Reference documentation for deal.II version GIT eef19498cf 2022-10-05 14:45:02+00:00
ReferenceCell Class Reference

#include <deal.II/grid/reference_cell.h>

## Public Member Functions

constexpr ReferenceCell ()

Querying information about the kind of reference cells
bool is_hyper_cube () const

bool is_simplex () const

unsigned int get_dimension () const

Shape functions, mappings, quadratures defined on a reference cell
template<int dim>
double d_linear_shape_function (const Point< dim > &xi, const unsigned int i) const

template<int dim>
Tensor< 1, dim > d_linear_shape_function_gradient (const Point< dim > &xi, const unsigned int i) const

template<int dim, int spacedim = dim>
std::unique_ptr< Mapping< dim, spacedim > > get_default_mapping (const unsigned int degree) const

template<int dim, int spacedim = dim>
const Mapping< dim, spacedim > & get_default_linear_mapping () const

template<int dim>

template<int dim>

template<int dim>

Querying the number of building blocks of a reference cell
unsigned int n_vertices () const

std_cxx20::ranges::iota_view< unsigned int, unsigned int > vertex_indices () const

template<int dim>
Point< dim > vertex (const unsigned int v) const

unsigned int n_lines () const

std_cxx20::ranges::iota_view< unsigned int, unsigned int > line_indices () const

unsigned int n_faces () const

std_cxx20::ranges::iota_view< unsigned int, unsigned int > face_indices () const

unsigned int n_isotropic_children () const

std_cxx20::ranges::iota_view< unsigned int, unsigned int > isotropic_child_indices () const

ReferenceCell face_reference_cell (const unsigned int face_no) const

double volume () const

template<int dim>
Point< dim > barycenter () const

template<int dim>
bool contains_point (const Point< dim > &p, const double tolerance=0) const

template<int dim>
Tensor< 1, dim > unit_tangential_vectors (const unsigned int face_no, const unsigned int i) const

template<int dim>
Tensor< 1, dim > unit_normal_vectors (const unsigned int face_no) const

template<typename T , std::size_t N>
unsigned char compute_orientation (const std::array< T, N > &vertices_0, const std::array< T, N > &vertices_1) const

template<typename T , std::size_t N>
std::array< T, N > permute_according_orientation (const std::array< T, N > &vertices, const unsigned int orientation) const

ArrayView< const unsigned int > faces_for_given_vertex (const unsigned int vertex_index) const

Relationships between objects in the cell and on faces
unsigned int child_cell_on_face (const unsigned int face, const unsigned int subface, const unsigned char face_orientation=1) const

std::array< unsigned int, 2 > standard_vertex_to_face_and_vertex_index (const unsigned int vertex) const

std::array< unsigned int, 2 > standard_line_to_face_and_line_index (const unsigned int line) const

unsigned int face_to_cell_lines (const unsigned int face, const unsigned int line, const unsigned char face_orientation) const

unsigned int face_to_cell_vertices (const unsigned int face, const unsigned int vertex, const unsigned char face_orientation) const

unsigned int standard_to_real_face_vertex (const unsigned int vertex, const unsigned int face, const unsigned char face_orientation) const

unsigned int standard_to_real_face_line (const unsigned int line, const unsigned int face, const unsigned char face_orientation) const

bool standard_vs_true_line_orientation (const unsigned int line, const unsigned char face_orientation, const bool line_orientation) const

Translating between deal.II indexing and formats used by other programs
unsigned int exodusii_vertex_to_deal_vertex (const unsigned int vertex_n) const

unsigned int exodusii_face_to_deal_face (const unsigned int face_n) const

unsigned int unv_vertex_to_deal_vertex (const unsigned int vertex_n) const

unsigned int vtk_linear_type () const

unsigned int vtk_lagrange_type () const

unsigned int gmsh_element_type () const

Other functions
std::string to_string () const

constexpr operator std::uint8_t () const

constexpr bool operator== (const ReferenceCell &type) const

constexpr bool operator!= (const ReferenceCell &type) const

template<class Archive >
void serialize (Archive &archive, const unsigned int)

## Static Public Member Functions

static ReferenceCell n_vertices_to_type (const int dim, const unsigned int n_vertices)

## Private Member Functions

constexpr ReferenceCell (const std::uint8_t kind)

## Private Attributes

std::uint8_t kind

## Friends

constexpr friend ReferenceCell internal::ReferenceCell::make_reference_cell_from_int (const std::uint8_t)

std::ostream & operator<< (std::ostream &out, const ReferenceCell &reference_cell)

std::istream & operator>> (std::istream &in, ReferenceCell &reference_cell)

## Detailed Description

A type that describes the kinds of reference cells that can be used. This includes quadrilaterals and hexahedra (i.e., "hypercubes"), triangles and tetrahedra (simplices), and the pyramids and wedges necessary when using mixed 3d meshes. This class then describes geometric, topological, and other kinds of information about these kinds of reference cells. This includes how many vertices or faces a certain kind of reference cell has (topological information), where these vertices lie, what the cell's volume or center of mass is (geometric information), and how to output these cells in various output formats or what appropriate quadrature rules are. The documentation of this class is separated into a number of sections to group the many member functions into different categories such as those mentioned above.

Objects of this type should not be created in user code, and as a consequence the class does not have a user-accessible constructor other than the default constructor (which creates an invalid object). Rather, there is a finite number of specific reference cell objects defined in the ReferenceCells namespace that completely enumerate all of the possible values. User codes should therefore rely exclusively on assigning ReferenceCell objects from these special objects, and comparing against those special objects.

The purposes and intents of this class are described in the reference cell glossary entry.

Definition at line 100 of file reference_cell.h.

## ◆ ReferenceCell() [1/2]

 constexpr ReferenceCell::ReferenceCell ( )
inlineconstexpr

Default constructor. Initialize this object as an invalid object. The end result is that the current object equals ReferenceCells::Invalid.

Generally, ReferenceCell objects are created by assignment from the special objects in namespace ReferenceCells, which is the only way to obtain a valid object.

Definition at line 830 of file reference_cell.h.

## ◆ ReferenceCell() [2/2]

 constexpr ReferenceCell::ReferenceCell ( const std::uint8_t kind )
inlineconstexprprivate

Constructor. This is the constructor used to create the different static member variables of this class. It is private but can be called by a function in an internal namespace that is a friend of this class.

Definition at line 729 of file reference_cell.h.

## ◆ n_vertices_to_type()

 ReferenceCell ReferenceCell::n_vertices_to_type ( const int dim, const unsigned int n_vertices )
inlinestatic

Return the correct ReferenceCell for a given structural dimension and number of vertices. For example, if dim==2 and n_vertices==4, this function will return ReferenceCells::Quadrilateral. But if dim==3 and n_vertices==4, it will return ReferenceCells::Tetrahedron.

Definition at line 1849 of file reference_cell.h.

## ◆ is_hyper_cube()

 bool ReferenceCell::is_hyper_cube ( ) const
inline

Return true if the object is a ReferenceCells::Vertex, ReferenceCells::Line, ReferenceCells::Quadrilateral, or ReferenceCells::Hexahedron.

Definition at line 912 of file reference_cell.h.

## ◆ is_simplex()

 bool ReferenceCell::is_simplex ( ) const
inline

Return true if the object is a Vertex, Line, Triangle, or Tetrahedron.

Definition at line 922 of file reference_cell.h.

## ◆ get_dimension()

 unsigned int ReferenceCell::get_dimension ( ) const
inline

Return the dimension of the reference cell represented by the current object.

Definition at line 932 of file reference_cell.h.

## ◆ d_linear_shape_function()

template<int dim>
 double ReferenceCell::d_linear_shape_function ( const Point< dim > & xi, const unsigned int i ) const
inline

Compute the value of the $$i$$-th linear shape function at location $$\xi$$ for the current reference-cell type.

Definition at line 1891 of file reference_cell.h.

template<int dim>
 Tensor< 1, dim > ReferenceCell::d_linear_shape_function_gradient ( const Point< dim > & xi, const unsigned int i ) const
inline

Compute the gradient of the $$i$$-th linear shape function at location $$\xi$$ for the current reference-cell type.

Definition at line 1985 of file reference_cell.h.

## ◆ get_default_mapping()

template<int dim, int spacedim>
 std::unique_ptr< Mapping< dim, spacedim > > ReferenceCell::get_default_mapping ( const unsigned int degree ) const

Return a default mapping of degree degree matching the current reference cell. If this reference cell is a hypercube, then the returned mapping is a MappingQ; otherwise, it is an object of type MappingFE initialized with FE_SimplexP (if the reference cell is a triangle or tetrahedron), with FE_PyramidP (if the reference cell is a pyramid), or with FE_WedgeP (if the reference cell is a wedge).

Definition at line 111 of file reference_cell.cc.

## ◆ get_default_linear_mapping()

template<int dim, int spacedim>
 const Mapping< dim, spacedim > & ReferenceCell::get_default_linear_mapping

Return a default linear mapping matching the current reference cell. If this reference cell is a hypercube, then the returned mapping is a MappingQ1; otherwise, it is an object of type MappingFE initialized with FE_SimplexP (if the reference cell is a triangle or tetrahedron), with FE_PyramidP (if the reference cell is a pyramid), or with FE_WedgeP (if the reference cell is a wedge). In other words, the term "linear" in the name of the function has to be understood as $$d$$-linear (i.e., bilinear or trilinear) for some of the coordinate directions.

Definition at line 138 of file reference_cell.cc.

template<int dim>

Return a Gauss-type quadrature matching the given reference cell (QGauss, QGaussSimplex, QGaussPyramid, QGaussWedge).

Parameters
 [in] n_points_1D The number of quadrature points in each direction (QGauss) or an indication of what polynomial degree needs to be integrated exactly for the other types.

Definition at line 176 of file reference_cell.cc.

template<int dim>

Return a quadrature object that has a single quadrature point at the barycenter of the cell with quadrature weight equal to the volume of the reference cell. This quadrature formula is exact for integrals of constant and linear integrands.

The object returned by this function generalizes what the QMidpoint class represents to other reference cells.

Definition at line 955 of file reference_cell.h.

template<int dim>

Return a quadrature rule whose quadrature points are the vertices of the given reference cell. For 1d line segments, this corresponds to the quadrature points of the trapezoidal rule, which by taking tensor products easily generalizes also to other hypercube elements (see also QTrapezoid). For all reference cell shapes, the quadrature points are ordered in the same order as the vertices of the reference cell.

Note
The weights of the quadrature object are left unfilled and consequently the object cannot usefully be used for actually computing integrals. This is in contrast to, for example, the QTrapezoid class that correctly sets quadrature weights.

Definition at line 198 of file reference_cell.cc.

## ◆ n_vertices()

 unsigned int ReferenceCell::n_vertices ( ) const
inline

Return the number of vertices that make up the reference cell in question. A vertex is a "corner" (a zero-dimensional object) of the reference cell.

Definition at line 964 of file reference_cell.h.

## ◆ vertex_indices()

 std_cxx20::ranges::iota_view< unsigned int, unsigned int > ReferenceCell::vertex_indices ( ) const
inline

Return an object that can be thought of as an array containing all indices from zero to n_vertices().

Definition at line 1185 of file reference_cell.h.

## ◆ vertex()

template<int dim>
 Point< dim > ReferenceCell::vertex ( const unsigned int v ) const

Return the location of the vth vertex of the reference cell that corresponds to the current object.

Because the ReferenceCell class does not have a dim argument, it has to be explicitly specified in the call to this function.

Definition at line 1017 of file reference_cell.h.

## ◆ n_lines()

 unsigned int ReferenceCell::n_lines ( ) const
inline

Return the number of lines that make up the reference cell in question. A line is an "edge" (a one-dimensional object) of the reference cell.

Definition at line 990 of file reference_cell.h.

## ◆ line_indices()

 std_cxx20::ranges::iota_view< unsigned int, unsigned int > ReferenceCell::line_indices ( ) const
inline

Return an object that can be thought of as an array containing all indices from zero to n_lines().

Definition at line 1193 of file reference_cell.h.

## ◆ n_faces()

 unsigned int ReferenceCell::n_faces ( ) const
inline

Return the number of faces that make up the reference cell in question. A face is a (dim-1)-dimensional object bounding the reference cell.

Definition at line 1112 of file reference_cell.h.

## ◆ face_indices()

 std_cxx20::ranges::iota_view< unsigned int, unsigned int > ReferenceCell::face_indices ( ) const
inline

Return an object that can be thought of as an array containing all indices from zero to n_faces().

Definition at line 1138 of file reference_cell.h.

## ◆ n_isotropic_children()

 unsigned int ReferenceCell::n_isotropic_children ( ) const
inline

Return the number of cells one would get by isotropically refining the current cell. Here, "isotropic refinement" means that we subdivide in each "direction" of a cell. For example, a square would be refined into four children by introducing new vertices along each edge and a new vertex in the cell center. For triangles, one would introduce new vertices at the center of each edge, and connect them to obtain four children. Similar constructions can be done for the other reference cell types.

Definition at line 1146 of file reference_cell.h.

## ◆ isotropic_child_indices()

 std_cxx20::ranges::iota_view< unsigned int, unsigned int > ReferenceCell::isotropic_child_indices ( ) const
inline

Return an object that can be thought of as an array containing all indices from zero to n_isotropic_children().

Definition at line 1177 of file reference_cell.h.

## ◆ face_reference_cell()

 ReferenceCell ReferenceCell::face_reference_cell ( const unsigned int face_no ) const
inline

Return the reference-cell type of face face_no of the current object. For example, if the current object is ReferenceCells::Tetrahedron, then face_no must be between in the interval $$[0,4)$$ and the function will always return ReferenceCells::Triangle. If the current object is ReferenceCells::Hexahedron, then face_no must be between in the interval $$[0,6)$$ and the function will always return ReferenceCells::Quadrilateral. For wedges and pyramids, the returned object may be either ReferenceCells::Triangle or ReferenceCells::Quadrilateral, depending on the given index.

Definition at line 1201 of file reference_cell.h.

## ◆ child_cell_on_face()

 unsigned int ReferenceCell::child_cell_on_face ( const unsigned int face, const unsigned int subface, const unsigned char face_orientation = 1 ) const
inline

Return which child cells are adjacent to a certain face of the mother cell.

For example, in 2D the layout of a quadrilateral cell is as follows:

*      3
*   2-->--3
*   |     |
* 0 ^     ^ 1
*   |     |
*   0-->--1
*      2
* 

Vertices and faces are indicated with their numbers, faces also with their directions.

Now, when refined, the layout is like this:

* *---*---*
* | 2 | 3 |
* *---*---*
* | 0 | 1 |
* *---*---*
* 

Thus, the child cells on face 0 are (ordered in the direction of the face) 0 and 2, on face 3 they are 2 and 3, etc.

For three spatial dimensions, the exact order of the children is laid down in the general documentation of this class.

The face_orientation argument is meant exclusively for quadrilaterals and hexahedra at the moment. It determines how this function handles faces oriented in the standard and non-standard orientation. It represents a bit-code for the overall face_orientation, face_flip and face_rotation and defaults to the standard orientation. The concept of face orientations is explained in this glossary entry.

Definition at line 1239 of file reference_cell.h.

## ◆ standard_vertex_to_face_and_vertex_index()

 std::array< unsigned int, 2 > ReferenceCell::standard_vertex_to_face_and_vertex_index ( const unsigned int vertex ) const
inline

For a given vertex in a cell, return a pair of a face index and a vertex index within this face.

Note
In practice, a vertex is of course generally part of more than one face, and one could return different faces and the corresponding index within. Which face this function chooses is often not of importance (and not exposed by this function on purpose).

Definition at line 1310 of file reference_cell.h.

## ◆ standard_line_to_face_and_line_index()

 std::array< unsigned int, 2 > ReferenceCell::standard_line_to_face_and_line_index ( const unsigned int line ) const
inline

For a given line in a cell, return a pair of a face index and a line index within this face.

Note
In practice, a line is of course generally part of more than one face, and one could return different faces and the corresponding index within. Which face this function chooses is often not of importance (and not exposed by this function on purpose).

Definition at line 1370 of file reference_cell.h.

## ◆ face_to_cell_lines()

 unsigned int ReferenceCell::face_to_cell_lines ( const unsigned int face, const unsigned int line, const unsigned char face_orientation ) const
inline

Map face line number to cell line number.

Definition at line 1438 of file reference_cell.h.

## ◆ face_to_cell_vertices()

 unsigned int ReferenceCell::face_to_cell_vertices ( const unsigned int face, const unsigned int vertex, const unsigned char face_orientation ) const
inline

Map face vertex number to cell vertex number.

Definition at line 1520 of file reference_cell.h.

## ◆ standard_to_real_face_vertex()

 unsigned int ReferenceCell::standard_to_real_face_vertex ( const unsigned int vertex, const unsigned int face, const unsigned char face_orientation ) const
inline

Correct vertex index depending on face orientation.

Definition at line 1605 of file reference_cell.h.

## ◆ standard_to_real_face_line()

 unsigned int ReferenceCell::standard_to_real_face_line ( const unsigned int line, const unsigned int face, const unsigned char face_orientation ) const
inline

Correct line index depending on face orientation.

Definition at line 1703 of file reference_cell.h.

## ◆ standard_vs_true_line_orientation()

 bool ReferenceCell::standard_vs_true_line_orientation ( const unsigned int line, const unsigned char face_orientation, const bool line_orientation ) const
inline

Return whether the line with index line is oriented in standard direction within a cell, given the face_orientation of the face within the current cell, and line_orientation flag for the line within that face. true indicates that the line is oriented from vertex 0 to vertex 1, whereas it is the other way around otherwise. In 1d and 2d, this is always true, but in 3d it may be different, see the respective discussion in the documentation of the GeometryInfo class.

Definition at line 2239 of file reference_cell.h.

## ◆ volume()

 double ReferenceCell::volume ( ) const
inline

Return the $$d$$-dimensional volume of the reference cell that corresponds to the current object, where $$d$$ is the dimension of the space it lives in. For example, since the quadrilateral reference cell is $$[0,1]^2$$, its volume is one, whereas the volume of the reference triangle is 0.5 because it occupies the area $$\{0 \le x,y \le 1, x+y\le 1\}$$.

For ReferenceCells::Vertex, the reference cell is a zero-dimensional point in a zero-dimensional space. As a consequence, one cannot meaningfully define a volume for it. The function returns one for this case, because this makes it possible to define useful quadrature rules based on the center of a reference cell and its volume.

Definition at line 2015 of file reference_cell.h.

## ◆ barycenter()

template<int dim>
 Point< dim > ReferenceCell::barycenter
inline

Return the barycenter (i.e., the center of mass) of the reference cell that corresponds to the current object. The function is not called center() because one can define the center of an object in a number of different ways whereas the barycenter of a reference cell $$K$$ is unambiguously defined as

$\mathbf x_K = \frac{1}{V} \int_K \mathbf x \; dx$

where $$V$$ is the volume of the reference cell (see also the volume() function).

Definition at line 2042 of file reference_cell.h.

## ◆ contains_point()

template<int dim>
 bool ReferenceCell::contains_point ( const Point< dim > & p, const double tolerance = 0 ) const
inline

Return true if the given point is inside the reference cell of the present space dimension up to some tolerance. This function accepts an additional parameter (which defaults to zero) which specifies by how much the point position may actually be outside the true reference cell. This is useful because in practice we may often not be able to compute the coordinates of a point in reference coordinates exactly, but only up to numerical roundoff. For example, strictly speaking one would expect that for points on the boundary of the reference cell, the function would return true if the tolerance was zero. But in practice, this may or may not actually be true; for example, the point $$(1/3, 2/3)$$ is on the boundary of the reference triangle because $$1/3+2/3 \le 1$$, but since neither of its coordinates are exactly representable in floating point arithmetic, the floating point representations of $$1/3$$ and $$2/3$$ may or may not add up to anything that is less than or equal to one.

The tolerance parameter may be less than zero, indicating that the point should be safely inside the cell.

Definition at line 2071 of file reference_cell.h.

## ◆ unit_tangential_vectors()

template<int dim>
 Tensor< 1, dim > ReferenceCell::unit_tangential_vectors ( const unsigned int face_no, const unsigned int i ) const
inline

Definition at line 2133 of file reference_cell.h.

## ◆ unit_normal_vectors()

template<int dim>
 Tensor< 1, dim > ReferenceCell::unit_normal_vectors ( const unsigned int face_no ) const
inline

Return the unit normal vector of a face of the reference cell.

Definition at line 2209 of file reference_cell.h.

## ◆ compute_orientation()

template<typename T , std::size_t N>
 unsigned char ReferenceCell::compute_orientation ( const std::array< T, N > & vertices_0, const std::array< T, N > & vertices_1 ) const
inline

Determine the orientation of the current entity described by its vertices var_1 relative to an entity described by var_0.

Definition at line 2332 of file reference_cell.h.

## ◆ permute_according_orientation()

template<typename T , std::size_t N>
 std::array< T, N > ReferenceCell::permute_according_orientation ( const std::array< T, N > & vertices, const unsigned int orientation ) const
inline

Inverse function of compute_orientation().

Definition at line 2427 of file reference_cell.h.

## ◆ faces_for_given_vertex()

 ArrayView< const unsigned int > ReferenceCell::faces_for_given_vertex ( const unsigned int vertex_index ) const
inline

Return a vector of faces a given vertex_index belongs to.

Definition at line 846 of file reference_cell.h.

## ◆ exodusii_vertex_to_deal_vertex()

 unsigned int ReferenceCell::exodusii_vertex_to_deal_vertex ( const unsigned int vertex_n ) const

Map an ExodusII vertex number to a deal.II vertex number.

Definition at line 243 of file reference_cell.cc.

## ◆ exodusii_face_to_deal_face()

 unsigned int ReferenceCell::exodusii_face_to_deal_face ( const unsigned int face_n ) const

Map an ExodusII face number to a deal.II face number.

Definition at line 289 of file reference_cell.cc.

## ◆ unv_vertex_to_deal_vertex()

 unsigned int ReferenceCell::unv_vertex_to_deal_vertex ( const unsigned int vertex_n ) const

Map a UNV vertex number to a deal.II vertex number.

Definition at line 339 of file reference_cell.cc.

## ◆ vtk_linear_type()

 unsigned int ReferenceCell::vtk_linear_type ( ) const

Return a VTK linear shape constant that corresponds to the reference cell.

Definition at line 375 of file reference_cell.cc.

 unsigned int ReferenceCell::vtk_quadratic_type ( ) const

Return a VTK quadratic shape constant that corresponds to the reference cell.

Definition at line 404 of file reference_cell.cc.

## ◆ vtk_lagrange_type()

 unsigned int ReferenceCell::vtk_lagrange_type ( ) const

Return a VTK Lagrange shape constant that corresponds to the reference cell.

Definition at line 433 of file reference_cell.cc.

## ◆ gmsh_element_type()

 unsigned int ReferenceCell::gmsh_element_type ( ) const

Return the GMSH element type code that corresponds to the reference cell.

Definition at line 462 of file reference_cell.cc.

## ◆ to_string()

 std::string ReferenceCell::to_string ( ) const

Return a text representation of the reference cell represented by the current object.

Definition at line 81 of file reference_cell.cc.

## ◆ operator std::uint8_t()

 constexpr ReferenceCell::operator std::uint8_t ( ) const
inlineconstexpr

Conversion operator to an integer.

Definition at line 735 of file reference_cell.h.

## ◆ operator==()

 constexpr bool ReferenceCell::operator== ( const ReferenceCell & type ) const
inlineconstexpr

Operator for equality comparison.

Definition at line 743 of file reference_cell.h.

## ◆ operator!=()

 constexpr bool ReferenceCell::operator!= ( const ReferenceCell & type ) const
inlineconstexpr

Operator for inequality comparison.

Definition at line 751 of file reference_cell.h.

## ◆ serialize()

template<class Archive >
 void ReferenceCell::serialize ( Archive & archive, const unsigned int )
inline

Write and read the data of this object from a stream for the purpose of serialization using the BOOST serialization library.

Definition at line 838 of file reference_cell.h.

## ◆ internal::ReferenceCell::make_reference_cell_from_int

 constexpr friend ReferenceCell internal::ReferenceCell::make_reference_cell_from_int ( const std::uint8_t )
friend

A kind of constructor – not quite private because it can be called by anyone, but at least hidden in an internal namespace.

## ◆ operator<<

 std::ostream& operator<< ( std::ostream & out, const ReferenceCell & reference_cell )
friend

Output operator that writes the reference_cell object to the stream in a text format in which the object is represented by an integer. The details of which integer value represents each kind of reference cell is unimportant and consequently not specified. If you want a string representation of what a ReferenceCell is, use ReferenceCell::to_string().

Definition at line 546 of file reference_cell.cc.

## ◆ operator>>

 std::istream& operator>> ( std::istream & in, ReferenceCell & reference_cell )
friend

Input operator that reads the reference_cell object from the stream in a text format in which the object is represented by an integer. Which specific integer value represents which reference cell is unspecified, but the function uses the same translation as the corresponding output operator<<.

Definition at line 560 of file reference_cell.cc.

## ◆ kind

 std::uint8_t ReferenceCell::kind
private

The variable that stores what this object actually corresponds to.

Definition at line 683 of file reference_cell.h.

The documentation for this class was generated from the following files: