--- /dev/null
+// ---------------------------------------------------------------------
+//
+// 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// This test verifies that we can use transfinite interpolation on 2D cells
+// that have large aspect ratios: if the initial guess of a chart point is not
+// accurate enough then we will fail to calculate the weighted average in
+// chart coordinates. This test is based on a minimum working example provided
+// by Juan Carlos Araujo Cabarcas which did not work with the changes made to
+// transfinite interpolation in late 2017 but worked with an earlier version.
+
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/numerics/data_out.h>
+
+#include <fstream>
+#include <sstream>
+
+#include "../tests.h"
+
+//---------------------------- GRID DEFINITION ---------------------------------
+
+struct Geom_parameters
+{
+ unsigned int n_balls;
+
+ std::vector<Point<2>> ball_centers;
+ std::vector<double> radius;
+};
+
+void concentric_disks(Triangulation<2> &tria,
+ const double s,
+ const std::vector<double> &x,
+ Geom_parameters &gp)
+{
+ double r = x[0], d = 0.5 * x[0],
+ q = 1.0 / sqrt(2.0); // q: corner points factor
+
+ const unsigned int nlay = x.size() - 1, vlayer = 8, lcells = 8,
+ n_vert = (2 + nlay) * vlayer + 1,
+ n_cell = 3 + (1 + nlay) * lcells + 1; // 19
+
+ int fc = 4; // fv = 1, f: fixed, displacement of index on the vertexes and
+ // cells ... inner objects
+
+ // geometric information-----------------------
+ gp.n_balls = x.size(); // the resonator and all other centered at the origin
+ gp.ball_centers.resize(gp.n_balls);
+ gp.radius.resize(gp.n_balls);
+ gp.radius[0] = x[0];
+ gp.ball_centers[0] = Point<2>(s, 0.0);
+
+ for (unsigned int k = 1; k < x.size(); k++)
+ {
+ gp.radius[k] = x[k];
+ gp.ball_centers[k] = Point<2>(0.0, 0.0);
+ }
+
+ std::vector<Point<2>> vertices(n_vert);
+
+ vertices[0] = Point<2>(0.0 + s, 0.0);
+
+ // inner 4 squares
+ vertices[1] = Point<2>(d + s, 0.0);
+ vertices[2] = Point<2>(.5 * d + s, .5 * d);
+ vertices[3] = Point<2>(0.0 + s, d);
+ vertices[4] = Point<2>(-.5 * d + s, .5 * d);
+ vertices[5] = Point<2>(-d + s, 0.0);
+ vertices[6] = Point<2>(-.5 * d + s, -.5 * d);
+ vertices[7] = Point<2>(0.0 + s, -d);
+ vertices[8] = Point<2>(.5 * d + s, -.5 * d);
+
+ // touching circle
+ for (unsigned int k = 0; k < x.size(); k++)
+ {
+ double z = (k == 0) ? s : 0.0;
+ r = x[k];
+ vertices[8 + k * vlayer + 1] = Point<2>(r + z, 0.0);
+ vertices[8 + k * vlayer + 2] = Point<2>(r * q + z, r * q);
+ vertices[8 + k * vlayer + 3] = Point<2>(0.0 + z, r);
+ vertices[8 + k * vlayer + 4] = Point<2>(-r * q + z, r * q);
+ vertices[8 + k * vlayer + 5] = Point<2>(-r + z, 0.0);
+ vertices[8 + k * vlayer + 6] = Point<2>(-r * q + z, -r * q);
+ vertices[8 + k * vlayer + 7] = Point<2>(0.0 + z, -r);
+ vertices[8 + k * vlayer + 8] = Point<2>(r * q + z, -r * q);
+ }
+
+ std::vector<std::vector<int>> cell_v(n_cell, std::vector<int>(4));
+
+ cell_v[0][0] = 0; // cell, i = 0
+ cell_v[0][1] = 8;
+ cell_v[0][2] = 2;
+ cell_v[0][3] = 1;
+
+ cell_v[1][0] = 0; // cell, i = 1
+ cell_v[1][1] = 2;
+ cell_v[1][2] = 4;
+ cell_v[1][3] = 3;
+
+ cell_v[2][0] = 0; // cell, i = 2
+ cell_v[2][1] = 4;
+ cell_v[2][2] = 6;
+ cell_v[2][3] = 5;
+
+ cell_v[3][0] = 0; // cell, i = 3
+ cell_v[3][1] = 6;
+ cell_v[3][2] = 8;
+ cell_v[3][3] = 7;
+
+ cell_v[4][0] = 8; // cell, i = 4
+ cell_v[4][1] = 16;
+ cell_v[4][2] = 1;
+ cell_v[4][3] = 9;
+
+ cell_v[5][0] = 2; // cell, i = 5
+ cell_v[5][1] = 1;
+ cell_v[5][2] = 10;
+ cell_v[5][3] = 9;
+
+ cell_v[6][0] = 2; // cell, i = 6
+ cell_v[6][1] = 10;
+ cell_v[6][2] = 3;
+ cell_v[6][3] = 11;
+
+ cell_v[7][0] = 4; // cell, i = 7
+ cell_v[7][1] = 3;
+ cell_v[7][2] = 12;
+ cell_v[7][3] = 11;
+
+ cell_v[8][0] = 4; // cell, i = 8
+ cell_v[8][1] = 12;
+ cell_v[8][2] = 5;
+ cell_v[8][3] = 13;
+
+ cell_v[9][0] = 6; // cell, i = 9
+ cell_v[9][1] = 5;
+ cell_v[9][2] = 14;
+ cell_v[9][3] = 13;
+
+ cell_v[10][0] = 6; // cell, i = 10
+ cell_v[10][1] = 14;
+ cell_v[10][2] = 7;
+ cell_v[10][3] = 15;
+
+ cell_v[11][0] = 8; // cell, i = 11
+ cell_v[11][1] = 7;
+ cell_v[11][2] = 16;
+ cell_v[11][3] = 15;
+
+ // layer cells
+ for (unsigned int k = 1; k < x.size(); k++)
+ {
+ const unsigned int m = k + 1;
+
+ // cell 12
+ cell_v[fc + k * lcells + 0][0] = 7 + 8 * k + 1; // 16; // cell, i = 12
+ cell_v[fc + k * lcells + 0][1] = 7 + 8 * m + 1; // 24;
+ cell_v[fc + k * lcells + 0][2] = 0 + 8 * k + 1; // 9;
+ cell_v[fc + k * lcells + 0][3] = 0 + 8 * m + 1; // 17;
+
+ // cell 13
+ cell_v[fc + k * lcells + 1][0] = 1 + 8 * k + 1; // 10; // cell, i = 13
+ cell_v[fc + k * lcells + 1][1] = 0 + 8 * k + 1; // 9;
+ cell_v[fc + k * lcells + 1][2] = 1 + 8 * m + 1; // 18;
+ cell_v[fc + k * lcells + 1][3] = 0 + 8 * m + 1; // 17;
+
+ // cell 14
+ cell_v[fc + k * lcells + 2][0] = 1 + 8 * k + 1; // 10; // cell, i = 14
+ cell_v[fc + k * lcells + 2][1] = 1 + 8 * m + 1; // 18;
+ cell_v[fc + k * lcells + 2][2] = 2 + 8 * k + 1; // 11;
+ cell_v[fc + k * lcells + 2][3] = 2 + 8 * m + 1; // 19;
+
+ // cell 15
+ cell_v[fc + k * lcells + 3][0] = 3 + 8 * k + 1; // 12; // cell, i = 15
+ cell_v[fc + k * lcells + 3][1] = 2 + 8 * k + 1; // 11;
+ cell_v[fc + k * lcells + 3][2] = 3 + 8 * m + 1; // 20;
+ cell_v[fc + k * lcells + 3][3] = 2 + 8 * m + 1; // 19;
+
+ // cell 16
+ cell_v[fc + k * lcells + 4][0] = 3 + 8 * k + 1; // 12; // cell, i = 16
+ cell_v[fc + k * lcells + 4][1] = 3 + 8 * m + 1; // 20;
+ cell_v[fc + k * lcells + 4][2] = 4 + 8 * k + 1; // 13;
+ cell_v[fc + k * lcells + 4][3] = 4 + 8 * m + 1; // 21;
+
+ // cell 17
+ cell_v[fc + k * lcells + 5][0] = 5 + 8 * k + 1; // 14; // cell, i = 17
+ cell_v[fc + k * lcells + 5][1] = 4 + 8 * k + 1; // 13;
+ cell_v[fc + k * lcells + 5][2] = 5 + 8 * m + 1; // 22;
+ cell_v[fc + k * lcells + 5][3] = 4 + 8 * m + 1; // 21;
+
+ // cell 18
+ cell_v[fc + k * lcells + 6][0] = 5 + 8 * k + 1; // 14; // cell, i = 18
+ cell_v[fc + k * lcells + 6][1] = 5 + 8 * m + 1; // 22;
+ cell_v[fc + k * lcells + 6][2] = 6 + 8 * k + 1; // 15;
+ cell_v[fc + k * lcells + 6][3] = 6 + 8 * m + 1; // 23;
+
+ // cell 19
+ cell_v[fc + k * lcells + 7][0] = 7 + 8 * k + 1; // 16; // cell, i =
+ cell_v[fc + k * lcells + 7][1] = 6 + 8 * k + 1; // 15;
+ cell_v[fc + k * lcells + 7][2] = 7 + 8 * m + 1; // 24;
+ cell_v[fc + k * lcells + 7][3] = 6 + 8 * m + 1; // 23;
+ }
+
+ std::vector<CellData<2>> cells(n_cell, CellData<2>());
+
+ unsigned int cell_idx = 0;
+ for (unsigned int i = 0; i < n_cell; ++i)
+ {
+ for (unsigned int j = 0; j < 4; ++j)
+ {
+ cells[i].vertices[j] = cell_v[i][j];
+ }
+ cell_idx++;
+ }
+
+ tria.create_triangulation(std::vector<Point<2>>(&vertices[0], &vertices[n_vert]),
+ cells,
+ SubCellData()); // no boundary information
+
+ double eps = 1e-5 * x[0];
+ unsigned int label = 100;
+
+ for (Triangulation<2>::active_cell_iterator cell = tria.begin_active();
+ cell != tria.end();
+ ++cell)
+ {
+ cell->set_all_manifold_ids(1); // not faces ... for Transfinite interpolation
+ for (unsigned int k = 0; k < gp.n_balls; ++k)
+ {
+ for (unsigned int f = 0; f < GeometryInfo<2>::faces_per_cell; ++f)
+ {
+ const Point<2>
+ p0 = cell->face(f)->vertex(0),
+ p1 = cell->face(f)->vertex(1);
+ const double d0 = p0.distance(gp.ball_centers[k]),
+ d1 = p1.distance(gp.ball_centers[k]);
+
+ if ((std::abs(d0 - gp.radius[k]) < eps) &&
+ (std::abs(d1 - gp.radius[k]) < eps))
+ {
+ cell->face(f)->set_all_manifold_ids(label + k);
+ }
+ }
+ } // face
+ } // cell
+
+ // end-colorizing
+ // --------------------------------------------------------------------------------
+}
+
+void concentric_disks(Triangulation<2> &tria,
+ std::vector<double> x,
+ Geom_parameters &gp)
+{
+ concentric_disks(tria, 0.0, x, gp);
+}
+
+//--------------------- MAIN CLASS ---------------------------------------------
+
+template <int dim>
+class Mygrid
+{
+public:
+ Mygrid(unsigned int r);
+ void run();
+
+private:
+ void make_grid();
+
+ Geom_parameters gp;
+ std::vector<PolarManifold<dim>> balls;
+ TransfiniteInterpolationManifold<dim> inner_manifold;
+ Triangulation<dim> triangulation;
+ unsigned int refinement;
+};
+
+template <int dim>
+Mygrid<dim>::Mygrid(unsigned int r)
+ : refinement(r)
+{}
+
+template <int dim>
+void Mygrid<dim>::make_grid()
+{
+ const double s = 0.1;
+ std::vector<double> x {1.0, 1.5, 2.0, 2.5, 3.0};
+ concentric_disks(triangulation, s, x, gp);
+ for (unsigned int i = 0; i < gp.n_balls; i++)
+ {
+ balls.emplace_back(gp.ball_centers[i]);
+ }
+
+ // assigning manifolds, with layers 100, 101, 102, 103
+ for (unsigned int i = 0; i < gp.n_balls; i++)
+ {
+ triangulation.set_manifold(100 + i, balls[i]);
+ }
+
+ const unsigned int not_curved = 1;
+ inner_manifold.initialize(triangulation);
+ triangulation.set_manifold(not_curved, inner_manifold);
+
+ GridOut grid_out;
+ grid_out.write_vtk(triangulation, deallog.get_file_stream());
+ triangulation.refine_global(refinement);
+ grid_out.write_vtk(triangulation, deallog.get_file_stream());
+}
+
+template <int dim>
+void Mygrid<dim>::run()
+{
+ make_grid();
+}
+
+int main(int argc, char **argv)
+{
+ initlog();
+
+ Mygrid<2> problem_2d(1);
+ problem_2d.run();
+}
--- /dev/null
+
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