--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 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.
+//
+// ---------------------------------------------------------------------
+
+#ifndef dealii__tensor_product_manifold_h
+#define dealii__tensor_product_manifold_h
+
+#include <deal.II/base/config.h>
+#include <deal.II/base/subscriptor.h>
+#include <deal.II/base/point.h>
+#include <deal.II/grid/manifold.h>
+
+DEAL_II_NAMESPACE_OPEN
+
+
+
+/**
+ * @brief Tensor product manifold of two ChartManifolds.
+ *
+ * This manifold will combine the ChartManifolds @p A and @p B given in the
+ * constructor to form a new ChartManifold by building the tensor product
+ * $A\cross B$. The first @p spacedim_A
+ * dimensions in the real space and the first @p chartdim_A dimensions
+ * of the chart will be given by manifold @p A, while the remaining
+ * coordinates are given by @p B. The manifold is to be used by a
+ * <tt>Triangulation@<dim, space_dim_A+space_dim_B@></tt>.
+ *
+ * An example usage would be the combination of a SphericalManifold with
+ * space dimension 2 and a FlatManifold with space dimension 1 to form
+ * a cylindrical manifold.
+ *
+ * pull_back(), push_forward(), and push_forward_gradient() are implemented
+ * by splitting the input argument into inputs for @p A and @p B according
+ * to the given dimensions and applying the corresponding operations before
+ * concatenating the result.
+ *
+ * @note The dimension arguments @p dim_A and @p dim_B are not used.
+ *
+ * @tparam dim Dimension of cells (needs to match first template argument of
+ * the Triangulation to be attached to.
+ * @tparam dim_A Dimension of ChartManifold A.
+ * @tparam spacedim_A Spacial dimension of ChartManifold A.
+ * @tparam chartdim_A Chart dimension of ChartManifold A.
+ * @tparam dim_B Dimension of ChartManifold B.
+ * @tparam spacedim_B Spacial dimension of ChartManifold B.
+ * @tparam chartdim_B Chart dimension of ChartManifold B.
+ *
+ * @author Luca Heltai, Timo Heister, 2016
+ */
+template <int dim,
+ int dim_A, int spacedim_A, int chartdim_A,
+ int dim_B, int spacedim_B, int chartdim_B>
+class TensorProductManifold :
+ public ChartManifold<dim,spacedim_A+spacedim_B,chartdim_A+chartdim_B>
+{
+public:
+ /**
+ * The chart dimension is the sum of the chart dimensions of the manifolds
+ * @p A and @p B.
+ */
+ static const unsigned int chartdim = chartdim_A+chartdim_B;
+ /**
+ * The space dimension is the sum of the space dimensions of the manifolds
+ * @p A and @p B.
+ */
+ static const unsigned int spacedim = spacedim_A+spacedim_B;
+
+ /**
+ * Constructor.
+ */
+ TensorProductManifold (
+ const ChartManifold<dim_A, spacedim_A, chartdim_A> &manifold_A,
+ const ChartManifold<dim_B, spacedim_B, chartdim_B> &manifold_B);
+
+ /**
+ * Pull back operation.
+ */
+ virtual
+ Point<chartdim>
+ pull_back(const Point<spacedim> &space_point) const;
+
+ /**
+ * Push forward operation.
+ */
+ virtual
+ Point<spacedim>
+ push_forward(const Point<chartdim> &chart_point) const;
+
+ /**
+ * Gradient.
+ */
+ virtual
+ DerivativeForm<1,chartdim,spacedim>
+ push_forward_gradient(const Point<chartdim> &chart_point) const;
+
+private:
+ SmartPointer<const ChartManifold<dim_A, spacedim_A, chartdim_A>,
+ TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B> > manifold_A;
+
+ SmartPointer<const ChartManifold<dim_B, spacedim_B, chartdim_B>,
+ TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B> > manifold_B;
+};
+
+
+
+/*------------------Template Implementations------------------------*/
+
+
+
+namespace internal
+{
+ namespace TensorProductManifold
+ {
+ template <int dim1, int dim2>
+ Tensor<1,dim1+dim2> concat(const Tensor<1,dim1> &p1, const Tensor<1,dim2> &p2)
+ {
+ Tensor<1,dim1+dim2> r;
+ for (unsigned int d=0; d<dim1; ++d)
+ r[d] = p1[d];
+ for (unsigned int d=0; d<dim2; ++d)
+ r[dim1+d] = p2[d];
+ return r;
+ }
+
+ template <int dim1, int dim2>
+ Point<dim1+dim2> concat(const Point<dim1> &p1, const Point<dim2> &p2)
+ {
+ Point<dim1+dim2> r;
+ for (unsigned int d=0; d<dim1; ++d)
+ r[d] = p1[d];
+ for (unsigned int d=0; d<dim2; ++d)
+ r[dim1+d] = p2[d];
+ return r;
+ }
+
+ template <int dim1, int dim2>
+ void split_point(const Point<dim1+dim2> &source, Point<dim1> &p1, Point<dim2> &p2)
+ {
+ for (unsigned int d=0; d<dim1; ++d)
+ p1[d] = source[d];
+ for (unsigned int d=0; d<dim2; ++d)
+ p2[d] = source[dim1+d];
+ }
+
+ }
+}
+
+template <int dim,
+ int dim_A, int spacedim_A, int chartdim_A,
+ int dim_B, int spacedim_B, int chartdim_B>
+TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+::TensorProductManifold(
+ const ChartManifold<dim_A, spacedim_A, chartdim_A> &manifold_A,
+ const ChartManifold<dim_B, spacedim_B, chartdim_B> &manifold_B)
+ : ChartManifold<dim,spacedim_A+spacedim_B,chartdim_A+chartdim_B> (
+ internal::TensorProductManifold::concat(
+ manifold_A.get_periodicity(),
+ manifold_B.get_periodicity())),
+ manifold_A (&manifold_A),
+ manifold_B (&manifold_B)
+{}
+
+template <int dim,
+ int dim_A, int spacedim_A, int chartdim_A,
+ int dim_B, int spacedim_B, int chartdim_B>
+Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim>
+TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+::pull_back(const Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::spacedim> &space_point) const
+{
+ Point<spacedim_A> space_point_A;
+ Point<spacedim_B> space_point_B;
+ internal::TensorProductManifold::split_point(space_point, space_point_A, space_point_B);
+
+ Point<chartdim_A> result_A = manifold_A->pull_back(space_point_A);
+ Point<chartdim_B> result_B = manifold_B->pull_back(space_point_B);
+
+ return internal::TensorProductManifold::concat(result_A, result_B);
+}
+
+template <int dim,
+ int dim_A, int spacedim_A, int chartdim_A,
+ int dim_B, int spacedim_B, int chartdim_B>
+Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::spacedim>
+TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+::push_forward(const Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim> &chart_point) const
+{
+ Point<chartdim_A> chart_point_A;
+ Point<chartdim_B> chart_point_B;
+ internal::TensorProductManifold::split_point(chart_point, chart_point_A, chart_point_B);
+
+ Point<spacedim_A> result_A = manifold_A->push_forward(chart_point_A);
+ Point<spacedim_B> result_B = manifold_B->push_forward(chart_point_B);
+
+ return internal::TensorProductManifold::concat(result_A, result_B);
+}
+
+template <int dim,
+ int dim_A, int spacedim_A, int chartdim_A,
+ int dim_B, int spacedim_B, int chartdim_B>
+DerivativeForm<1,
+ TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim,
+ TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::spacedim>
+
+ TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>
+ ::push_forward_gradient(const Point<TensorProductManifold<dim, dim_A, spacedim_A, chartdim_A, dim_B, spacedim_B, chartdim_B>::chartdim> &chart_point) const
+{
+ Point<chartdim_A> chart_point_A;
+ Point<chartdim_B> chart_point_B;
+ internal::TensorProductManifold::split_point(chart_point, chart_point_A, chart_point_B);
+
+ DerivativeForm<1,chartdim_A,spacedim_A> result_A
+ = manifold_A->push_forward_gradient(chart_point_A);
+ DerivativeForm<1,chartdim_B,spacedim_B> result_B
+ = manifold_B->push_forward_gradient(chart_point_B);
+
+
+ DerivativeForm<1,chartdim,spacedim> result;
+ for (unsigned int i = 0; i<chartdim_A; ++i)
+ for (unsigned int j = 0; j<spacedim_A; ++j)
+ result[j][i] = result_A[j][i];
+ for (unsigned int i = 0; i<chartdim_B; ++i)
+ for (unsigned int j = 0; j<spacedim_B; ++j)
+ result[j+spacedim_A][i+chartdim_A] = result_B[j][i];
+
+ return result;
+}
+
+
+
+
+DEAL_II_NAMESPACE_CLOSE
+
+#endif
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Test TensorProductManifold
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+#include <deal.II/grid/tensor_product_manifold.h>
+#include <deal.II/grid/manifold_lib.h>
+
+
+void test1()
+{
+ const int dim=2, spacedim=2+1;
+
+ FunctionManifold<1,2,1> F("x;x^2", "x");
+ FunctionManifold<1,1,1> G("1.0+2*x", "0.5*(x-1.0)");
+
+ TensorProductManifold<1, 1,2,1, 1,1,1> manifold(F, G);
+
+ // Chart points.
+ Point<2> cp[2];
+ cp[1][0] = 1.0;
+ cp[1][1] = 0.5;
+
+ // Spacedim points
+ std::vector<Point<spacedim> > sp(2);
+
+ // Weights
+ std::vector<double> w(2);
+
+ sp[0] = manifold.push_forward(cp[0]);
+ sp[1] = manifold.push_forward(cp[1]);
+
+ for (unsigned int d=0; d<2; ++d)
+ if (cp[d].distance(manifold.pull_back(sp[d])) > 1e-10)
+ deallog << "Error! "
+ << cp[d] << "->" << sp[d] << "->" << manifold.pull_back(sp[d])
+ << std::endl;
+
+ unsigned int n_intermediates = 8;
+
+ deallog << "P0: " << sp[0]
+ << ", P1: " << sp[1] << std::endl;
+
+ for (unsigned int i=0; i<n_intermediates+1; ++i)
+ {
+ w[0] = 1.0-(double)i/((double)n_intermediates);
+ w[1] = 1.0 - w[0];
+
+ Point<spacedim> ip = manifold.get_new_point(Quadrature<spacedim>(sp, w));
+ Tensor<1,spacedim> t1 = manifold.get_tangent_vector(ip, sp[0]);
+ Tensor<1,spacedim> t2 = manifold.get_tangent_vector(ip, sp[1]);
+
+ deallog << "P: " << ip
+ << ", T(P, P0): " << t1
+ << ", T(P, P1): " << t2 << std::endl;
+
+ }
+}
+
+
+
+int main ()
+{
+ initlog();
+
+ test1();
+
+
+ return 0;
+}
+
--- /dev/null
+
+DEAL::P0: 0.00000 0.00000 1.00000, P1: 1.00000 1.00000 2.00000
+DEAL::P: 0.00000 0.00000 1.00000, T(P, P0): 0.00000 0.00000 0.00000, T(P, P1): 1.00000 0.00000 1.00000
+DEAL::P: 0.125000 0.0156250 1.12500, T(P, P0): -0.125000 -0.0312500 -0.125000, T(P, P1): 0.875000 0.218750 0.875000
+DEAL::P: 0.250000 0.0625000 1.25000, T(P, P0): -0.250000 -0.125000 -0.250000, T(P, P1): 0.750000 0.375000 0.750000
+DEAL::P: 0.375000 0.140625 1.37500, T(P, P0): -0.375000 -0.281250 -0.375000, T(P, P1): 0.625000 0.468750 0.625000
+DEAL::P: 0.500000 0.250000 1.50000, T(P, P0): -0.500000 -0.500000 -0.500000, T(P, P1): 0.500000 0.500000 0.500000
+DEAL::P: 0.625000 0.390625 1.62500, T(P, P0): -0.625000 -0.781250 -0.625000, T(P, P1): 0.375000 0.468750 0.375000
+DEAL::P: 0.750000 0.562500 1.75000, T(P, P0): -0.750000 -1.12500 -0.750000, T(P, P1): 0.250000 0.375000 0.250000
+DEAL::P: 0.875000 0.765625 1.87500, T(P, P0): -0.875000 -1.53125 -0.875000, T(P, P1): 0.125000 0.218750 0.125000
+DEAL::P: 1.00000 1.00000 2.00000, T(P, P0): -1.00000 -2.00000 -1.00000, T(P, P1): 0.00000 0.00000 0.00000
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2016 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Test TensorProductManifold by refining and generating normals for
+// a manually constructed cylinder hull.
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+#include <deal.II/grid/tensor_product_manifold.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+
+
+void test()
+{
+ std::ostream &out = deallog.get_file_stream();
+
+ FunctionManifold<1,1> F("x","x");
+ SphericalManifold<2,2> G;
+
+ TensorProductManifold<2, 1,1,1, 2,2,2> manifold(F, G);
+
+ // make a hull of a cylinder
+ Triangulation<2,3> tria;
+ {
+ Triangulation<3,3> volume_tria;
+ GridGenerator::cylinder(volume_tria);
+ std::set<types::boundary_id> boundary_ids;
+ boundary_ids.insert(0);
+ GridGenerator::extract_boundary_mesh(volume_tria, tria, boundary_ids);
+ }
+ tria.set_all_manifold_ids(0);
+ tria.set_manifold(0, manifold);
+
+ tria.refine_global(1);
+
+ out << "set view equal xyz" << std::endl
+ << "splot '-' with lines, '-' with vectors " << std::endl;
+ GridOut().write_gnuplot (tria, out);
+ out << "e" << std::endl;
+
+ Triangulation<2,3>::active_cell_iterator it = tria.begin_active();
+ for (; it!=tria.end(); ++it)
+ {
+ Point<3> p = it->center(true);
+ Tensor<1,3> t1 = manifold.get_tangent_vector(p, it->vertex(0));
+ Tensor<1,3> t2 = manifold.get_tangent_vector(p, it->vertex(1));
+ Tensor<1,3> n = cross_product_3d(t1, t2);
+ n/=-n.norm();
+ out << it->center() << " " << n << std::endl;
+ }
+ out << "e" << std::endl;
+}
+
+
+
+int main ()
+{
+ initlog();
+
+ test();
+
+ return 0;
+}
+
--- /dev/null
+
+set view equal xyz
+splot '-' with lines, '-' with vectors
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projects / dealii.git / commitdiff