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data_out_base.cc
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data_out_base.cc
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// ---------------------------------------------------------------------
//
// Copyright (C) 1999 - 2021 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.
//
// ---------------------------------------------------------------------
// TODO: Do neighbors for dx and povray smooth triangles
//--------------------------------------------------------------------
// Remarks on the implementations
//
// Variable names: in most functions, variable names have been
// standardized in the following way:
//
// n1, n2, ni Number of points in coordinate direction 1, 2, i
// will be 1 if i>=dim
//
// i1, i2, ii Loop variable running up to ni
//
// d1, d2, di Multiplicators for ii to find positions in the
// array of nodes.
//--------------------------------------------------------------------
#include <deal.II/base/data_out_base.h>
#include <deal.II/base/memory_consumption.h>
#include <deal.II/base/mpi.h>
#include <deal.II/base/parameter_handler.h>
#include <deal.II/base/thread_management.h>
#include <deal.II/base/utilities.h>
#include <deal.II/numerics/data_component_interpretation.h>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <ctime>
#include <fstream>
#include <iomanip>
#include <memory>
#include <set>
#include <sstream>
// we use uint32_t and uint8_t below, which are declared here:
#include <cstdint>
#include <vector>
#ifdef DEAL_II_WITH_ZLIB
# include <zlib.h>
#endif
#ifdef DEAL_II_WITH_HDF5
# include <hdf5.h>
#endif
DEAL_II_NAMESPACE_OPEN
// we need the following exception from a global function, so can't declare it
// in the usual way inside a class
namespace
{
DeclException2(ExcUnexpectedInput,
std::string,
std::string,
<< "Unexpected input: expected line\n <" << arg1
<< ">\nbut got\n <" << arg2 << ">");
}
namespace
{
#ifdef DEAL_II_WITH_ZLIB
/**
* Convert between the enum specified inside VtkFlags and the preprocessor
* constant defined by zlib.
*/
int
get_zlib_compression_level(
const DataOutBase::VtkFlags::ZlibCompressionLevel level)
{
switch (level)
{
case (DataOutBase::VtkFlags::no_compression):
return Z_NO_COMPRESSION;
case (DataOutBase::VtkFlags::best_speed):
return Z_BEST_SPEED;
case (DataOutBase::VtkFlags::best_compression):
return Z_BEST_COMPRESSION;
case (DataOutBase::VtkFlags::default_compression):
return Z_DEFAULT_COMPRESSION;
default:
Assert(false, ExcNotImplemented());
return Z_NO_COMPRESSION;
}
}
/**
* Do a zlib compression followed by a base64 encoding of the given data. The
* result is then written to the given stream.
*/
template <typename T>
void
write_compressed_block(const std::vector<T> & data,
const DataOutBase::VtkFlags &flags,
std::ostream & output_stream)
{
if (data.size() != 0)
{
// allocate a buffer for compressing data and do so
auto compressed_data_length = compressBound(data.size() * sizeof(T));
std::vector<unsigned char> compressed_data(compressed_data_length);
int err =
compress2(&compressed_data[0],
&compressed_data_length,
reinterpret_cast<const Bytef *>(data.data()),
data.size() * sizeof(T),
get_zlib_compression_level(flags.compression_level));
(void)err;
Assert(err == Z_OK, ExcInternalError());
// Discard the unnecessary bytes
compressed_data.resize(compressed_data_length);
// now encode the compression header
const uint32_t compression_header[4] = {
1, /* number of blocks */
static_cast<uint32_t>(data.size() * sizeof(T)), /* size of block */
static_cast<uint32_t>(data.size() *
sizeof(T)), /* size of last block */
static_cast<uint32_t>(
compressed_data_length)}; /* list of compressed sizes of blocks */
const auto header_start =
reinterpret_cast<const unsigned char *>(&compression_header[0]);
output_stream << Utilities::encode_base64(
{header_start, header_start + 4 * sizeof(uint32_t)})
<< Utilities::encode_base64(compressed_data);
}
}
#endif
} // namespace
// some declarations of functions and locally used classes
namespace DataOutBase
{
namespace
{
/**
* Class holding the data of one cell of a patch in two space dimensions for
* output. It is the projection of a cell in three-dimensional space (two
* coordinates, one height value) to the direction of sight.
*/
class SvgCell
{
public:
// Center of the cell (three-dimensional)
Point<3> center;
/**
* Vector of vertices of this cell (three-dimensional)
*/
Point<3> vertices[4];
/**
* Depth into the picture, which is defined as the distance from an
* observer at an the origin in direction of the line of sight.
*/
float depth;
/**
* Vector of vertices of this cell (projected, two-dimensional).
*/
Point<2> projected_vertices[4];
// Center of the cell (projected, two-dimensional)
Point<2> projected_center;
/**
* Comparison operator for sorting.
*/
bool
operator<(const SvgCell &) const;
};
bool
SvgCell::operator<(const SvgCell &e) const
{
// note the "wrong" order in which we sort the elements
return depth > e.depth;
}
/**
* Class holding the data of one cell of a patch in two space dimensions for
* output. It is the projection of a cell in three-dimensional space (two
* coordinates, one height value) to the direction of sight.
*/
class EpsCell2d
{
public:
/**
* Vector of vertices of this cell.
*/
Point<2> vertices[4];
/**
* Data value from which the actual colors will be computed by the
* colorization function stated in the <tt>EpsFlags</tt> class.
*/
float color_value;
/**
* Depth into the picture, which is defined as the distance from an
* observer at an the origin in direction of the line of sight.
*/
float depth;
/**
* Comparison operator for sorting.
*/
bool
operator<(const EpsCell2d &) const;
};
bool
EpsCell2d::operator<(const EpsCell2d &e) const
{
// note the "wrong" order in which we sort the elements
return depth > e.depth;
}
/**
* This is a helper function for the write_gmv() function. There, the data
* in the patches needs to be copied around as output is one variable
* globally at a time, rather than all data on each vertex at a time. This
* copying around can be done detached from the main thread, and is thus
* moved into this separate function.
*
* Note that because of the similarity of the formats, this function is also
* used by the Vtk and Tecplot output functions.
*/
template <int dim, int spacedim, typename Number = double>
void
write_gmv_reorder_data_vectors(
const std::vector<Patch<dim, spacedim>> &patches,
Table<2, Number> & data_vectors)
{
// If there is nothing to write, just return
if (patches.size() == 0)
return;
// unlike in the main function, we don't have here the data_names field,
// so we initialize it with the number of data sets in the first patch.
// the equivalence of these two definitions is checked in the main
// function.
// we have to take care, however, whether the points are appended to the
// end of the patch.data table
const unsigned int n_data_sets = patches[0].points_are_available ?
(patches[0].data.n_rows() - spacedim) :
patches[0].data.n_rows();
Assert(data_vectors.size()[0] == n_data_sets, ExcInternalError());
// loop over all patches
unsigned int next_value = 0;
for (const auto &patch : patches)
{
const unsigned int n_subdivisions = patch.n_subdivisions;
(void)n_subdivisions;
Assert((patch.data.n_rows() == n_data_sets &&
!patch.points_are_available) ||
(patch.data.n_rows() == n_data_sets + spacedim &&
patch.points_are_available),
ExcDimensionMismatch(patch.points_are_available ?
(n_data_sets + spacedim) :
n_data_sets,
patch.data.n_rows()));
Assert(patch.reference_cell != ReferenceCells::get_hypercube<dim>() ||
(n_data_sets == 0) ||
(patch.data.n_cols() ==
Utilities::fixed_power<dim>(n_subdivisions + 1)),
ExcInvalidDatasetSize(patch.data.n_cols(),
n_subdivisions + 1));
for (unsigned int i = 0; i < patch.data.n_cols(); ++i, ++next_value)
for (unsigned int data_set = 0; data_set < n_data_sets; ++data_set)
data_vectors[data_set][next_value] = patch.data(data_set, i);
}
for (unsigned int data_set = 0; data_set < n_data_sets; ++data_set)
Assert(data_vectors[data_set].size() == next_value, ExcInternalError());
}
} // namespace
DataOutFilter::DataOutFilter()
: flags(false, true)
, node_dim(numbers::invalid_unsigned_int)
, num_cells(numbers::invalid_unsigned_int)
{}
DataOutFilter::DataOutFilter(const DataOutBase::DataOutFilterFlags &flags)
: flags(flags)
, node_dim(numbers::invalid_unsigned_int)
, num_cells(numbers::invalid_unsigned_int)
{}
template <int dim>
void
DataOutFilter::write_point(const unsigned int index, const Point<dim> &p)
{
node_dim = dim;
Point<3> int_pt;
for (unsigned int d = 0; d < dim; ++d)
int_pt(d) = p(d);
const Map3DPoint::const_iterator it = existing_points.find(int_pt);
unsigned int internal_ind;
// If the point isn't in the set, or we're not filtering duplicate points,
// add it
if (it == existing_points.end() || !flags.filter_duplicate_vertices)
{
internal_ind = existing_points.size();
existing_points.insert(std::make_pair(int_pt, internal_ind));
}
else
{
internal_ind = it->second;
}
// Now add the index to the list of filtered points
filtered_points[index] = internal_ind;
}
void
DataOutFilter::internal_add_cell(const unsigned int cell_index,
const unsigned int pt_index)
{
filtered_cells[cell_index] = filtered_points[pt_index];
// (Re)-initialize counter at any first call to this method.
if (cell_index == 0)
num_cells = 1;
}
void
DataOutFilter::fill_node_data(std::vector<double> &node_data) const
{
node_data.resize(existing_points.size() * node_dim);
for (const auto &existing_point : existing_points)
{
for (unsigned int d = 0; d < node_dim; ++d)
node_data[node_dim * existing_point.second + d] =
existing_point.first(d);
}
}
void
DataOutFilter::fill_cell_data(const unsigned int local_node_offset,
std::vector<unsigned int> &cell_data) const
{
cell_data.resize(filtered_cells.size());
for (const auto &filtered_cell : filtered_cells)
{
cell_data[filtered_cell.first] =
filtered_cell.second + local_node_offset;
}
}
std::string
DataOutFilter::get_data_set_name(const unsigned int set_num) const
{
return data_set_names.at(set_num);
}
unsigned int
DataOutFilter::get_data_set_dim(const unsigned int set_num) const
{
return data_set_dims.at(set_num);
}
const double *
DataOutFilter::get_data_set(const unsigned int set_num) const
{
return data_sets[set_num].data();
}
unsigned int
DataOutFilter::n_nodes() const
{
return existing_points.size();
}
unsigned int
DataOutFilter::n_cells() const
{
return num_cells;
}
unsigned int
DataOutFilter::n_data_sets() const
{
return data_set_names.size();
}
void
DataOutFilter::flush_points()
{}
void
DataOutFilter::flush_cells()
{}
template <int dim>
void
DataOutFilter::write_cell(const unsigned int index,
const unsigned int start,
const unsigned int d1,
const unsigned int d2,
const unsigned int d3)
{
++num_cells;
const unsigned int base_entry =
index * GeometryInfo<dim>::vertices_per_cell;
internal_add_cell(base_entry + 0, start);
if (dim >= 1)
{
internal_add_cell(base_entry + 1, start + d1);
if (dim >= 2)
{
internal_add_cell(base_entry + 2, start + d2 + d1);
internal_add_cell(base_entry + 3, start + d2);
if (dim >= 3)
{
internal_add_cell(base_entry + 4, start + d3);
internal_add_cell(base_entry + 5, start + d3 + d1);
internal_add_cell(base_entry + 6, start + d3 + d2 + d1);
internal_add_cell(base_entry + 7, start + d3 + d2);
}
}
}
}
void
DataOutFilter::write_cell_single(const unsigned int index,
const unsigned int start,
const unsigned int n_points,
const ReferenceCell &reference_cell)
{
++num_cells;
const unsigned int base_entry = index * n_points;
static const std::array<unsigned int, 5> table = {{0, 1, 3, 2, 4}};
for (unsigned int i = 0; i < n_points; ++i)
internal_add_cell(base_entry + i,
start + (reference_cell == ReferenceCells::Pyramid ?
table[i] :
i));
}
void
DataOutFilter::write_data_set(const std::string & name,
const unsigned int dimension,
const unsigned int set_num,
const Table<2, double> &data_vectors)
{
unsigned int new_dim;
// HDF5/XDMF output only supports 1D or 3D output, so force rearrangement if
// needed
if (flags.xdmf_hdf5_output && dimension != 1)
new_dim = 3;
else
new_dim = dimension;
// Record the data set name, dimension, and allocate space for it
data_set_names.push_back(name);
data_set_dims.push_back(new_dim);
data_sets.emplace_back(new_dim * existing_points.size());
// TODO: averaging, min/max, etc for merged vertices
for (unsigned int i = 0; i < filtered_points.size(); ++i)
{
const unsigned int r = filtered_points[i];
for (unsigned int d = 0; d < new_dim; ++d)
{
if (d < dimension)
data_sets.back()[r * new_dim + d] = data_vectors(set_num + d, i);
else
data_sets.back()[r * new_dim + d] = 0;
}
}
}
} // namespace DataOutBase
//----------------------------------------------------------------------//
// Auxiliary data
//----------------------------------------------------------------------//
namespace
{
const char *gmv_cell_type[4] = {"", "line 2", "quad 4", "hex 8"};
const char *ucd_cell_type[4] = {"pt", "line", "quad", "hex"};
const char *tecplot_cell_type[4] = {"", "lineseg", "quadrilateral", "brick"};
#ifdef DEAL_II_HAVE_TECPLOT
const unsigned int tecplot_binary_cell_type[4] = {0, 0, 1, 3};
#endif
// Define cell id using VTK nomenclature for linear, quadratic and
// high-order Lagrange cells
enum vtk_linear_cell_type
{
VTK_VERTEX = 1,
VTK_LINE = 3,
VTK_TRIANGLE = 5,
VTK_QUAD = 9,
VTK_TETRA = 10,
VTK_HEXAHEDRON = 12,
VTK_WEDGE = 13,
VTK_PYRAMID = 14
};
enum vtk_quadratic_cell_type
{
VTK_QUADRATIC_EDGE = 21,
VTK_QUADRATIC_TRIANGLE = 22,
VTK_QUADRATIC_QUAD = 23,
VTK_QUADRATIC_TETRA = 24,
VTK_QUADRATIC_HEXAHEDRON = 25,
VTK_QUADRATIC_WEDGE = 26,
VTK_QUADRATIC_PYRAMID = 27
};
enum vtk_lagrange_cell_type
{
VTK_LAGRANGE_CURVE = 68,
VTK_LAGRANGE_TRIANGLE = 69,
VTK_LAGRANGE_QUADRILATERAL = 70,
VTK_LAGRANGE_TETRAHEDRON = 71,
VTK_LAGRANGE_HEXAHEDRON = 72,
VTK_LAGRANGE_WEDGE = 73,
VTK_LAGRANGE_PYRAMID = 74
};
/**
* Return the tuple (vtk cell type, number of cells, number of vertices)
* for a patch.
*/
template <int dim, int spacedim>
std::array<unsigned int, 3>
extract_vtk_patch_info(const DataOutBase::Patch<dim, spacedim> &patch,
const bool write_higher_order_cells)
{
std::array<unsigned int, 3> vtk_cell_id{};
if (write_higher_order_cells)
{
if (patch.reference_cell == ReferenceCells::get_hypercube<dim>())
{
const std::array<unsigned int, 4> cell_type_by_dim{
{VTK_VERTEX,
VTK_LAGRANGE_CURVE,
VTK_LAGRANGE_QUADRILATERAL,
VTK_LAGRANGE_HEXAHEDRON}};
vtk_cell_id[0] = cell_type_by_dim[dim];
vtk_cell_id[1] = 1;
}
else if (patch.reference_cell == ReferenceCells::Triangle)
{
vtk_cell_id[0] = VTK_LAGRANGE_TRIANGLE;
vtk_cell_id[1] = 1;
}
else
{
Assert(false, ExcNotImplemented());
}
}
else if (patch.reference_cell == ReferenceCells::Triangle &&
patch.data.n_cols() == 3)
{
vtk_cell_id[0] = VTK_TRIANGLE;
vtk_cell_id[1] = 1;
}
else if (patch.reference_cell == ReferenceCells::Triangle &&
patch.data.n_cols() == 6)
{
vtk_cell_id[0] = VTK_QUADRATIC_TRIANGLE;
vtk_cell_id[1] = 1;
}
else if (patch.reference_cell == ReferenceCells::Tetrahedron &&
patch.data.n_cols() == 4)
{
vtk_cell_id[0] = VTK_TETRA;
vtk_cell_id[1] = 1;
}
else if (patch.reference_cell == ReferenceCells::Tetrahedron &&
patch.data.n_cols() == 10)
{
vtk_cell_id[0] = VTK_QUADRATIC_TETRA;
vtk_cell_id[1] = 1;
}
else if (patch.reference_cell == ReferenceCells::Wedge &&
patch.data.n_cols() == 6)
{
vtk_cell_id[0] = VTK_WEDGE;
vtk_cell_id[1] = 1;
}
else if (patch.reference_cell == ReferenceCells::Pyramid &&
patch.data.n_cols() == 5)
{
vtk_cell_id[0] = VTK_PYRAMID;
vtk_cell_id[1] = 1;
}
else if (patch.reference_cell == ReferenceCells::get_hypercube<dim>())
{
const std::array<unsigned int, 4> cell_type_by_dim{
{VTK_VERTEX, VTK_LINE, VTK_QUAD, VTK_HEXAHEDRON}};
vtk_cell_id[0] = cell_type_by_dim[dim];
vtk_cell_id[1] = Utilities::pow(patch.n_subdivisions, dim);
}
else
{
Assert(false, ExcNotImplemented());
}
if (patch.reference_cell != ReferenceCells::get_hypercube<dim>() ||
write_higher_order_cells)
vtk_cell_id[2] = patch.data.n_cols();
else
vtk_cell_id[2] = GeometryInfo<dim>::vertices_per_cell;
return vtk_cell_id;
}
//----------------------------------------------------------------------//
// Auxiliary functions
//----------------------------------------------------------------------//
// For a given patch that corresponds to a hypercube cell, compute the
// location of a node interpolating the corner nodes linearly
// at the point lattice_location/n_subdivisions where lattice_location
// is a dim-dimensional integer vector. If the points are
// saved in the patch.data member, return the saved point instead.
template <int dim, int spacedim>
inline Point<spacedim>
get_equispaced_location(
const DataOutBase::Patch<dim, spacedim> & patch,
const std::initializer_list<unsigned int> &lattice_location,
const unsigned int n_subdivisions)
{
// This function only makes sense when called on hypercube cells
Assert(patch.reference_cell == ReferenceCells::get_hypercube<dim>(),
ExcInternalError());
Assert(lattice_location.size() == dim, ExcInternalError());
const unsigned int xstep = (dim > 0 ? *(lattice_location.begin() + 0) : 0);
const unsigned int ystep = (dim > 1 ? *(lattice_location.begin() + 1) : 0);
const unsigned int zstep = (dim > 2 ? *(lattice_location.begin() + 2) : 0);
// If the patch stores the locations of nodes (rather than of only the
// vertices), then obtain the location by direct lookup.
if (patch.points_are_available)
{
Assert(n_subdivisions == patch.n_subdivisions, ExcNotImplemented());
unsigned int point_no = 0;
switch (dim)
{
case 3:
AssertIndexRange(zstep, n_subdivisions + 1);
point_no += (n_subdivisions + 1) * (n_subdivisions + 1) * zstep;
DEAL_II_FALLTHROUGH;
case 2:
AssertIndexRange(ystep, n_subdivisions + 1);
point_no += (n_subdivisions + 1) * ystep;
DEAL_II_FALLTHROUGH;
case 1:
AssertIndexRange(xstep, n_subdivisions + 1);
point_no += xstep;
DEAL_II_FALLTHROUGH;
case 0:
// break here for dim<=3
break;
default:
Assert(false, ExcNotImplemented());
}
Point<spacedim> node;
for (unsigned int d = 0; d < spacedim; ++d)
node[d] = patch.data(patch.data.size(0) - spacedim + d, point_no);
return node;
}
else
// The patch does not store node locations, so we have to interpolate
// between its vertices:
{
if (dim == 0)
return patch.vertices[0];
else
{
// perform a dim-linear interpolation
const double stepsize = 1. / n_subdivisions;
const double xfrac = xstep * stepsize;
Point<spacedim> node =
(patch.vertices[1] * xfrac) + (patch.vertices[0] * (1 - xfrac));
if (dim > 1)
{
const double yfrac = ystep * stepsize;
node *= 1 - yfrac;
node += ((patch.vertices[3] * xfrac) +
(patch.vertices[2] * (1 - xfrac))) *
yfrac;
if (dim > 2)
{
const double zfrac = zstep * stepsize;
node *= (1 - zfrac);
node += (((patch.vertices[5] * xfrac) +
(patch.vertices[4] * (1 - xfrac))) *
(1 - yfrac) +
((patch.vertices[7] * xfrac) +
(patch.vertices[6] * (1 - xfrac))) *
yfrac) *
zfrac;
}
}
return node;
}
}
}
// For a given patch, compute the nodes for arbitrary (non-hypercube) cells.
// If the points are saved in the patch.data member, return the saved point
// instead.
template <int dim, int spacedim>
inline Point<spacedim>
get_node_location(const DataOutBase::Patch<dim, spacedim> &patch,
const unsigned int node_index)
{
// Due to a historical accident, we are using a different indexing
// for pyramids in this file than we do where we create patches.
// So translate if necessary.
unsigned int point_no_actual = node_index;
if (patch.reference_cell == ReferenceCells::Pyramid)
{
AssertDimension(patch.n_subdivisions, 1);
static const std::array<unsigned int, 5> table = {{0, 1, 3, 2, 4}};
point_no_actual = table[node_index];
}
// If the patch stores the locations of nodes (rather than of only the
// vertices), then obtain the location by direct lookup.
if (patch.points_are_available)
{
Point<spacedim> node;
for (unsigned int d = 0; d < spacedim; ++d)
node[d] =
patch.data(patch.data.size(0) - spacedim + d, point_no_actual);
return node;
}
else
// The patch does not store node locations, so we have to interpolate
// between its vertices. This isn't currently implemented for anything
// other than one subdivision, but would go here.
//
// For n_subdivisions==1, the locations are simply those of vertices, so
// get the information from there.
{
AssertDimension(patch.n_subdivisions, 1);
return patch.vertices[point_no_actual];
}
}
/**
* Given (i,j,k) coordinates within the Lagrange quadrilateral, return an
* offset into the local connectivity array.
*
* Modified from
* https://github.com/Kitware/VTK/blob/265ca48a/Common/DataModel/vtkLagrangeQuadrilateral.cxx#L558
*/
int
vtk_point_index_from_ijk(const unsigned i,
const unsigned j,
const unsigned,
const std::array<unsigned, 2> &order)
{
const bool ibdy = (i == 0 || i == order[0]);
const bool jbdy = (j == 0 || j == order[1]);
// How many boundaries do we lie on at once?
const int nbdy = (ibdy ? 1 : 0) + (jbdy ? 1 : 0);
if (nbdy == 2) // Vertex DOF
{ // ijk is a corner node. Return the proper index (somewhere in [0,3]):
return (i != 0u ? (j != 0u ? 2 : 1) : (j != 0u ? 3 : 0));
}
int offset = 4;
if (nbdy == 1) // Edge DOF
{
if (!ibdy)
{ // On i axis
return (i - 1) + (j != 0u ? order[0] - 1 + order[1] - 1 : 0) +
offset;
}
if (!jbdy)
{ // On j axis
return (j - 1) +
(i != 0u ? order[0] - 1 :
2 * (order[0] - 1) + order[1] - 1) +
offset;
}
}
offset += 2 * (order[0] - 1 + order[1] - 1);
// nbdy == 0: Face DOF
return offset + (i - 1) + (order[0] - 1) * ((j - 1));
}
/**
* Given (i,j,k) coordinates within the Lagrange hexahedron, return an
* offset into the local connectivity array.
*
* Modified from
* https://github.com/Kitware/VTK/blob/265ca48a/Common/DataModel/vtkLagrangeHexahedron.cxx#L734
*/
int
vtk_point_index_from_ijk(const unsigned i,
const unsigned j,
const unsigned k,
const std::array<unsigned, 3> &order)
{
const bool ibdy = (i == 0 || i == order[0]);
const bool jbdy = (j == 0 || j == order[1]);
const bool kbdy = (k == 0 || k == order[2]);
// How many boundaries do we lie on at once?
const int nbdy = (ibdy ? 1 : 0) + (jbdy ? 1 : 0) + (kbdy ? 1 : 0);
if (nbdy == 3) // Vertex DOF
{ // ijk is a corner node. Return the proper index (somewhere in [0,7]):
return (i != 0u ? (j != 0u ? 2 : 1) : (j != 0u ? 3 : 0)) +
(k != 0u ? 4 : 0);
}
int offset = 8;
if (nbdy == 2) // Edge DOF
{
if (!ibdy)
{ // On i axis
return (i - 1) + (j != 0u ? order[0] - 1 + order[1] - 1 : 0) +
(k != 0u ? 2 * (order[0] - 1 + order[1] - 1) : 0) + offset;
}
if (!jbdy)
{ // On j axis
return (j - 1) +
(i != 0u ? order[0] - 1 :
2 * (order[0] - 1) + order[1] - 1) +
(k != 0u ? 2 * (order[0] - 1 + order[1] - 1) : 0) + offset;
}
// !kbdy, On k axis
offset += 4 * (order[0] - 1) + 4 * (order[1] - 1);
return (k - 1) +
(order[2] - 1) *
(i != 0u ? (j != 0u ? 3 : 1) : (j != 0u ? 2 : 0)) +
offset;
}
offset += 4 * (order[0] - 1 + order[1] - 1 + order[2] - 1);
if (nbdy == 1) // Face DOF
{
if (ibdy) // On i-normal face
{
return (j - 1) + ((order[1] - 1) * (k - 1)) +
(i != 0u ? (order[1] - 1) * (order[2] - 1) : 0) + offset;
}
offset += 2 * (order[1] - 1) * (order[2] - 1);
if (jbdy) // On j-normal face
{
return (i - 1) + ((order[0] - 1) * (k - 1)) +
(j != 0u ? (order[2] - 1) * (order[0] - 1) : 0) + offset;
}
offset += 2 * (order[2] - 1) * (order[0] - 1);
// kbdy, On k-normal face
return (i - 1) + ((order[0] - 1) * (j - 1)) +
(k != 0u ? (order[0] - 1) * (order[1] - 1) : 0) + offset;
}
// nbdy == 0: Body DOF
offset +=
2 * ((order[1] - 1) * (order[2] - 1) + (order[2] - 1) * (order[0] - 1) +
(order[0] - 1) * (order[1] - 1));
return offset + (i - 1) +
(order[0] - 1) * ((j - 1) + (order[1] - 1) * ((k - 1)));
}
int
vtk_point_index_from_ijk(const unsigned,
const unsigned,
const unsigned,
const std::array<unsigned, 0> &)
{
Assert(false, ExcNotImplemented());
return 0;
}
int
vtk_point_index_from_ijk(const unsigned,
const unsigned,
const unsigned,
const std::array<unsigned, 1> &)
{
Assert(false, ExcNotImplemented());
return 0;
}
template <int dim, int spacedim>
static void
compute_sizes(const std::vector<DataOutBase::Patch<dim, spacedim>> &patches,
unsigned int & n_nodes,
unsigned int & n_cells)
{
n_nodes = 0;
n_cells = 0;