -0.396447, 0.00000 +DEAL::0.396447, -0.396447, 0.500000 +DEAL::0.396447, -0.396447, 1.00000 +DEAL::0.396447, 0.396447, 0.250000 +DEAL::0.396447, 0.396447, 0.750000 +DEAL::0.396447, 0.396447, 0.00000 +DEAL::0.396447, 0.396447, 0.500000 +DEAL::0.396447, 0.396447, 1.00000 +DEAL::0.469670, -1.38778e-17, 0.00000 +DEAL::0.469670, -1.38778e-17, 0.500000 +DEAL::0.469670, -1.38778e-17, 1.00000 +DEAL::0.469670, 0.00000, 0.250000 +DEAL::0.469670, 0.00000, 0.750000 +DEAL::0.500000, -0.500000, 0.125000 +DEAL::0.500000, -0.500000, 0.375000 +DEAL::0.500000, -0.500000, 0.625000 +DEAL::0.500000, -0.500000, 0.875000 +DEAL::0.500000, 0.500000, 0.125000 +DEAL::0.500000, 0.500000, 0.375000 +DEAL::0.500000, 0.500000, 0.625000 +DEAL::0.500000, 0.500000, 0.875000 +DEAL::0.573223, -0.250000, 0.00000 +DEAL::0.573223, -0.250000, 0.500000 +DEAL::0.573223, -0.250000, 1.00000 +DEAL::0.573223, -0.250000, 0.250000 +DEAL::0.573223, -0.250000, 0.750000 +DEAL::0.573223, 0.250000, 0.250000 +DEAL::0.573223, 0.250000, 0.750000 +DEAL::0.573223, 0.250000, 0.00000 +DEAL::0.573223, 0.250000, 0.500000 +DEAL::0.573223, 0.250000, 1.00000 +DEAL::0.603553, -0.603553, 0.250000 +DEAL::0.603553, -0.603553, 0.750000 +DEAL::0.603553, -0.603553, 0.00000 +DEAL::0.603553, -0.603553, 0.500000 +DEAL::0.603553, -0.603553, 1.00000 +DEAL::0.603553, 0.603553, 0.250000 +DEAL::0.603553, 0.603553, 0.750000 +DEAL::0.603553, 0.603553, 0.00000 +DEAL::0.603553, 0.603553, 0.500000 +DEAL::0.603553, 0.603553, 1.00000 +DEAL::0.646447, -1.38778e-17, 0.125000 +DEAL::0.646447, -1.38778e-17, 0.375000 +DEAL::0.646447, -1.38778e-17, 0.625000 +DEAL::0.646447, -1.38778e-17, 0.875000 +DEAL::0.823223, -2.77556e-17, 0.250000 +DEAL::0.823223, -2.77556e-17, 0.750000 +DEAL::0.823223, -4.16334e-17, 0.00000 +DEAL::0.823223, -4.16334e-17, 0.500000 +DEAL::0.823223, -4.16334e-17, 1.00000 +DEAL::manifold id: 4294967295 +DEAL::-0.292893, -0.292893, 0.125000 +DEAL::-0.292893, -0.292893, 0.375000 +DEAL::-0.292893, -0.292893, 0.625000 +DEAL::-0.292893, -0.292893, 0.875000 +DEAL::-0.292893, -0.146447, 0.00000 +DEAL::-0.292893, -0.146447, 0.250000 +DEAL::-0.292893, -0.146447, 0.500000 +DEAL::-0.292893, -0.146447, 0.750000 +DEAL::-0.292893, -0.146447, 1.00000 +DEAL::-0.292893, 0.00000, 0.125000 +DEAL::-0.292893, 0.00000, 0.375000 +DEAL::-0.292893, 0.00000, 0.625000 +DEAL::-0.292893, 0.00000, 0.875000 +DEAL::-0.292893, 0.146447, 0.00000 +DEAL::-0.292893, 0.146447, 0.250000 +DEAL::-0.292893, 0.146447, 0.500000 +DEAL::-0.292893, 0.146447, 0.750000 +DEAL::-0.292893, 0.146447, 1.00000 +DEAL::-0.292893, 0.292893, 0.125000 +DEAL::-0.292893, 0.292893, 0.375000 +DEAL::-0.292893, 0.292893, 0.625000 +DEAL::-0.292893, 0.292893, 0.875000 +DEAL::-0.146447, -0.292893, 0.00000 +DEAL::-0.146447, -0.292893, 0.250000 +DEAL::-0.146447, -0.292893, 0.500000 +DEAL::-0.146447, -0.292893, 0.750000 +DEAL::-0.146447, -0.292893, 1.00000 +DEAL::-0.146447, 0.00000, 0.00000 +DEAL::-0.146447, 0.00000, 0.250000 +DEAL::-0.146447, 0.00000, 0.500000 +DEAL::-0.146447, 0.00000, 0.750000 +DEAL::-0.146447, 0.00000, 1.00000 +DEAL::-0.146447, 0.292893, 0.00000 +DEAL::-0.146447, 0.292893, 0.250000 +DEAL::-0.146447, 0.292893, 0.500000 +DEAL::-0.146447, 0.292893, 0.750000 +DEAL::-0.146447, 0.292893, 1.00000 +DEAL::0.00000, -0.292893, 0.125000 +DEAL::0.00000, -0.292893, 0.375000 +DEAL::0.00000, -0.292893, 0.625000 +DEAL::0.00000, -0.292893, 0.875000 +DEAL::0.00000, -0.146447, 0.00000 +DEAL::0.00000, -0.146447, 0.250000 +DEAL::0.00000, -0.146447, 0.500000 +DEAL::0.00000, -0.146447, 0.750000 +DEAL::0.00000, -0.146447, 1.00000 +DEAL::0.00000, 0.00000, 0.125000 +DEAL::0.00000, 0.00000, 0.375000 +DEAL::0.00000, 0.00000, 0.625000 +DEAL::0.00000, 0.00000, 0.875000 +DEAL::0.00000, 0.146447, 0.00000 +DEAL::0.00000, 0.146447, 0.250000 +DEAL::0.00000, 0.146447, 0.500000 +DEAL::0.00000, 0.146447, 0.750000 +DEAL::0.00000, 0.146447, 1.00000 +DEAL::0.00000, 0.292893, 0.125000 +DEAL::0.00000, 0.292893, 0.375000 +DEAL::0.00000, 0.292893, 0.625000 +DEAL::0.00000, 0.292893, 0.875000 +DEAL::0.146447, -0.292893, 0.00000 +DEAL::0.146447, -0.292893, 0.250000 +DEAL::0.146447, -0.292893, 0.500000 +DEAL::0.146447, -0.292893, 0.750000 +DEAL::0.146447, -0.292893, 1.00000 +DEAL::0.146447, 0.00000, 0.00000 +DEAL::0.146447, 0.00000, 0.250000 +DEAL::0.146447, 0.00000, 0.500000 +DEAL::0.146447, 0.00000, 0.750000 +DEAL::0.146447, 0.00000, 1.00000 +DEAL::0.146447, 0.292893, 0.00000 +DEAL::0.146447, 0.292893, 0.250000 +DEAL::0.146447, 0.292893, 0.500000 +DEAL::0.146447, 0.292893, 0.750000 +DEAL::0.146447, 0.292893, 1.00000 +DEAL::0.292893, -0.292893, 0.125000 +DEAL::0.292893, -0.292893, 0.375000 +DEAL::0.292893, -0.292893, 0.625000 +DEAL::0.292893, -0.292893, 0.875000 +DEAL::0.292893, -0.146447, 0.00000 +DEAL::0.292893, -0.146447, 0.250000 +DEAL::0.292893, -0.146447, 0.500000 +DEAL::0.292893, -0.146447, 0.750000 +DEAL::0.292893, -0.146447, 1.00000 +DEAL::0.292893, 0.00000, 0.125000 +DEAL::0.292893, 0.00000, 0.375000 +DEAL::0.292893, 0.00000, 0.625000 +DEAL::0.292893, 0.00000, 0.875000 +DEAL::0.292893, 0.146447, 0.00000 +DEAL::0.292893, 0.146447, 0.250000 +DEAL::0.292893, 0.146447, 0.500000 +DEAL::0.292893, 0.146447, 0.750000 +DEAL::0.292893, 0.146447, 1.00000 +DEAL::0.292893, 0.292893, 0.125000 +DEAL::0.292893, 0.292893, 0.375000 +DEAL::0.292893, 0.292893, 0.625000 +DEAL::0.292893, 0.292893, 0.875000