From 5e61df4d17e657409a7a50893bdc6c1f93aa772a Mon Sep 17 00:00:00 2001 From: Martin Kronbichler Date: Thu, 16 May 2019 09:37:18 +0200 Subject: [PATCH] Three new test cases to verify the transfinite manifold --- source/grid/manifold_lib.cc | 142 +- tests/manifold/transfinite_manifold_08.cc | 146 ++ tests/manifold/transfinite_manifold_08.output | 865 ++++++++++++ tests/manifold/transfinite_manifold_09.cc | 82 ++ tests/manifold/transfinite_manifold_09.output | 66 + tests/manifold/transfinite_manifold_10.cc | 176 +++ tests/manifold/transfinite_manifold_10.output | 1227 +++++++++++++++++ 7 files changed, 2639 insertions(+), 65 deletions(-) create mode 100644 tests/manifold/transfinite_manifold_08.cc create mode 100644 tests/manifold/transfinite_manifold_08.output create mode 100644 tests/manifold/transfinite_manifold_09.cc create mode 100644 tests/manifold/transfinite_manifold_09.output create mode 100644 tests/manifold/transfinite_manifold_10.cc create mode 100644 tests/manifold/transfinite_manifold_10.output diff --git a/source/grid/manifold_lib.cc b/source/grid/manifold_lib.cc index ca94d1a519..c61028bc39 100644 --- a/source/grid/manifold_lib.cc +++ b/source/grid/manifold_lib.cc @@ -2092,16 +2092,16 @@ TransfiniteInterpolationManifold::pull_back( // and we should fail as early as possible. Since we cannot really // distinguish the two, we must continue here in any case. if (alpha <= 1e-4) - return outside; - // must_recompute_jacobian = true; + must_recompute_jacobian = true; // update the inverse Jacobian with "Broyden's good method" and // Sherman-Morrison formula for the update of the inverse, see // https://en.wikipedia.org/wiki/Broyden%27s_method - const Tensor<1, dim> delta_x = alpha * update; + // J^{-1}_n = J^{-1}_{n-1} + (delta x_n - J^{-1}_{n-1} delta f_n) / + // (delta x_n^T J_{-1}_{n-1} delta f_n) delta x_n^T J^{-1}_{n-1} - // switch sign in residual as compared to the wikipedia article because - // we use a negative definition of the residual with respect to the + // switch sign in residual as compared to the formula above because we + // use a negative definition of the residual with respect to the // Jacobian const Tensor<1, spacedim> delta_f = old_residual - residual; @@ -2110,8 +2110,12 @@ TransfiniteInterpolationManifold::pull_back( for (unsigned int e = 0; e < dim; ++e) Jinv_deltaf[e] += inv_grad[d][e] * delta_f[d]; - // prevent division by zero - if (delta_x * Jinv_deltaf != 0) + const Tensor<1, dim> delta_x = alpha * update; + + // prevent division by zero. This number should be scale-invariant + // because Jinv_deltaf carries no units and x is in reference + // coordinates. + if (std::abs(delta_x * Jinv_deltaf) > 1e-12) { const Tensor<1, dim> factor = (delta_x - Jinv_deltaf) / (delta_x * Jinv_deltaf); @@ -2345,65 +2349,73 @@ TransfiniteInterpolationManifold::compute_chart_points( - auto compute_chart_point = [&](const typename Triangulation:: - cell_iterator & cell, - const unsigned int i) { - Point guess; - // an optimization: keep track of whether or not we used the affine - // approximation so that we don't call pull_back with the same - // initial guess twice (i.e., if pull_back fails the first time, - // don't try again with the same function arguments). - bool used_affine_approximation = false; - // if we have already computed three points, we can guess the fourth - // to be the missing corner point of a rectangle - if (i == 3 && surrounding_points.size() >= 8) - guess = chart_points[1] + (chart_points[2] - chart_points[0]); - else if (use_structdim_2_guesses && 3 < i) - guess = guess_chart_point_structdim_2(i); - else if (use_structdim_3_guesses && 4 < i) - guess = guess_chart_point_structdim_3(i); - else if (dim == 3 && i > 7 && surrounding_points.size() == 26) - { - if (i < 20) - guess = - 0.5 * - chart_points[GeometryInfo::line_to_cell_vertices(i - 8, 0)] + - 0.5 * - chart_points[GeometryInfo::line_to_cell_vertices(i - 8, 1)]; - else - guess = - 0.25 * - (chart_points[GeometryInfo::face_to_cell_vertices(i - 20, 0)] + - chart_points[GeometryInfo::face_to_cell_vertices(i - 20, 1)] + - chart_points[GeometryInfo::face_to_cell_vertices(i - 20, 2)] + - chart_points[GeometryInfo::face_to_cell_vertices(i - 20, 3)]); - } - else - { - guess = - cell->real_to_unit_cell_affine_approximation(surrounding_points[i]); - used_affine_approximation = true; - } - chart_points[i] = pull_back(cell, surrounding_points[i], guess); - - // the initial guess may not have been good enough: if applicable, - // try again with the affine approximation (which is more accurate - // than the cheap methods used above) - if (chart_points[i][0] == internal::invalid_pull_back_coordinate && - !used_affine_approximation) - { - guess = - cell->real_to_unit_cell_affine_approximation(surrounding_points[i]); - chart_points[i] = pull_back(cell, surrounding_points[i], guess); - } + auto compute_chart_point = + [&](const typename Triangulation::cell_iterator &cell, + const unsigned int point_index) { + Point guess; + // an optimization: keep track of whether or not we used the affine + // approximation so that we don't call pull_back with the same + // initial guess twice (i.e., if pull_back fails the first time, + // don't try again with the same function arguments). + bool used_affine_approximation = false; + // if we have already computed three points, we can guess the fourth + // to be the missing corner point of a rectangle + if (point_index == 3 && surrounding_points.size() >= 8) + guess = chart_points[1] + (chart_points[2] - chart_points[0]); + else if (use_structdim_2_guesses && 3 < point_index) + guess = guess_chart_point_structdim_2(point_index); + else if (use_structdim_3_guesses && 4 < point_index) + guess = guess_chart_point_structdim_3(point_index); + else if (dim == 3 && point_index > 7 && surrounding_points.size() == 26) + { + if (point_index < 20) + guess = + 0.5 * (chart_points[GeometryInfo::line_to_cell_vertices( + point_index - 8, 0)] + + chart_points[GeometryInfo::line_to_cell_vertices( + point_index - 8, 1)]); + else + guess = + 0.25 * (chart_points[GeometryInfo::face_to_cell_vertices( + point_index - 20, 0)] + + chart_points[GeometryInfo::face_to_cell_vertices( + point_index - 20, 1)] + + chart_points[GeometryInfo::face_to_cell_vertices( + point_index - 20, 2)] + + chart_points[GeometryInfo::face_to_cell_vertices( + point_index - 20, 3)]); + } + else + { + guess = cell->real_to_unit_cell_affine_approximation( + surrounding_points[point_index]); + used_affine_approximation = true; + } + chart_points[point_index] = + pull_back(cell, surrounding_points[point_index], guess); + + // the initial guess may not have been good enough: if applicable, + // try again with the affine approximation (which is more accurate + // than the cheap methods used above) + if (chart_points[point_index][0] == + internal::invalid_pull_back_coordinate && + !used_affine_approximation) + { + guess = cell->real_to_unit_cell_affine_approximation( + surrounding_points[point_index]); + chart_points[point_index] = + pull_back(cell, surrounding_points[point_index], guess); + } - if (chart_points[i][0] == internal::invalid_pull_back_coordinate) - { - for (unsigned int d = 0; d < dim; ++d) - guess[d] = 0.5; - chart_points[i] = pull_back(cell, surrounding_points[i], guess); - } - }; + if (chart_points[point_index][0] == + internal::invalid_pull_back_coordinate) + { + for (unsigned int d = 0; d < dim; ++d) + guess[d] = 0.5; + chart_points[point_index] = + pull_back(cell, surrounding_points[point_index], guess); + } + }; // check whether all points are inside the unit cell of the current chart for (unsigned int c = 0; c < nearby_cells.size(); ++c) diff --git a/tests/manifold/transfinite_manifold_08.cc b/tests/manifold/transfinite_manifold_08.cc new file mode 100644 index 0000000000..2ef1060428 --- /dev/null +++ b/tests/manifold/transfinite_manifold_08.cc @@ -0,0 +1,146 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2019 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. +// +// --------------------------------------------------------------------- + + +// This test verifies that the transfinite interpolation works on a cylinder +// with oblique faces + +#include +#include +#include +#include + +#include "../tests.h" + + +int +main() +{ + initlog(); + deallog << std::setprecision(9); + + const double radius = 1.; + const double length = 3.; + constexpr int dim = 3; + Triangulation tria; + + // position of auxiliary point to achieve an angle of 120 degrees in corner + // of inner cell + const double ycord = + 0.55 * radius * std::cos(numbers::PI / 12) / + (std::sin(numbers::PI / 12) + std::cos(numbers::PI / 12)); + // vertices for quarter of circle + std::vector> vertices{{0, 0, 0}, + {0.55 * radius, 0, 0}, + {ycord, ycord, 0}, + {radius, 0, 0}, + {radius * std::sqrt(0.5), + radius * std::sqrt(0.5), + 0}}; + + // create additional vertices for other three quarters of circle -> gives 17 + // vertices in total + for (unsigned int a = 1; a < 4; ++a) + { + Tensor<2, 3> transform; + transform[0][0] = a == 2 ? -1. : 0; + transform[1][0] = a == 2 ? 0 : (a == 1 ? 1 : -1); + transform[0][1] = -transform[1][0]; + transform[1][1] = transform[0][0]; + transform[2][2] = 1; + for (unsigned int i = 1; i < 5; ++i) + vertices.push_back(Point<3>(transform * vertices[i])); + } + const unsigned int n_base_vertices = vertices.size(); + for (unsigned int i = 0; i < n_base_vertices; ++i) + { + Point<3> new_point; + for (unsigned int d = 0; d < 2; ++d) + new_point[d] = vertices[i][d]; + new_point[2] = + length - std::tan(numbers::PI / 8) * std::abs(vertices[i][0]) / radius; + vertices.push_back(new_point); + } + + // create cells for mesh on z=0; the first four elements are at the + // center of the circle + std::vector> cell_data(12); + cell_data[0].vertices[0] = 0; + cell_data[0].vertices[1] = 1; + cell_data[0].vertices[2] = 5; + cell_data[0].vertices[3] = 2; + cell_data[1].vertices[0] = 9; + cell_data[1].vertices[1] = 0; + cell_data[1].vertices[2] = 6; + cell_data[1].vertices[3] = 5; + cell_data[2].vertices[0] = 10; + cell_data[2].vertices[1] = 13; + cell_data[2].vertices[2] = 9; + cell_data[2].vertices[3] = 0; + cell_data[3].vertices[0] = 13; + cell_data[3].vertices[1] = 14; + cell_data[3].vertices[2] = 0; + cell_data[3].vertices[3] = 1; + + // the next 8 elements describe the rim; we take one quarter of the circle + // in each loop iteration + for (unsigned int a = 0; a < 4; ++a) + { + cell_data[4 + a * 2].vertices[0] = 1 + a * 4; + cell_data[4 + a * 2].vertices[1] = 3 + a * 4; + cell_data[4 + a * 2].vertices[2] = 2 + a * 4; + cell_data[4 + a * 2].vertices[3] = 4 + a * 4; + cell_data[5 + a * 2].vertices[0] = 2 + a * 4; + cell_data[5 + a * 2].vertices[1] = 4 + a * 4; + AssertIndexRange(4 + a * 4, vertices.size()); + cell_data[5 + a * 2].vertices[2] = a == 3 ? 1 : 5 + a * 4; + cell_data[5 + a * 2].vertices[3] = a == 3 ? 3 : 7 + a * 4; + } + + // create extrusion of the base mesh + for (unsigned int i = 0; i < cell_data.size(); ++i) + for (unsigned int v = 0; v < 4; ++v) + cell_data[i].vertices[4 + v] = n_base_vertices + cell_data[i].vertices[v]; + + SubCellData subcell_data; + tria.create_triangulation(vertices, cell_data, subcell_data); + + // set manifolds on circumferential direction (face ids between 0 and 4) + tria.set_all_manifold_ids(1); + for (auto &cell : tria.active_cell_iterators()) + for (unsigned int f = 0; f < 4; ++f) + if (cell->at_boundary(f)) + cell->face(f)->set_all_manifold_ids(2); + + // attach 3 cylindrical manifolds to mesh + tria.set_manifold(2, + CylindricalManifold(Point{0, 0, 1}, + Point{0, 0, 0})); + TransfiniteInterpolationManifold transfinite; + transfinite.initialize(tria); + tria.set_manifold(1, transfinite); + + for (unsigned int l = 0; l < 2; ++l) + { + for (auto &cell : tria.active_cell_iterators()) + { + deallog << "Face centers:" << std::endl; + for (unsigned int f = 0; f < GeometryInfo::faces_per_cell; ++f) + deallog << cell->face(f)->center(true) << std::endl; + deallog << std::endl; + } + tria.refine_global(); + } +} diff --git a/tests/manifold/transfinite_manifold_08.output b/tests/manifold/transfinite_manifold_08.output new file mode 100644 index 0000000000..771e783946 --- /dev/null +++ b/tests/manifold/transfinite_manifold_08.output @@ -0,0 +1,865 @@ + +DEAL::Face centers: +DEAL::-5.30227280e-16 0.275000000 1.50000000 +DEAL::0.491885662 0.216885662 1.39812714 +DEAL::0.275000000 2.18441115e-16 1.44304564 +DEAL::0.216885662 0.491885662 1.45508151 +DEAL::0.245942831 0.245942831 -1.37045863e-16 +DEAL::0.245942831 0.245942831 2.89812714 +DEAL:: +DEAL::Face centers: +DEAL::-0.491885662 0.216885662 1.39812714 +DEAL::-5.30227280e-16 0.275000000 1.50000000 +DEAL::-0.275000000 1.39701736e-15 1.44304564 +DEAL::-0.216885662 0.491885662 1.45508151 +DEAL::-0.245942831 0.245942831 -9.14863125e-15 +DEAL::-0.245942831 0.245942831 2.89812714 +DEAL:: +DEAL::Face centers: +DEAL::-0.491885662 -0.216885662 1.39812714 +DEAL::4.80570453e-15 -0.275000000 1.50000000 +DEAL::-0.216885662 -0.491885662 1.45508151 +DEAL::-0.275000000 1.39701736e-15 1.44304564 +DEAL::-0.245942831 -0.245942831 8.47816049e-15 +DEAL::-0.245942831 -0.245942831 2.89812714 +DEAL:: +DEAL::Face centers: +DEAL::4.80570453e-15 -0.275000000 1.50000000 +DEAL::0.491885662 -0.216885662 1.39812714 +DEAL::0.216885662 -0.491885662 1.45508151 +DEAL::0.275000000 2.18441115e-16 1.44304564 +DEAL::0.245942831 -0.245942831 -9.01166560e-15 +DEAL::0.245942831 -0.245942831 2.89812714 +DEAL:: +DEAL::Face centers: +DEAL::0.491885662 0.216885662 1.39812714 +DEAL::0.923879533 0.382683432 1.32322330 +DEAL::0.775000000 1.29803225e-12 1.33949224 +DEAL::0.570439053 0.570439053 1.38185820 +DEAL::0.707882597 0.299784547 4.89758830e-18 +DEAL::0.707882597 0.299784547 2.72135045 +DEAL:: +DEAL::Face centers: +DEAL::0.216885662 0.491885662 1.45508151 +DEAL::0.382683432 0.923879533 1.42677670 +DEAL::0.570439053 0.570439053 1.38185820 +DEAL::-1.27183200e-12 0.775000000 1.50000000 +DEAL::0.299784547 0.707882597 5.24541063e-15 +DEAL::0.299784547 0.707882597 2.88185820 +DEAL:: +DEAL::Face centers: +DEAL::-0.216885662 0.491885662 1.45508151 +DEAL::-0.382683432 0.923879533 1.42677670 +DEAL::-1.27183200e-12 0.775000000 1.50000000 +DEAL::-0.570439053 0.570439053 1.38185820 +DEAL::-0.299784547 0.707882597 -3.20075600e-15 +DEAL::-0.299784547 0.707882597 2.88185820 +DEAL:: +DEAL::Face centers: +DEAL::-0.491885662 0.216885662 1.39812714 +DEAL::-0.923879533 0.382683432 1.32322330 +DEAL::-0.570439053 0.570439053 1.38185820 +DEAL::-0.775000000 -1.29805149e-12 1.33949224 +DEAL::-0.707882597 0.299784547 -1.88042954e-20 +DEAL::-0.707882597 0.299784547 2.72135045 +DEAL:: +DEAL::Face centers: +DEAL::-0.491885662 -0.216885662 1.39812714 +DEAL::-0.923879533 -0.382683432 1.32322330 +DEAL::-0.775000000 -1.29805149e-12 1.33949224 +DEAL::-0.570439053 -0.570439053 1.38185820 +DEAL::-0.707882597 -0.299784547 -6.83084261e-20 +DEAL::-0.707882597 -0.299784547 2.72135045 +DEAL:: +DEAL::Face centers: +DEAL::-0.216885662 -0.491885662 1.45508151 +DEAL::-0.382683432 -0.923879533 1.42677670 +DEAL::-0.570439053 -0.570439053 1.38185820 +DEAL::1.27205404e-12 -0.775000000 1.50000000 +DEAL::-0.299784547 -0.707882597 3.20049840e-15 +DEAL::-0.299784547 -0.707882597 2.88185820 +DEAL:: +DEAL::Face centers: +DEAL::0.216885662 -0.491885662 1.45508151 +DEAL::0.382683432 -0.923879533 1.42677670 +DEAL::1.27205404e-12 -0.775000000 1.50000000 +DEAL::0.570439053 -0.570439053 1.38185820 +DEAL::0.299784547 -0.707882597 -3.20075600e-15 +DEAL::0.299784547 -0.707882597 2.88185820 +DEAL:: +DEAL::Face centers: +DEAL::0.491885662 -0.216885662 1.39812714 +DEAL::0.923879533 -0.382683432 1.32322330 +DEAL::0.570439053 -0.570439053 1.38185820 +DEAL::0.775000000 1.29803225e-12 1.33949224 +DEAL::0.707882597 -0.299784547 -3.36413850e-21 +DEAL::0.707882597 -0.299784547 2.72135045 +DEAL:: +DEAL::Face centers: +DEAL::0.00000000 0.137500000 0.750000000 +DEAL::0.260471416 0.122971416 0.723027302 +DEAL::0.137500000 -4.62690180e-16 0.735761409 +DEAL::0.122971416 0.260471416 0.737265893 +DEAL::0.130235708 0.130235708 4.78157171e-15 +DEAL::0.130235708 0.130235708 1.47302730 +DEAL:: +DEAL::Face centers: +DEAL::0.260471416 0.122971416 0.723027302 +DEAL::0.520942831 0.108442831 0.696054604 +DEAL::0.412500000 0.00000000 0.707284226 +DEAL::0.368914247 0.231414247 0.711797679 +DEAL::0.390707123 0.115707123 2.10191468e-15 +DEAL::0.390707123 0.115707123 1.41908191 +DEAL:: +DEAL::Face centers: +DEAL::-3.15595785e-16 0.412500000 0.750000000 +DEAL::0.231414247 0.368914247 0.726036270 +DEAL::0.122971416 0.260471416 0.737265893 +DEAL::0.108442831 0.520942831 0.738770377 +DEAL::0.115707123 0.390707123 0.00000000 +DEAL::0.115707123 0.390707123 1.47603627 +DEAL:: +DEAL::Face centers: +DEAL::0.231414247 0.368914247 0.726036270 +DEAL::0.462828493 0.325328493 0.702072540 +DEAL::0.368914247 0.231414247 0.711797679 +DEAL::0.325328493 0.462828493 0.716311131 +DEAL::0.347121370 0.347121370 -2.88404277e-28 +DEAL::0.347121370 0.347121370 1.42810881 +DEAL:: +DEAL::Face centers: +DEAL::4.12652653e-16 0.137500000 2.25000000 +DEAL::0.260471416 0.122971416 2.16908191 +DEAL::0.137500000 0.00000000 2.20728423 +DEAL::0.122971416 0.260471416 2.21179768 +DEAL::0.130235708 0.130235708 1.47302730 +DEAL::0.130235708 0.130235708 2.94605460 +DEAL:: +DEAL::Face centers: +DEAL::0.260471416 0.122971416 2.16908191 +DEAL::0.520942831 0.108442831 2.08816381 +DEAL::0.412500000 5.05415827e-13 2.12185268 +DEAL::0.368914247 0.231414247 2.13539304 +DEAL::0.390707123 0.115707123 1.41908191 +DEAL::0.390707123 0.115707123 2.83816381 +DEAL:: +DEAL::Face centers: +DEAL::-5.13348455e-13 0.412500000 2.25000000 +DEAL::0.231414247 0.368914247 2.17810881 +DEAL::0.122971416 0.260471416 2.21179768 +DEAL::0.108442831 0.520942831 2.21631113 +DEAL::0.115707123 0.390707123 1.47603627 +DEAL::0.115707123 0.390707123 2.95207254 +DEAL:: +DEAL::Face centers: +DEAL::0.231414247 0.368914247 2.17810881 +DEAL::0.462828493 0.325328493 2.10621762 +DEAL::0.368914247 0.231414247 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+DEAL::-0.635903443 -0.130104704 1.37109647 +DEAL::-0.635903443 -0.130104704 2.74219294 +DEAL:: +DEAL::Face centers: +DEAL::-0.750864056 -0.151766577 2.02512560 +DEAL::-0.980785280 -0.195090322 1.96208739 +DEAL::-0.887500000 -1.46301296e-12 1.97428910 +DEAL::-0.815881065 -0.341233990 2.01292390 +DEAL::-0.865824668 -0.173428449 1.32907100 +DEAL::-0.865824668 -0.173428449 2.65814200 +DEAL:: +DEAL::Face centers: +DEAL::-0.462828493 -0.325328493 2.10621762 +DEAL::-0.647149053 -0.440449363 2.05690007 +DEAL::-0.599884130 -0.258335105 2.06910178 +DEAL::-0.502105188 -0.502105188 2.09401592 +DEAL::-0.554988773 -0.382888928 1.38770590 +DEAL::-0.554988773 -0.382888928 2.77541179 +DEAL:: +DEAL::Face centers: +DEAL::-0.647149053 -0.440449363 2.05690007 +DEAL::-0.831469612 -0.555570233 2.00758252 +DEAL::-0.815881065 -0.341233990 2.01292390 +DEAL::-0.638772917 -0.638772917 2.05155870 +DEAL::-0.739309332 -0.498009798 1.35482753 +DEAL::-0.739309332 -0.498009798 2.70965506 +DEAL:: +DEAL::Face centers: 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+DEAL::-0.341233990 -0.815881065 0.716926449 +DEAL::1.10396962e-12 -0.887500000 0.750000000 +DEAL::-0.173428449 -0.865824668 -7.86428573e-16 +DEAL::-0.173428449 -0.865824668 1.46692645 +DEAL:: +DEAL::Face centers: +DEAL::-0.325328493 -0.462828493 2.14893339 +DEAL::-0.440449363 -0.647149053 2.11709048 +DEAL::-0.502105188 -0.502105188 2.09401592 +DEAL::-0.258335105 -0.599884130 2.17200796 +DEAL::-0.382888928 -0.554988773 1.42200796 +DEAL::-0.382888928 -0.554988773 2.84401592 +DEAL:: +DEAL::Face centers: +DEAL::-0.440449363 -0.647149053 2.11709048 +DEAL::-0.555570233 -0.831469612 2.08524756 +DEAL::-0.638772917 -0.638772917 2.05155870 +DEAL::-0.341233990 -0.815881065 2.15077935 +DEAL::-0.498009798 -0.739309332 1.40077935 +DEAL::-0.498009798 -0.739309332 2.80155870 +DEAL:: +DEAL::Face centers: +DEAL::-0.108442831 -0.520942831 2.21631113 +DEAL::-0.151766577 -0.750864056 2.20569683 +DEAL::-0.258335105 -0.599884130 2.17200796 +DEAL::1.55226787e-12 -0.662500000 2.25000000 +DEAL::-0.130104704 -0.635903443 1.47400265 +DEAL::-0.130104704 -0.635903443 2.94800531 +DEAL:: +DEAL::Face centers: +DEAL::-0.151766577 -0.750864056 2.20569683 +DEAL::-0.195090322 -0.980785280 2.19508252 +DEAL::-0.341233990 -0.815881065 2.15077935 +DEAL::1.60940487e-12 -0.887500000 2.25000000 +DEAL::-0.173428449 -0.865824668 1.46692645 +DEAL::-0.173428449 -0.865824668 2.93385290 +DEAL:: +DEAL::Face centers: +DEAL::0.108442831 -0.520942831 0.738770377 +DEAL::0.151766577 -0.750864056 0.735232275 +DEAL::2.26589083e-12 -0.662500000 0.750000000 +DEAL::0.258335105 -0.599884130 0.724002653 +DEAL::0.130104704 -0.635903443 0.00000000 +DEAL::0.130104704 -0.635903443 1.47400265 +DEAL:: +DEAL::Face centers: +DEAL::0.151766577 -0.750864056 0.735232275 +DEAL::0.195090322 -0.980785280 0.731694174 +DEAL::1.10396962e-12 -0.887500000 0.750000000 +DEAL::0.341233990 -0.815881065 0.716926449 +DEAL::0.173428449 -0.865824668 -8.38681001e-17 +DEAL::0.173428449 -0.865824668 1.46692645 +DEAL:: +DEAL::Face centers: +DEAL::0.325328493 -0.462828493 0.716311131 +DEAL::0.440449363 -0.647149053 0.705696826 +DEAL::0.258335105 -0.599884130 0.724002653 +DEAL::0.502105188 -0.502105188 0.698005305 +DEAL::0.382888928 -0.554988773 -1.58586887e-15 +DEAL::0.382888928 -0.554988773 1.42200796 +DEAL:: +DEAL::Face centers: +DEAL::0.440449363 -0.647149053 0.705696826 +DEAL::0.555570233 -0.831469612 0.695082521 +DEAL::0.341233990 -0.815881065 0.716926449 +DEAL::0.638772917 -0.638772917 0.683852899 +DEAL::0.498009798 -0.739309332 -2.58707084e-15 +DEAL::0.498009798 -0.739309332 1.40077935 +DEAL:: +DEAL::Face centers: +DEAL::0.108442831 -0.520942831 2.21631113 +DEAL::0.151766577 -0.750864056 2.20569683 +DEAL::1.55226787e-12 -0.662500000 2.25000000 +DEAL::0.258335105 -0.599884130 2.17200796 +DEAL::0.130104704 -0.635903443 1.47400265 +DEAL::0.130104704 -0.635903443 2.94800531 +DEAL:: +DEAL::Face centers: +DEAL::0.151766577 -0.750864056 2.20569683 +DEAL::0.195090322 -0.980785280 2.19508252 +DEAL::1.60940487e-12 -0.887500000 2.25000000 +DEAL::0.341233990 -0.815881065 2.15077935 +DEAL::0.173428449 -0.865824668 1.46692645 +DEAL::0.173428449 -0.865824668 2.93385290 +DEAL:: +DEAL::Face centers: +DEAL::0.325328493 -0.462828493 2.14893339 +DEAL::0.440449363 -0.647149053 2.11709048 +DEAL::0.258335105 -0.599884130 2.17200796 +DEAL::0.502105188 -0.502105188 2.09401592 +DEAL::0.382888928 -0.554988773 1.42200796 +DEAL::0.382888928 -0.554988773 2.84401592 +DEAL:: +DEAL::Face centers: +DEAL::0.440449363 -0.647149053 2.11709048 +DEAL::0.555570233 -0.831469612 2.08524756 +DEAL::0.341233990 -0.815881065 2.15077935 +DEAL::0.638772917 -0.638772917 2.05155870 +DEAL::0.498009798 -0.739309332 1.40077935 +DEAL::0.498009798 -0.739309332 2.80155870 +DEAL:: +DEAL::Face centers: +DEAL::0.462828493 -0.325328493 0.702072540 +DEAL::0.647149053 -0.440449363 0.685633357 +DEAL::0.502105188 -0.502105188 0.698005305 +DEAL::0.599884130 -0.258335105 0.689700592 +DEAL::0.554988773 -0.382888928 0.00000000 +DEAL::0.554988773 -0.382888928 1.38770590 +DEAL:: +DEAL::Face centers: +DEAL::0.647149053 -0.440449363 0.685633357 +DEAL::0.831469612 -0.555570233 0.669194174 +DEAL::0.638772917 -0.638772917 0.683852899 +DEAL::0.815881065 -0.341233990 0.670974632 +DEAL::0.739309332 -0.498009798 2.23518464e-14 +DEAL::0.739309332 -0.498009798 1.35482753 +DEAL:: +DEAL::Face centers: +DEAL::0.520942831 -0.108442831 0.696054604 +DEAL::0.750864056 -0.151766577 0.675041867 +DEAL::0.599884130 -0.258335105 0.689700592 +DEAL::0.662500000 2.19576823e-12 0.681395879 +DEAL::0.635903443 -0.130104704 7.28177805e-15 +DEAL::0.635903443 -0.130104704 1.37109647 +DEAL:: +DEAL::Face centers: +DEAL::0.750864056 -0.151766577 0.675041867 +DEAL::0.980785280 -0.195090322 0.654029131 +DEAL::0.815881065 -0.341233990 0.670974632 +DEAL::0.887500000 1.08765619e-12 0.658096366 +DEAL::0.865824668 -0.173428449 -3.27700010e-15 +DEAL::0.865824668 -0.173428449 1.32907100 +DEAL:: +DEAL::Face centers: +DEAL::0.462828493 -0.325328493 2.10621762 +DEAL::0.647149053 -0.440449363 2.05690007 +DEAL::0.502105188 -0.502105188 2.09401592 +DEAL::0.599884130 -0.258335105 2.06910178 +DEAL::0.554988773 -0.382888928 1.38770590 +DEAL::0.554988773 -0.382888928 2.77541179 +DEAL:: +DEAL::Face centers: +DEAL::0.647149053 -0.440449363 2.05690007 +DEAL::0.831469612 -0.555570233 2.00758252 +DEAL::0.638772917 -0.638772917 2.05155870 +DEAL::0.815881065 -0.341233990 2.01292390 +DEAL::0.739309332 -0.498009798 1.35482753 +DEAL::0.739309332 -0.498009798 2.70965506 +DEAL:: +DEAL::Face centers: +DEAL::0.520942831 -0.108442831 2.08816381 +DEAL::0.750864056 -0.151766577 2.02512560 +DEAL::0.599884130 -0.258335105 2.06910178 +DEAL::0.662500000 1.58504737e-12 2.04418764 +DEAL::0.635903443 -0.130104704 1.37109647 +DEAL::0.635903443 -0.130104704 2.74219294 +DEAL:: +DEAL::Face centers: +DEAL::0.750864056 -0.151766577 2.02512560 +DEAL::0.980785280 -0.195090322 1.96208739 +DEAL::0.815881065 -0.341233990 2.01292390 +DEAL::0.887500000 1.46303299e-12 1.97428910 +DEAL::0.865824668 -0.173428449 1.32907100 +DEAL::0.865824668 -0.173428449 2.65814200 +DEAL:: diff --git a/tests/manifold/transfinite_manifold_09.cc b/tests/manifold/transfinite_manifold_09.cc new file mode 100644 index 0000000000..56c135ba04 --- /dev/null +++ b/tests/manifold/transfinite_manifold_09.cc @@ -0,0 +1,82 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2019 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. +// +// --------------------------------------------------------------------- + + +// This test verifies that the transfinite interpolation works on a distorted +// cylinder with some given coordinates + +#include +#include +#include +#include + +#include "../tests.h" + + +int +main() +{ + initlog(); + deallog << std::setprecision(9); + + const double radius = 1.; + const double length = 3.; + constexpr int dim = 3; + Triangulation tria; + + // position of auxiliary point to achieve an angle of 120 degrees in corner + // of inner cell + std::vector> vertices{ + {1.6666666666666663, 0., -0.69035593728849154}, + {2.4033740890369071, 0., 0.046351485081748842}, + {2., 0., -0.82842712474618985}, + {2.7222718241315023, 0., -0.10615530061468759}, + {1.5548344933395739, 0.44817247098067337, -0.64403353438675115}, + {2.2998293798138509, 0.44396471873216636, 0.073847495332288168}, + {1.9264041086678665, 0.53755670408577649, -0.79794270842148385}, + {2.6272400227990982, 0.52932727817817915, -0.10032762350281543}}; + + std::vector> cell_data(1); + for (unsigned int v = 0; v < 8; ++v) + cell_data[0].vertices[v] = v; + + SubCellData subcell_data; + tria.create_triangulation(vertices, cell_data, subcell_data); + + // set cylindrical manifold on face 3 + tria.set_all_manifold_ids(1); + tria.begin_active()->face(3)->set_all_manifold_ids(2); + + // attach 3 cylindrical manifolds to mesh + tria.set_manifold( + 2, + CylindricalManifold(Point{std::sqrt(0.5), 0., std::sqrt(0.5)}, + Point())); + TransfiniteInterpolationManifold transfinite; + transfinite.initialize(tria); + tria.set_manifold(1, transfinite); + + deallog << "Cell center " << tria.begin_active()->center(true, true) + << std::endl; + + tria.refine_global(); + for (auto &cell : tria.active_cell_iterators()) + { + deallog << "Face centers:" << std::endl; + for (unsigned int f = 0; f < GeometryInfo::faces_per_cell; ++f) + deallog << cell->face(f)->center(true) << std::endl; + deallog << std::endl; + } +} diff --git a/tests/manifold/transfinite_manifold_09.output b/tests/manifold/transfinite_manifold_09.output new file mode 100644 index 0000000000..5b1781ce6f --- /dev/null +++ b/tests/manifold/transfinite_manifold_09.output @@ -0,0 +1,66 @@ + +DEAL::Cell center 2.15645306 0.246102405 -0.387255898 +DEAL::Face centers: +DEAL::1.72686639 0.118021667 -0.716717669 +DEAL::2.09348518 0.117360966 -0.352666356 +DEAL::1.82340345 0.111780133 -0.495775131 +DEAL::1.99694814 0.123602502 -0.573608919 +DEAL::1.93327463 5.82867088e-16 -0.541599103 +DEAL::1.88545778 0.235227227 -0.526165775 +DEAL:: +DEAL::Face centers: +DEAL::2.09348518 0.117360966 -0.352666356 +DEAL::2.46010386 0.116700256 0.0113850583 +DEAL::2.19279309 0.111254164 -0.129774718 +DEAL::2.36079598 0.122807060 -0.211506604 +DEAL::2.29982389 2.44249065e-15 -0.175049842 +DEAL::2.25217134 0.233909456 -0.164637645 +DEAL:: +DEAL::Face centers: +DEAL::1.90318191 0.129978764 -0.792602334 +DEAL::2.26425899 0.129048601 -0.432449218 +DEAL::1.99694814 0.123602502 -0.573608919 +DEAL::2.17049284 0.135424870 -0.651442708 +DEAL::2.09813685 8.57647287e-15 -0.612439147 +DEAL::2.06444662 0.258561147 -0.607754968 +DEAL:: +DEAL::Face centers: +DEAL::2.26425899 0.129048601 -0.432449218 +DEAL::2.62533577 0.128118408 -0.0722958004 +DEAL::2.36079598 0.122807060 -0.211506604 +DEAL::2.52879886 0.134359956 -0.293238489 +DEAL::2.46107721 3.58046925e-15 -0.249498785 +DEAL::2.42373612 0.256711711 -0.250464804 +DEAL:: +DEAL::Face centers: +DEAL::1.67571475 0.353436728 -0.695521133 +DEAL::2.04254855 0.351469274 -0.336541670 +DEAL::1.76852329 0.335340400 -0.474967228 +DEAL::1.94974023 0.369565666 -0.557095797 +DEAL::1.88545778 0.235227227 -0.526165775 +DEAL::1.83121627 0.469215465 -0.504307774 +DEAL:: +DEAL::Face centers: +DEAL::2.04254855 0.351469274 -0.336541670 +DEAL::2.40938146 0.349501562 0.0224386816 +DEAL::2.13998480 0.333762493 -0.113673414 +DEAL::2.31194543 0.367208407 -0.200429796 +DEAL::2.25217134 0.233909456 -0.164637645 +DEAL::2.19819384 0.466608879 -0.147900503 +DEAL:: +DEAL::Face centers: +DEAL::1.86155918 0.388051477 -0.775335130 +DEAL::2.21913756 0.385304928 -0.420984367 +DEAL::1.94974023 0.369565666 -0.557095797 +DEAL::2.13095717 0.403790933 -0.639224365 +DEAL::2.06444662 0.258561147 -0.607754968 +DEAL::2.01148237 0.513405328 -0.583796769 +DEAL:: +DEAL::Face centers: +DEAL::2.21913756 0.385304928 -0.420984367 +DEAL::2.57671328 0.382557607 -0.0666309407 +DEAL::2.31194543 0.367208407 -0.200429796 +DEAL::2.48390607 0.400654321 -0.287186177 +DEAL::2.42373612 0.256711711 -0.250464804 +DEAL::2.36742019 0.509793323 -0.232455984 +DEAL:: diff --git a/tests/manifold/transfinite_manifold_10.cc b/tests/manifold/transfinite_manifold_10.cc new file mode 100644 index 0000000000..ca79261197 --- /dev/null +++ b/tests/manifold/transfinite_manifold_10.cc @@ -0,0 +1,176 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2019 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. +// +// --------------------------------------------------------------------- + + +// This test verifies that the transfinite interpolation works on a torus + +#include + +#include +#include + +#include "../tests.h" + + +class InnerTorusManifold : public ChartManifold<3, 3, 3> +{ +public: + static const unsigned int dim = 3; + static const unsigned int spacedim = 3; + static const unsigned int chartdim = 3; + + InnerTorusManifold() + : ChartManifold(Tensor<1, 3>({0., 0., 2 * numbers::PI})) + {} + + virtual std::unique_ptr> + clone() const override + { + return std_cxx14::make_unique(); + } + + virtual Point + pull_back(const Point &space_point) const override + { + const double phi = std::atan2(space_point[2], space_point[0]); + const double radius = std::sqrt(space_point[0] * space_point[0] + + space_point[2] * space_point[2]); + return Point<3>(radius, space_point[1], phi); + } + + virtual Point + push_forward(const Point &chart_point) const override + { + return Point<3>(chart_point[0] * std::cos(chart_point[2]), + chart_point[1], + chart_point[0] * std::sin(chart_point[2])); + } +}; + + + +int +main() +{ + initlog(); + deallog << std::setprecision(9); + + const unsigned int dim = 3; + Triangulation tria; + + const double R = 2; + const double r = 0.5; + const unsigned int n_cells = 3; + + // the first 8 vertices are in the x-y-plane + Point<3> const p = Point<3>(R, 0.0, 0.0); + double const a = 1. / (1 + std::sqrt(2.0)); + std::vector> vertices(8 * n_cells); + vertices[0] = p + Point<3>(-1, -1, 0) * (r / std::sqrt(2.0)), + vertices[1] = p + Point<3>(+1, -1, 0) * (r / std::sqrt(2.0)), + vertices[2] = p + Point<3>(-1, -1, 0) * (r / std::sqrt(2.0) * a), + vertices[3] = p + Point<3>(+1, -1, 0) * (r / std::sqrt(2.0) * a), + vertices[4] = p + Point<3>(-1, +1, 0) * (r / std::sqrt(2.0) * a), + vertices[5] = p + Point<3>(+1, +1, 0) * (r / std::sqrt(2.0) * a), + vertices[6] = p + Point<3>(-1, +1, 0) * (r / std::sqrt(2.0)), + vertices[7] = p + Point<3>(+1, +1, 0) * (r / std::sqrt(2.0)); + + // create remaining vertices by rotating around positive y-axis + double phi_cell = 2.0 * numbers::PI / n_cells; + for (unsigned int c = 1; c < n_cells; ++c) + { + for (unsigned int v = 0; v < 8; ++v) + { + double const r_2d = vertices[v][0]; + vertices[8 * c + v][0] = r_2d * std::cos(phi_cell * c); + vertices[8 * c + v][1] = vertices[v][1]; + vertices[8 * c + v][2] = r_2d * std::sin(phi_cell * c); + } + } + + // cell connectivity + std::vector> cells(5 * n_cells); + for (unsigned int c = 0; c < n_cells; ++c) + { + for (unsigned int j = 0; j < 2; ++j) + { + unsigned int offset = (8 * (c + j)) % (8 * n_cells); + // cell 0 in x-y-plane + cells[5 * c].vertices[0 + j * 4] = offset + 0; + cells[5 * c].vertices[1 + j * 4] = offset + 1; + cells[5 * c].vertices[2 + j * 4] = offset + 2; + cells[5 * c].vertices[3 + j * 4] = offset + 3; + // cell 1 in x-y-plane + cells[5 * c + 1].vertices[0 + j * 4] = offset + 2; + cells[5 * c + 1].vertices[1 + j * 4] = offset + 3; + cells[5 * c + 1].vertices[2 + j * 4] = offset + 4; + cells[5 * c + 1].vertices[3 + j * 4] = offset + 5; + // cell 2 in x-y-plane + cells[5 * c + 2].vertices[0 + j * 4] = offset + 4; + cells[5 * c + 2].vertices[1 + j * 4] = offset + 5; + cells[5 * c + 2].vertices[2 + j * 4] = offset + 6; + cells[5 * c + 2].vertices[3 + j * 4] = offset + 7; + // cell 3 in x-y-plane + cells[5 * c + 3].vertices[0 + j * 4] = offset + 0; + cells[5 * c + 3].vertices[1 + j * 4] = offset + 2; + cells[5 * c + 3].vertices[2 + j * 4] = offset + 6; + cells[5 * c + 3].vertices[3 + j * 4] = offset + 4; + // cell 4 in x-y-plane + cells[5 * c + 4].vertices[0 + j * 4] = offset + 3; + cells[5 * c + 4].vertices[1 + j * 4] = offset + 1; + cells[5 * c + 4].vertices[2 + j * 4] = offset + 5; + cells[5 * c + 4].vertices[3 + j * 4] = offset + 7; + } + + cells[5 * c].material_id = 0; + cells[5 * c + 1].material_id = 0; + cells[5 * c + 2].material_id = 0; + cells[5 * c + 3].material_id = 0; + cells[5 * c + 4].material_id = 0; + } + + tria.create_triangulation(vertices, cells, SubCellData()); + + tria.set_all_manifold_ids(0); + + for (auto &cell : tria.cell_iterators()) + { + bool cell_at_boundary = false; + for (unsigned int f = 0; f < GeometryInfo::faces_per_cell; ++f) + if (cell->at_boundary(f)) + cell_at_boundary = true; + if (cell_at_boundary == false) + cell->set_all_manifold_ids(2); + } + tria.set_all_manifold_ids_on_boundary(1); + tria.set_manifold(1, TorusManifold(2, 0.5)); + tria.set_manifold(2, InnerTorusManifold()); + TransfiniteInterpolationManifold transfinite; + transfinite.initialize(tria); + tria.set_manifold(0, transfinite); + + for (unsigned int cycle = 0; cycle < 2; ++cycle) + { + tria.refine_global(1); + deallog << "Cycle " << cycle << std::endl; + deallog << "Number of active cells: " << tria.n_active_cells() + << std::endl; + deallog << "Vertices: " << std::endl; + for (auto &v : tria.get_vertices()) + deallog << v << std::endl; + deallog << std::endl; + } + return 0; +} diff --git a/tests/manifold/transfinite_manifold_10.output b/tests/manifold/transfinite_manifold_10.output new file mode 100644 index 0000000000..fe9af3090d --- /dev/null +++ b/tests/manifold/transfinite_manifold_10.output @@ -0,0 +1,1227 @@ + +DEAL::Cycle 0 +DEAL::Number of active cells: 120 +DEAL::Vertices: +DEAL::1.64644661 -0.353553391 0.00000000 +DEAL::2.35355339 -0.353553391 0.00000000 +DEAL::1.85355339 -0.146446609 0.00000000 +DEAL::2.14644661 -0.146446609 0.00000000 +DEAL::1.85355339 0.146446609 0.00000000 +DEAL::2.14644661 0.146446609 0.00000000 +DEAL::1.64644661 0.353553391 0.00000000 +DEAL::2.35355339 0.353553391 0.00000000 +DEAL::-0.823223305 -0.353553391 1.42586459 +DEAL::-1.17677670 -0.353553391 2.03823703 +DEAL::-0.926776695 -0.146446609 1.60522432 +DEAL::-1.07322330 -0.146446609 1.85887729 +DEAL::-0.926776695 0.146446609 1.60522432 +DEAL::-1.07322330 0.146446609 1.85887729 +DEAL::-0.823223305 0.353553391 1.42586459 +DEAL::-1.17677670 0.353553391 2.03823703 +DEAL::-0.823223305 -0.353553391 -1.42586459 +DEAL::-1.17677670 -0.353553391 -2.03823703 +DEAL::-0.926776695 -0.146446609 -1.60522432 +DEAL::-1.07322330 -0.146446609 -1.85887729 +DEAL::-0.926776695 0.146446609 -1.60522432 +DEAL::-1.07322330 0.146446609 -1.85887729 +DEAL::-0.823223305 0.353553391 -1.42586459 +DEAL::-1.17677670 0.353553391 -2.03823703 +DEAL::2.00000000 -0.500000000 0.00000000 +DEAL::1.75000000 -0.250000000 -2.52976221e-14 +DEAL::1.50000000 6.12323400e-17 0.00000000 +DEAL::0.823223305 -0.353553391 1.42586459 +DEAL::2.25000000 -0.250000000 4.30090529e-15 +DEAL::2.50000000 0.00000000 0.00000000 +DEAL::1.17677670 -0.353553391 2.03823703 +DEAL::2.00000000 -0.146446609 0.00000000 +DEAL::1.85355339 0.00000000 0.00000000 +DEAL::0.926776695 -0.146446609 1.60522432 +DEAL::2.14644661 0.00000000 0.00000000 +DEAL::1.07322330 -0.146446609 1.85887729 +DEAL::2.00000000 0.146446609 0.00000000 +DEAL::1.75000000 0.250000000 -3.53725085e-15 +DEAL::0.926776695 0.146446609 1.60522432 +DEAL::2.25000000 0.250000000 4.30096961e-15 +DEAL::1.07322330 0.146446609 1.85887729 +DEAL::2.00000000 0.500000000 0.00000000 +DEAL::0.823223305 0.353553391 1.42586459 +DEAL::1.17677670 0.353553391 2.03823703 +DEAL::-1.00000000 -0.500000000 1.73205081 +DEAL::-0.875000000 -0.250000000 1.51554446 +DEAL::-0.750000000 6.12323400e-17 1.29903811 +DEAL::-1.64644661 -0.353553391 1.66396990e-15 +DEAL::-1.12500000 -0.250000000 1.94855716 +DEAL::-1.25000000 0.00000000 2.16506351 +DEAL::-2.35355339 -0.353553391 2.37860249e-15 +DEAL::-1.00000000 -0.146446609 1.73205081 +DEAL::-0.926776695 0.00000000 1.60522432 +DEAL::-1.85355339 -0.146446609 1.87328094e-15 +DEAL::-1.07322330 0.00000000 1.85887729 +DEAL::-2.14644661 -0.146446609 2.16929145e-15 +DEAL::-1.00000000 0.146446609 1.73205081 +DEAL::-0.875000000 0.250000000 1.51554446 +DEAL::-1.85355339 0.146446609 1.87328094e-15 +DEAL::-1.12500000 0.250000000 1.94855716 +DEAL::-2.14644661 0.146446609 2.16929145e-15 +DEAL::-1.00000000 0.500000000 1.73205081 +DEAL::-1.64644661 0.353553391 1.66396990e-15 +DEAL::-2.35355339 0.353553391 2.37860249e-15 +DEAL::0.823223305 -0.353553391 -1.42586459 +DEAL::-1.00000000 -0.500000000 -1.73205081 +DEAL::-0.875000000 -0.250000000 -1.51554446 +DEAL::-0.750000000 6.12323400e-17 -1.29903811 +DEAL::1.17677670 -0.353553391 -2.03823703 +DEAL::-1.12500000 -0.250000000 -1.94855716 +DEAL::-1.25000000 0.00000000 -2.16506351 +DEAL::0.926776695 -0.146446609 -1.60522432 +DEAL::-1.00000000 -0.146446609 -1.73205081 +DEAL::-0.926776695 0.00000000 -1.60522432 +DEAL::1.07322330 -0.146446609 -1.85887729 +DEAL::-1.07322330 0.00000000 -1.85887729 +DEAL::0.926776695 0.146446609 -1.60522432 +DEAL::-1.00000000 0.146446609 -1.73205081 +DEAL::-0.875000000 0.250000000 -1.51554446 +DEAL::1.07322330 0.146446609 -1.85887729 +DEAL::-1.12500000 0.250000000 -1.94855716 +DEAL::0.823223305 0.353553391 -1.42586459 +DEAL::-1.00000000 0.500000000 -1.73205081 +DEAL::1.17677670 0.353553391 -2.03823703 +DEAL::1.00000000 -0.500000000 1.73205081 +DEAL::2.00000000 -0.323223305 1.44931457e-14 +DEAL::1.67677670 -5.97921627e-13 -4.50889981e-14 +DEAL::0.875000000 -0.250000000 1.51554446 +DEAL::0.750000000 2.83276945e-16 1.29903811 +DEAL::1.12500000 -0.250000000 1.94855716 +DEAL::1.25000000 -1.22464680e-16 2.16506351 +DEAL::1.00000000 -0.146446609 1.73205081 +DEAL::2.00000000 0.00000000 0.00000000 +DEAL::0.926776695 0.00000000 1.60522432 +DEAL::2.32322330 -7.22743012e-14 -2.63246240e-15 +DEAL::1.07322330 0.00000000 1.85887729 +DEAL::1.00000000 0.146446609 1.73205081 +DEAL::2.00000000 0.323223305 -2.26621556e-15 +DEAL::0.875000000 0.250000000 1.51554446 +DEAL::1.12500000 0.250000000 1.94855716 +DEAL::1.00000000 0.500000000 1.73205081 +DEAL::-2.00000000 -0.500000000 2.02128620e-15 +DEAL::-1.00000000 -0.323223305 1.73205081 +DEAL::-0.838388348 2.26821425e-13 1.45213121 +DEAL::-1.75000000 -0.250000000 2.14313190e-16 +DEAL::-1.50000000 6.12323400e-17 1.51596465e-15 +DEAL::-2.25000000 -0.250000000 1.22659542e-14 +DEAL::-2.50000000 -1.22464680e-16 2.52660775e-15 +DEAL::-2.00000000 -0.146446609 2.02128620e-15 +DEAL::-1.00000000 0.00000000 1.73205081 +DEAL::-1.85355339 0.00000000 1.87328094e-15 +DEAL::-1.16161165 -7.32041130e-14 2.01197040 +DEAL::-2.14644661 0.00000000 2.16929145e-15 +DEAL::-2.00000000 0.146446609 2.02128620e-15 +DEAL::-1.00000000 0.323223305 1.73205081 +DEAL::-1.75000000 0.250000000 -1.33999904e-15 +DEAL::-2.25000000 0.250000000 -6.73185741e-13 +DEAL::-2.00000000 0.500000000 2.02128620e-15 +DEAL::0.875000000 -0.250000000 -1.51554446 +DEAL::0.750000000 6.12323400e-17 -1.29903811 +DEAL::1.00000000 -0.500000000 -1.73205081 +DEAL::-1.00000000 -0.323223305 -1.73205081 +DEAL::-0.838388348 1.87831780e-13 -1.45213121 +DEAL::1.12500000 -0.250000000 -1.94855716 +DEAL::1.25000000 -1.22464680e-16 -2.16506351 +DEAL::0.926776695 0.00000000 -1.60522432 +DEAL::1.00000000 -0.146446609 -1.73205081 +DEAL::-1.00000000 0.00000000 -1.73205081 +DEAL::1.07322330 0.00000000 -1.85887729 +DEAL::-1.16161165 -6.37533395e-14 -2.01197040 +DEAL::0.875000000 0.250000000 -1.51554446 +DEAL::1.00000000 0.146446609 -1.73205081 +DEAL::-1.00000000 0.323223305 -1.73205081 +DEAL::1.12500000 0.250000000 -1.94855716 +DEAL::1.00000000 0.500000000 -1.73205081 +DEAL::1.00000000 -0.323223305 1.73205081 +DEAL::1.00000000 0.00000000 1.73205081 +DEAL::1.00000000 0.323223305 1.73205081 +DEAL::0.838388348 -8.19801709e-14 1.45213121 +DEAL::1.16161165 -2.32163213e-14 2.01197040 +DEAL::-2.00000000 -0.323223305 -9.03492694e-14 +DEAL::-2.00000000 0.00000000 7.35035672e-15 +DEAL::-2.00000000 0.323223305 1.31695335e-13 +DEAL::-1.67677670 -7.93711468e-14 -1.28393095e-15 +DEAL::-2.32322330 -2.32440769e-14 2.84512798e-16 +DEAL::1.00000000 -0.323223305 -1.73205081 +DEAL::1.00000000 0.00000000 -1.73205081 +DEAL::1.00000000 0.323223305 -1.73205081 +DEAL::0.838388348 -7.79764291e-14 -1.45213121 +DEAL::1.16161165 -2.32440769e-14 -2.01197040 +DEAL:: +DEAL::Cycle 1 +DEAL::Number of active cells: 960 +DEAL::Vertices: +DEAL::1.64644661 -0.353553391 0.00000000 +DEAL::2.35355339 -0.353553391 0.00000000 +DEAL::1.85355339 -0.146446609 0.00000000 +DEAL::2.14644661 -0.146446609 0.00000000 +DEAL::1.85355339 0.146446609 0.00000000 +DEAL::2.14644661 0.146446609 0.00000000 +DEAL::1.64644661 0.353553391 0.00000000 +DEAL::2.35355339 0.353553391 0.00000000 +DEAL::-0.823223305 -0.353553391 1.42586459 +DEAL::-1.17677670 -0.353553391 2.03823703 +DEAL::-0.926776695 -0.146446609 1.60522432 +DEAL::-1.07322330 -0.146446609 1.85887729 +DEAL::-0.926776695 0.146446609 1.60522432 +DEAL::-1.07322330 0.146446609 1.85887729 +DEAL::-0.823223305 0.353553391 1.42586459 +DEAL::-1.17677670 0.353553391 2.03823703 +DEAL::-0.823223305 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