const std::array<unsigned int, 12> line_indices =
TriaAccessorImplementation::Implementation::
get_line_indices_of_cell(*hex);
- // avoid a compiler warning by fixing the max number of
- // loop iterations to 12
+
+ // For the tetrahedron the parent consists of the vertices
+ // 0,1,2,3, the new vertices 4-9 are defined as the
+ // midpoints fo the edges: 4 -> (0,1), 5 -> (1,2), 6 ->
+ // (2,0), 7 -> (0,3), 8 -> (1,3), 9 -> (2,3).
+ // Order is defined by the reference cell, see
+ // https://dealii.org/developer/doxygen/deal.II/group__simplex.html#simplex_reference_cells.
+
+ // Avoid a compiler warning by fixing the max number of loop
+ // iterations to 12
const unsigned int n_lines = std::min(hex->n_lines(), 12u);
for (unsigned int l = 0; l < n_lines; ++l)
{
}
}
+ unsigned int chosen_line_tetrahedron = 0;
// set up new lines
- {
- static constexpr dealii::ndarray<unsigned int, 6, 2>
- new_line_vertices_hex = {{{{22, 26}},
- {{26, 23}},
- {{20, 26}},
- {{26, 21}},
- {{24, 26}},
- {{26, 25}}}};
-
- static constexpr dealii::ndarray<unsigned int, 6, 2>
- new_line_vertices_tet = {{{{6, 8}},
- {{X, X}},
- {{X, X}},
- {{X, X}},
- {{X, X}},
- {{X, X}}}};
-
- const auto &new_line_vertices =
- (reference_cell_type == ReferenceCells::Hexahedron) ?
- new_line_vertices_hex :
- new_line_vertices_tet;
+ if (reference_cell_type == ReferenceCells::Hexahedron)
+ {
+ static constexpr dealii::ndarray<unsigned int, 6, 2>
+ new_line_vertices = {{{{22, 26}},
+ {{26, 23}},
+ {{20, 26}},
+ {{26, 21}},
+ {{24, 26}},
+ {{26, 25}}}};
+ for (unsigned int i = 0; i < n_new_lines; ++i)
+ new_lines[i]->set_bounding_object_indices(
+ {vertex_indices[new_line_vertices[i][0]],
+ vertex_indices[new_line_vertices[i][1]]});
+ }
+ else if (reference_cell_type == ReferenceCells::Tetrahedron)
+ {
+ // in the tetrahedron case, we have the three
+ // possibilities (6,8), (5,7), (4,9) -> pick the
+ // shortest line to guarantee the best possible aspect
+ // ratios
+ static constexpr dealii::ndarray<unsigned int, 3, 2>
+ new_line_vertices = {{{{6, 8}}, {{5, 7}}, {{4, 9}}}};
+
+ const auto &vertices = triangulation.get_vertices();
+ double min_distance =
+ std::numeric_limits<double>::infinity();
+ for (unsigned int i = 0; i < new_line_vertices.size();
+ ++i)
+ {
+ const double current_distance =
+ vertices[vertex_indices[new_line_vertices[i][0]]]
+ .distance(
+ vertices
+ [vertex_indices[new_line_vertices[i][1]]]);
+ if (current_distance < min_distance)
+ {
+ chosen_line_tetrahedron = i;
+ min_distance = current_distance;
+ }
+ }
- for (unsigned int i = 0; i < n_new_lines; ++i)
- new_lines[i]->set_bounding_object_indices(
- {vertex_indices[new_line_vertices[i][0]],
- vertex_indices[new_line_vertices[i][1]]});
- }
+ new_lines[0]->set_bounding_object_indices(
+ {vertex_indices
+ [new_line_vertices[chosen_line_tetrahedron][0]],
+ vertex_indices
+ [new_line_vertices[chosen_line_tetrahedron][1]]});
+ }
// set up new quads
{
}
else if (reference_cell_type == ReferenceCells::Tetrahedron)
{
+ // The order of the lines is defined by the ordering
+ // of the faces of the reference cell and the ordering
+ // of the lines within a face.
+ // Each face is split into 4 child triangels, the
+ // relevant lines are defined by the vertices of the
+ // center triangles: 0 -> (4,5), 1 -> (5,6), 2 -> (4,6),
+ // 3 -> (4,7), 4 -> (7,8), 5 -> (4,8), 6 -> (6,9), 7 ->
+ // (9,7), 8 -> (6,7), 9 -> (5,8), 10 -> (8,9), 11 ->
+ // (5,9), Line 12 is determined by
+ // chosen_line_tetrahedron i.e. (6,8), (5,7) or (4,9)
+
relevant_lines.resize(13);
unsigned int k = 0;
}
relevant_lines[k++] = new_lines[0];
-
AssertDimension(k, 13);
}
else
{{3, 25, 26, 12}},
{{25, 7, 27, 13}}}};
- static constexpr dealii::ndarray<unsigned int, 12, 4>
- new_quad_lines_tet = {{{{2, 3, 8, X}},
- {{0, 9, 5, X}},
- {{1, 6, 11, X}},
- {{4, 10, 7, X}},
- {{2, 12, 5, X}},
- {{1, 9, 12, X}},
- {{4, 8, 12, X}},
- {{6, 12, 10, X}},
- {{X, X, X, X}},
- {{X, X, X, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}};
+ // It is easierst to start at table cell_vertices_tet,
+ // there the vertices are listed which build up the
+ // 8 child tets. To build the child tets, 8 new faces are
+ // needed. The the vertices, which define the lines of these
+ // new faces are listed in table_tet. Now only the
+ // coresponding index of the lines and quads have to be
+ // listed in new_quad_lines_tet and cell_quads_tet.
+
+ // The first 4 define the faces which cut off the
+ // parent tetrahedron at the edges. the numbers are the
+ // index of the relevant_lines defined above the last 4
+ // faces cut apart the remaining octahedron, such that all
+ // of these contain line number 12. the ordering of the
+ // faces is arbitrary, the ordering within the faces has to
+ // follow the righthand convention for triangles
+ static constexpr dealii::ndarray<unsigned int, 3, 12, 4>
+ new_quad_lines_tet = {{// new line is (6,8)
+ {{{{2, 3, 8, X}},
+ {{0, 9, 5, X}},
+ {{1, 6, 11, X}},
+ {{4, 10, 7, X}},
+ {{2, 12, 5, X}},
+ {{1, 9, 12, X}},
+ {{4, 8, 12, X}},
+ {{6, 12, 10, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}}}},
+ // new line is (5,7)
+ {{{{2, 3, 8, X}},
+ {{0, 9, 5, X}},
+ {{1, 6, 11, X}},
+ {{4, 10, 7, X}},
+ {{0, 3, 12, X}},
+ {{1, 12, 8, X}},
+ {{4, 12, 9, X}},
+ {{7, 11, 12, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}}}},
+ // new line is (4,9)
+ {{{{2, 3, 8, X}},
+ {{0, 9, 5, X}},
+ {{1, 6, 11, X}},
+ {{4, 10, 7, X}},
+ {{0, 12, 11, X}},
+ {{2, 6, 12, X}},
+ {{3, 12, 7, X}},
+ {{5, 10, 12, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}},
+ {{X, X, X, X}}}}}};
static constexpr dealii::ndarray<unsigned int, 12, 4, 2>
table_hex = {
{{{{20, 18}}, {{26, 23}}, {{20, 26}}, {{18, 23}}}},
{{{{26, 23}}, {{21, 19}}, {{26, 21}}, {{23, 19}}}}}};
- static constexpr dealii::ndarray<unsigned int, 12, 4, 2>
+ // The table defines the vertices of the lines above
+ // see relevant_lines for mapping between line indices and
+ // vertex numbering
+ static constexpr dealii::ndarray<unsigned int, 3, 12, 4, 2>
table_tet = {
- {{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
- {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
- {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
- {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
- {{{{4, 6}}, {{6, 8}}, {{8, 4}}, {{X, X}}}},
- {{{{6, 5}}, {{5, 8}}, {{8, 6}}, {{X, X}}}},
- {{{{8, 7}}, {{7, 6}}, {{6, 8}}, {{X, X}}}},
- {{{{9, 6}}, {{6, 8}}, {{8, 9}}, {{X, X}}}},
- {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
- {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
- {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
- {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}};
+ {// new line is (6, 8)
+ {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
+ {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
+ {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
+ {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
+ {{{{4, 6}}, {{6, 8}}, {{8, 4}}, {{X, X}}}},
+ {{{{6, 5}}, {{5, 8}}, {{8, 6}}, {{X, X}}}},
+ {{{{8, 7}}, {{7, 6}}, {{6, 8}}, {{X, X}}}},
+ {{{{9, 6}}, {{6, 8}}, {{8, 9}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}},
+ // new line is (5, 7)
+ {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
+ {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
+ {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
+ {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
+ {{{{5, 4}}, {{4, 7}}, {{7, 5}}, {{X, X}}}},
+ {{{{6, 5}}, {{5, 7}}, {{7, 6}}, {{X, X}}}},
+ {{{{8, 7}}, {{7, 5}}, {{5, 8}}, {{X, X}}}},
+ {{{{7, 9}}, {{9, 5}}, {{5, 7}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}},
+ // new line is (4, 9)
+ {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
+ {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
+ {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
+ {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
+ {{{{5, 4}}, {{4, 9}}, {{9, 5}}, {{X, X}}}},
+ {{{{4, 6}}, {{6, 9}}, {{9, 4}}, {{X, X}}}},
+ {{{{7, 4}}, {{4, 9}}, {{9, 7}}, {{X, X}}}},
+ {{{{4, 8}}, {{8, 9}}, {{9, 4}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+ {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}}}};
const auto &new_quad_lines =
(reference_cell_type == ReferenceCells::Hexahedron) ?
new_quad_lines_hex :
- new_quad_lines_tet;
+ new_quad_lines_tet[chosen_line_tetrahedron];
const auto &table =
(reference_cell_type == ReferenceCells::Hexahedron) ?
table_hex :
- table_tet;
+ table_tet[chosen_line_tetrahedron];
static constexpr dealii::ndarray<unsigned int, 4, 2>
representative_lines{
}
else if (reference_cell_type == ReferenceCells::Tetrahedron)
{
+ // list of the indices of the surfaces which define the
+ // 8 new tets. the indices 0-7 are the new quads defined
+ // above (so 0-3 cut off the corners and 4-7 sperate the
+ // remaining octahedral), the indices between 8-11 are
+ // the children of the first face, from 12-15 of the
+ // second, etc.
for (unsigned int i = 0; i < n_new_quads; ++i)
quad_indices[i] = new_quads[i]->index();
{{3, 19, 7, 27, 11, 35}} //
}};
- static constexpr dealii::ndarray<unsigned int, 8, 6>
- cell_quads_tet{{{{8, 13, 16, 0, X, X}},
- {{9, 12, 1, 21, X, X}},
- {{10, 2, 17, 20, X, X}},
- {{3, 14, 18, 22, X, X}},
- {{11, 1, 4, 5, X, X}},
- {{15, 0, 4, 6, X, X}},
- {{19, 7, 6, 3, X, X}},
- {{23, 5, 2, 7, X, X}}}};
-
- static constexpr dealii::ndarray<unsigned int, 8, 6, 4>
- cell_face_vertices_tet{{{{{{0, 4, 6, X}},
- {{4, 0, 7, X}},
- {{0, 6, 7, X}},
- {{6, 4, 7, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}},
- {{{{4, 1, 5, X}},
- {{1, 4, 8, X}},
- {{4, 5, 8, X}},
- {{5, 1, 8, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}},
- {{{{6, 5, 2, X}},
- {{5, 6, 9, X}},
- {{6, 2, 9, X}},
- {{2, 5, 9, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}},
- {{{{7, 8, 9, X}},
- {{8, 7, 3, X}},
- {{7, 9, 3, X}},
- {{9, 8, 3, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}},
- {{{{4, 5, 6, X}},
- {{5, 4, 8, X}},
- {{4, 6, 8, X}},
- {{6, 5, 8, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}},
- {{{{4, 7, 8, X}},
- {{7, 4, 6, X}},
- {{4, 8, 6, X}},
- {{8, 7, 6, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}},
- {{{{6, 9, 7, X}},
- {{9, 6, 8, X}},
- {{6, 7, 8, X}},
- {{7, 9, 8, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}},
- {{{{5, 8, 9, X}},
- {{8, 5, 6, X}},
- {{5, 9, 6, X}},
- {{9, 8, 6, X}},
- {{X, X, X, X}},
- {{X, X, X, X}}}}}};
+ // indices of the faces which define the new tets
+ // the ordering of the tets is arbitrary
+ // the first 4 determine the tets cutting of the corners
+ // the last 4 are ordered after their appearance in the
+ // faces.
+ // the ordering within the faces is determined by
+ // convention for the tetrahedron unit cell, see
+ // cell_vertices_tet below
+ static constexpr dealii::ndarray<unsigned int, 3, 8, 6>
+ cell_quads_tet = {{// new line is (6, 8)
+ {{{{8, 13, 16, 0, X, X}},
+ {{9, 12, 1, 21, X, X}},
+ {{10, 2, 17, 20, X, X}},
+ {{3, 14, 18, 22, X, X}},
+ {{11, 1, 4, 5, X, X}},
+ {{15, 0, 4, 6, X, X}},
+ {{19, 7, 6, 3, X, X}},
+ {{23, 5, 2, 7, X, X}}}},
+ // new line is (5, 7)
+ {{
+ {{8, 13, 16, 0, X, X}},
+ {{9, 12, 1, 21, X, X}},
+ {{10, 2, 17, 20, X, X}},
+ {{3, 14, 18, 22, X, X}},
+ {{11, 4, 0, 5, X, X}},
+ {{15, 4, 1, 6, X, X}},
+ {{19, 2, 5, 7, X, X}},
+ {{23, 6, 7, 3, X, X}},
+ }},
+ // new line is (4, 9)
+ {{
+ {{8, 13, 16, 0, X, X}},
+ {{9, 12, 1, 21, X, X}},
+ {{10, 2, 17, 20, X, X}},
+ {{3, 14, 18, 22, X, X}},
+ {{11, 4, 5, 2, X, X}},
+ {{15, 6, 7, 3, X, X}},
+ {{19, 5, 0, 6, X, X}},
+ {{23, 1, 4, 7, X, X}},
+ }}}};
+
+ // the 4 faces of the reference tet are defined by 3
+ // vertices each and follow the order of the unit cell
+ static constexpr dealii::ndarray<unsigned int, 4, 3>
+ reference_cell_face_vertices = {
+ {{{0, 1, 2}}, {{1, 0, 3}}, {{0, 2, 3}}, {{2, 1, 3}}}};
+
+ // the 8 child tets are each defined by 4 vertices
+ // the ordering of the tets has to be consistent with above
+ // the ordering within the tets is given by the reference
+ // tet i.e. looking at the fifth line the first 3 vertices
+ // are given by face 11, the last vertex is the remaining of
+ // the tet
+ static constexpr dealii::ndarray<unsigned int, 3, 8, 4>
+ cell_vertices_tet = {{// new line is (6,8)
+ {{{{0, 4, 6, 7}},
+ {{4, 1, 5, 8}},
+ {{6, 5, 2, 9}},
+ {{7, 8, 9, 3}},
+ {{4, 5, 6, 8}},
+ {{4, 7, 8, 6}},
+ {{6, 9, 7, 8}},
+ {{5, 8, 9, 6}}}},
+ // new line is (5,7)
+ {{{{0, 4, 6, 7}},
+ {{4, 1, 5, 8}},
+ {{6, 5, 2, 9}},
+ {{7, 8, 9, 3}},
+ {{4, 5, 6, 7}},
+ {{4, 7, 8, 5}},
+ {{6, 9, 7, 5}},
+ {{5, 8, 9, 7}}}},
+ // new line is (4,9)
+ {{{{0, 4, 6, 7}},
+ {{4, 1, 5, 8}},
+ {{6, 5, 2, 9}},
+ {{7, 8, 9, 3}},
+ {{4, 5, 6, 9}},
+ {{4, 7, 8, 9}},
+ {{6, 9, 7, 4}},
+ {{5, 8, 9, 4}}}}}};
+
const auto &cell_quads =
(reference_cell_type == ReferenceCells::Hexahedron) ?
cell_quads_hex :
- cell_quads_tet;
+ cell_quads_tet[chosen_line_tetrahedron];
for (unsigned int c = 0;
c < GeometryInfo<dim>::max_children_per_cell;
quad_indices[cell_quads[c][2]],
quad_indices[cell_quads[c][3]]});
+
// for tets, we need to go through the faces and
// figure the orientation out the hard way
for (const auto f : new_hex->face_indices())
face->vertex_index(1),
face->vertex_index(2)}};
+ const auto &new_hex_vertices =
+ cell_vertices_tet[chosen_line_tetrahedron][c];
+ const auto face_f_vertices =
+ reference_cell_face_vertices[f];
+
const std::array<unsigned int, 3> vertices_1 = {
{
- vertex_indices[cell_face_vertices_tet[c][f]
- [0]],
- vertex_indices[cell_face_vertices_tet[c][f]
- [1]],
- vertex_indices[cell_face_vertices_tet[c][f]
- [2]],
+ vertex_indices
+ [new_hex_vertices[face_f_vertices[0]]],
+ vertex_indices
+ [new_hex_vertices[face_f_vertices[1]]],
+ vertex_indices
+ [new_hex_vertices[face_f_vertices[2]]],
}};
new_hex->set_combined_face_orientation(
# For a description of the GNUPLOT format see the GNUPLOT manual.
#
# <x> <y> <z> <solution>
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-
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projects / dealii.git / commitdiff