Reference documentation for deal.II version Git 1ecc23629d 20210518 09:57:04 +0200

#include <deal.II/grid/tria_accessor.h>
Public Types  
using  AccessorData = typename TriaAccessor< dim, dim, spacedim >::AccessorData 
using  Container = Triangulation< dim, spacedim > 
using  LocalData = void * 
Public Member Functions  
types::global_cell_index  global_active_cell_index () const 
types::global_cell_index  global_level_cell_index () const 
template<>  
bool  point_inside (const Point< 1 > &p) const 
template<>  
bool  point_inside (const Point< 2 > &p) const 
template<>  
bool  point_inside (const Point< 3 > &p) const 
template<>  
bool  point_inside (const Point< 2 > &p) const 
template<>  
bool  point_inside (const Point< 3 > &p) const 
template<>  
bool  point_inside (const Point< 3 > &p) const 
bool  used () const 
void  set_all_manifold_ids (const types::manifold_id manifold_ind) const 
double  extent_in_direction (const unsigned int axis) const 
double  extent_in_direction (const unsigned int axis) const 
double  extent_in_direction (const unsigned int axis) const 
double  extent_in_direction (const unsigned int axis) const 
double  extent_in_direction (const unsigned int axis) const 
Constructors  
CellAccessor (const Triangulation< dim, spacedim > *parent=nullptr, const int level=1, const int index=1, const AccessorData *local_data=nullptr)  
CellAccessor (const TriaAccessor< dim, dim, spacedim > &cell_accessor)  
template<int structdim2, int dim2, int spacedim2>  
CellAccessor (const InvalidAccessor< structdim2, dim2, spacedim2 > &)  
template<int structdim2, int dim2, int spacedim2>  
CellAccessor (const TriaAccessor< structdim2, dim2, spacedim2 > &)  
void  operator= (const CellAccessor< dim, spacedim > &)=delete 
Dealing with periodic neighbors  
bool  has_periodic_neighbor (const unsigned int i) const 
TriaIterator< CellAccessor< dim, spacedim > >  periodic_neighbor (const unsigned int i) const 
TriaIterator< CellAccessor< dim, spacedim > >  neighbor_or_periodic_neighbor (const unsigned int i) const 
TriaIterator< CellAccessor< dim, spacedim > >  periodic_neighbor_child_on_subface (const unsigned int face_no, const unsigned int subface_no) const 
std::pair< unsigned int, unsigned int >  periodic_neighbor_of_coarser_periodic_neighbor (const unsigned face_no) const 
int  periodic_neighbor_index (const unsigned int i) const 
int  periodic_neighbor_level (const unsigned int i) const 
unsigned int  periodic_neighbor_of_periodic_neighbor (const unsigned int i) const 
unsigned int  periodic_neighbor_face_no (const unsigned int i) const 
bool  periodic_neighbor_is_coarser (const unsigned int i) const 
Dealing with boundary indicators  
bool  at_boundary (const unsigned int i) const 
bool  at_boundary () const 
bool  has_boundary_lines () const 
Dealing with refinement indicators  
RefinementCase< dim >  refine_flag_set () const 
void  set_refine_flag (const RefinementCase< dim > ref_case=RefinementCase< dim >::isotropic_refinement) const 
void  clear_refine_flag () const 
bool  flag_for_face_refinement (const unsigned int face_no, const RefinementCase< dim  1 > &face_refinement_case=RefinementCase< dim  1 >::isotropic_refinement) const 
bool  flag_for_line_refinement (const unsigned int line_no) const 
::internal::SubfaceCase< dim >  subface_case (const unsigned int face_no) const 
bool  coarsen_flag_set () const 
void  set_coarsen_flag () const 
void  clear_coarsen_flag () const 
Dealing with material indicators  
types::material_id  material_id () const 
void  set_material_id (const types::material_id new_material_id) const 
void  recursively_set_material_id (const types::material_id new_material_id) const 
Dealing with subdomain indicators  
types::subdomain_id  subdomain_id () const 
void  set_subdomain_id (const types::subdomain_id new_subdomain_id) const 
types::subdomain_id  level_subdomain_id () const 
void  set_level_subdomain_id (const types::subdomain_id new_level_subdomain_id) const 
void  recursively_set_subdomain_id (const types::subdomain_id new_subdomain_id) const 
Dealing with codim 1 cell orientation  
bool  direction_flag () const 
unsigned int  active_cell_index () const 
int  parent_index () const 
TriaIterator< CellAccessor< dim, spacedim > >  parent () const 
Other functions  
bool  active () const 
bool  is_active () const 
bool  is_locally_owned () const 
bool  is_locally_owned_on_level () const 
bool  is_ghost () const 
bool  is_artificial () const 
bool  point_inside (const Point< spacedim > &p) const 
void  set_neighbor (const unsigned int i, const TriaIterator< CellAccessor< dim, spacedim >> &pointer) const 
CellId  id () const 
double  diameter (const Mapping< dim, spacedim > &mapping) const 
Accessing subobjects  
TriaIterator< TriaAccessor< 0, dim, spacedim > >  vertex_iterator (const unsigned int i) const 
unsigned int  vertex_index (const unsigned int i) const 
Point< spacedim > &  vertex (const unsigned int i) const 
typename ::internal::TriangulationImplementation::Iterators< dim, spacedim >::line_iterator  line (const unsigned int i) const 
unsigned int  line_index (const unsigned int i) const 
typename ::internal::TriangulationImplementation::Iterators< dim, spacedim >::quad_iterator  quad (const unsigned int i) const 
unsigned int  quad_index (const unsigned int i) const 
Orientation of subobjects  
bool  face_orientation (const unsigned int face) const 
bool  face_flip (const unsigned int face) const 
bool  face_rotation (const unsigned int face) const 
bool  line_orientation (const unsigned int line) const 
Accessing children  
bool  has_children () const 
unsigned int  n_children () const 
unsigned int  number_of_children () const 
unsigned int  n_active_descendants () const 
unsigned int  max_refinement_depth () const 
unsigned int  child_iterator_to_index (const TriaIterator< TriaAccessor< structdim, dim, spacedim >> &child) const 
TriaIterator< TriaAccessor< structdim, dim, spacedim > >  isotropic_child (const unsigned int i) const 
RefinementCase< structdim >  refinement_case () const 
int  child_index (const unsigned int i) const 
int  isotropic_child_index (const unsigned int i) const 
Dealing with boundary indicators  
types::boundary_id  boundary_id () const 
void  set_boundary_id (const types::boundary_id) const 
void  set_all_boundary_ids (const types::boundary_id) const 
const Manifold< dim, spacedim > &  get_manifold () const 
Dealing with manifold indicators  
types::manifold_id  manifold_id () const 
void  set_manifold_id (const types::manifold_id) const 
void  set_all_manifold_ids (const types::manifold_id) const 
User data  
bool  user_flag_set () const 
void  set_user_flag () const 
void  clear_user_flag () const 
void  recursively_set_user_flag () const 
void  recursively_clear_user_flag () const 
void  clear_user_data () const 
void  set_user_pointer (void *p) const 
void  clear_user_pointer () const 
void *  user_pointer () const 
void  recursively_set_user_pointer (void *p) const 
void  recursively_clear_user_pointer () const 
void  set_user_index (const unsigned int p) const 
void  clear_user_index () const 
unsigned int  user_index () const 
void  recursively_set_user_index (const unsigned int p) const 
void  recursively_clear_user_index () const 
Geometric information about an object  
double  diameter () const 
std::pair< Point< spacedim >, double >  enclosing_ball () const 
BoundingBox< spacedim >  bounding_box () const 
double  extent_in_direction (const unsigned int axis) const 
double  minimum_vertex_distance () const 
Point< spacedim >  intermediate_point (const Point< structdim > &coordinates) const 
Point< structdim >  real_to_unit_cell_affine_approximation (const Point< spacedim > &point) const 
Point< spacedim >  center (const bool respect_manifold=false, const bool interpolate_from_surrounding=false) const 
Point< spacedim >  barycenter () const 
double  measure () const 
bool  is_translation_of (const TriaIterator< TriaAccessor< structdim, dim, spacedim >> &o) const 
ReferenceCell  reference_cell () const 
unsigned int  n_vertices () const 
unsigned int  n_lines () const 
unsigned int  n_faces () const 
std_cxx20::ranges::iota_view< unsigned int, unsigned int >  vertex_indices () const 
std_cxx20::ranges::iota_view< unsigned int, unsigned int >  line_indices () const 
std_cxx20::ranges::iota_view< unsigned int, unsigned int >  face_indices () const 
Iterator address and state  
int  level () const 
int  index () const 
IteratorState::IteratorStates  state () const 
const Triangulation< dim, spacedim > &  get_triangulation () const 
Static Public Member Functions  
static ::ExceptionBase &  ExcRefineCellNotActive () 
static ::ExceptionBase &  ExcCellFlaggedForRefinement () 
static ::ExceptionBase &  ExcCellFlaggedForCoarsening () 
Static Public Attributes  
static const unsigned int  space_dimension = spacedim 
static const unsigned int  dimension = dim 
static const unsigned int  structure_dimension = structdim 
Protected Member Functions  
unsigned int  neighbor_of_neighbor_internal (const unsigned int neighbor) const 
template<int dim_, int spacedim_>  
bool  point_inside_codim (const Point< spacedim_ > &p) const 
void  copy_from (const TriaAccessorBase &) 
bool  operator< (const TriaAccessorBase &other) const 
bool  operator== (const TriaAccessorBase &) const 
bool  operator!= (const TriaAccessorBase &) const 
::internal::TriangulationImplementation::TriaObjects &  objects () const 
Advancement of iterators  
void  operator++ () 
void  operator () 
Protected Attributes  
typename ::internal::TriaAccessorImplementation::PresentLevelType< structdim, dim >::type  present_level 
int  present_index 
const Triangulation< dim, spacedim > *  tria 
Private Member Functions  
void  set_active_cell_index (const unsigned int active_cell_index) const 
void  set_global_active_cell_index (const types::global_cell_index index) const 
void  set_global_level_cell_index (const types::global_cell_index index) const 
void  set_parent (const unsigned int parent_index) 
void  set_direction_flag (const bool new_direction_flag) const 
Friends  
template<int , int >  
class  Triangulation 
template<int , int >  
class  parallel::TriangulationBase 
struct  ::internal::TriangulationImplementation::Implementation 
struct  ::internal::TriangulationImplementation::ImplementationMixedMesh 
Accessing subobjects and neighbors  
TriaIterator< CellAccessor< dim, spacedim > >  child (const unsigned int i) const 
boost::container::small_vector< TriaIterator< CellAccessor< dim, spacedim > >, GeometryInfo< dim >::max_children_per_cell >  child_iterators () const 
TriaIterator< TriaAccessor< dim  1, dim, spacedim > >  face (const unsigned int i) const 
unsigned int  face_iterator_to_index (const TriaIterator< TriaAccessor< dim  1, dim, spacedim >> &face) const 
boost::container::small_vector< TriaIterator< TriaAccessor< dim  1, dim, spacedim > >, GeometryInfo< dim >::faces_per_cell >  face_iterators () const 
unsigned int  face_index (const unsigned int i) const 
TriaIterator< CellAccessor< dim, spacedim > >  neighbor_child_on_subface (const unsigned int face_no, const unsigned int subface_no) const 
TriaIterator< CellAccessor< dim, spacedim > >  neighbor (const unsigned int face_no) const 
int  neighbor_index (const unsigned int face_no) const 
int  neighbor_level (const unsigned int face_no) const 
unsigned int  neighbor_of_neighbor (const unsigned int face_no) const 
bool  neighbor_is_coarser (const unsigned int face_no) const 
std::pair< unsigned int, unsigned int >  neighbor_of_coarser_neighbor (const unsigned int neighbor) const 
unsigned int  neighbor_face_no (const unsigned int neighbor) const 
static bool  is_level_cell () 
This class allows access to a cell: a line in one dimension, a quad in two dimension, etc.
The following refers to any dimension:
This class allows access to a cell
, which is a line in 1D and a quad in 2D. Cells have more functionality than lines or quads by themselves, for example they can be flagged for refinement, they have neighbors, they have the possibility to check whether they are at the boundary etc. This class offers access to all this data.
Definition at line 2804 of file tria_accessor.h.
using CellAccessor< dim, spacedim >::AccessorData = typename TriaAccessor<dim, dim, spacedim>::AccessorData 
Propagate the AccessorData type into the present class.
Definition at line 2810 of file tria_accessor.h.
using CellAccessor< dim, spacedim >::Container = Triangulation<dim, spacedim> 
Define the type of the container this is part of.
Definition at line 2815 of file tria_accessor.h.

inherited 
Data type to be used for passing parameters from iterators to the accessor classes in a unified way, no matter what the type of number of these parameters is.
Definition at line 441 of file tria_accessor.h.
CellAccessor< dim, spacedim >::CellAccessor  (  const Triangulation< dim, spacedim > *  parent = nullptr , 
const int  level = 1 , 

const int  index = 1 , 

const AccessorData *  local_data = nullptr 

) 
Constructor.
CellAccessor< dim, spacedim >::CellAccessor  (  const TriaAccessor< dim, dim, spacedim > &  cell_accessor  ) 
Copy constructor.
CellAccessor< dim, spacedim >::CellAccessor  (  const InvalidAccessor< structdim2, dim2, spacedim2 > &  ) 
Conversion constructor. This constructor exists to make certain constructs simpler to write in dimension independent code. For example, it allows assigning a face iterator to a line iterator, an operation that is useful in 2d but doesn't make any sense in 3d. The constructor here exists for the purpose of making the code conform to C++ but it will unconditionally abort; in other words, assigning a face iterator to a line iterator is better put into an ifstatement that checks that the dimension is two, and assign to a quad iterator in 3d (an operator that, without this constructor would be illegal if we happen to compile for 2d).
Definition at line 3885 of file tria_accessor.h.
CellAccessor< dim, spacedim >::CellAccessor  (  const TriaAccessor< structdim2, dim2, spacedim2 > &  ) 
Another conversion operator between objects that don't make sense, just like the previous one.
Definition at line 3915 of file tria_accessor.h.

delete 
Copy operator. These operators are usually used in a context like iterator a,b; *a=*b;
. Presumably, the intent here is to copy the object pointed to by b
to the object pointed to by a
. However, the result of dereferencing an iterator is not an object but an accessor; consequently, this operation is not useful for iterators on triangulations. Consequently, this operator is declared as deleted and can not be used.
TriaIterator<CellAccessor<dim, spacedim> > CellAccessor< dim, spacedim >::child  (  const unsigned int  i  )  const 
Return a pointer to the ith
child. Overloaded version which returns a more reasonable iterator class.
boost::container::small_vector<TriaIterator<CellAccessor<dim, spacedim> >, GeometryInfo<dim>::max_children_per_cell> CellAccessor< dim, spacedim >::child_iterators  (  )  const 
Return an array of iterators to all children of this cell.
TriaIterator<TriaAccessor<dim  1, dim, spacedim> > CellAccessor< dim, spacedim >::face  (  const unsigned int  i  )  const 
Return an iterator to the ith
face of this cell.
unsigned int CellAccessor< dim, spacedim >::face_iterator_to_index  (  const TriaIterator< TriaAccessor< dim  1, dim, spacedim >> &  face  )  const 
Return the face number of face
on the current cell. This is the inverse function of TriaAccessor::face().
boost::container::small_vector< TriaIterator<TriaAccessor<dim  1, dim, spacedim> >, GeometryInfo<dim>::faces_per_cell> CellAccessor< dim, spacedim >::face_iterators  (  )  const 
Return an array of iterators to all faces of this cell.
unsigned int CellAccessor< dim, spacedim >::face_index  (  const unsigned int  i  )  const 
Return the (global) index of the ith
face of this cell.
TriaIterator< CellAccessor< dim, spacedim > > CellAccessor< dim, spacedim >::neighbor_child_on_subface  (  const unsigned int  face_no, 
const unsigned int  subface_no  
)  const 
Return an iterator to that cell that neighbors the present cell on the given face and subface number.
To succeed, the present cell must not be further refined, and the neighbor on the given face must be further refined exactly once; the returned cell is then a child of that neighbor.
The function may not be called in 1d, since there we have no subfaces. The implementation of this function is rather straightforward in 2d, by first determining which face of the neighbor cell the present cell is bordering on (this is what the neighbor_of_neighbor
function does), and then asking GeometryInfo::child_cell_on_subface
for the index of the child.
However, the situation is more complicated in 3d, since there faces may have more than one orientation, and we have to use face_orientation
, face_flip
and face_rotation
for both this and the neighbor cell to figure out which cell we want to have.
This can lead to surprising results: if we are sitting on a cell and are asking for a cell behind subface sf
, then this means that we are considering the subface for the face in the natural direction for the present cell. However, if the face as seen from this cell has face_orientation()==false
, then the child of the face that separates the present cell from the neighboring cell's child is not necessarily the sfth
child of the face of this cell. This is so because the subface_no
on a cell corresponds to the subface with respect to the intrinsic ordering of the present cell, whereas children of face iterators are computed with respect to the intrinsic ordering of faces; these two orderings are only identical if the face orientation is true
, and reversed otherwise.
Similarly, effects of face_flip()==true
and face_rotation()==true()
, both of which indicate a nonstandard face have to be considered.
Fortunately, this is only very rarely of concern, since usually one simply wishes to loop over all finer neighbors at a given face of an active cell. Only in the process of refinement of a Triangulation we want to set neighbor information for both our child cells and the neighbor's children. Since we can respect orientation of faces from our current cell in that case, we do NOT respect face_orientation, face_flip and face_rotation of the present cell within this function, i.e. the returned neighbor's child is behind subface subface
concerning the intrinsic ordering of the given face.
Definition at line 2865 of file tria_accessor.cc.
TriaIterator<CellAccessor<dim, spacedim> > CellAccessor< dim, spacedim >::neighbor  (  const unsigned int  face_no  )  const 
Return an iterator to the neighboring cell on the other side of the face with number face_no
. If the neighbor does not exist, i.e., if the face with number face_no
of the current object is at the boundary, then an invalid iterator is returned.
Consequently, the index face_no
must be less than n_faces().
The neighbor of a cell has at most the same level as this cell. For example, consider the following situation:
Here, if you are on the top right cell and you ask for its left neighbor (which is, according to the conventions spelled out in the GeometryInfo class, its zeroth neighbor), then you will get the mother cell of the four small cells at the top left. In other words, the cell you get as neighbor has the same refinement level as the one you're on right now (the top right one) and it may have children.
On the other hand, if you were at the top right cell of the four small cells at the top left, and you asked for the right neighbor (which is associated with index face_no=1
), then you would get the large cell at the top right which in this case has a lower refinement level and no children of its own.
int CellAccessor< dim, spacedim >::neighbor_index  (  const unsigned int  face_no  )  const 
Return the cell index of the neighboring cell on the other side of the face with index face_no
. If the neighbor does not exist, this function returns 1.
This function is equivalent to cell>neighbor(face_no)>index()
. See neighbor() for more details.
int CellAccessor< dim, spacedim >::neighbor_level  (  const unsigned int  face_no  )  const 
Return the level of the neighboring cell on the other side of the face with number face_no
. If the neighbor does not exist, this function returns 1.
This function is equivalent to cell>neighbor(face_no)>level()
. See neighbor() for more details.
unsigned int CellAccessor< dim, spacedim >::neighbor_of_neighbor  (  const unsigned int  face_no  )  const 
Return the howmany'th neighbor this cell is of cell>neighbor(face_no)
, i.e. return other_face_no
such that cell>neighbor(face_no)>neighbor(other_face_no)==cell
. This function is the right one if you want to know how to get back from a neighbor to the present cell.
Note that this operation is only useful if the neighbor is not coarser than the present cell. If the neighbor is coarser this function throws an exception. Use the neighbor_of_coarser_neighbor
function in that case.
Definition at line 2333 of file tria_accessor.cc.
bool CellAccessor< dim, spacedim >::neighbor_is_coarser  (  const unsigned int  face_no  )  const 
Return, whether the neighbor is coarser then the present cell. This is important in case of anisotropic refinement where this information does not depend on the levels of the cells.
Note, that in an anisotropic setting, a cell can only be coarser than another one at a given face, not on a general basis. The face of the finer cell is contained in the corresponding face of the coarser cell, the finer face is either a child or a grandchild of the coarser face.
Definition at line 2347 of file tria_accessor.cc.
std::pair< unsigned int, unsigned int > CellAccessor< dim, spacedim >::neighbor_of_coarser_neighbor  (  const unsigned int  neighbor  )  const 
This function is a generalization of the neighbor_of_neighbor
function for the case of a coarser neighbor. It returns a pair of numbers, face_no and subface_no, with the following property, if the neighbor is not refined: cell>neighbor(neighbor)>neighbor_child_on_subface(face_no, subface_no)==cell
. In 3D, a coarser neighbor can still be refined. In that case subface_no denotes the child index of the neighbors face that relates to our face: cell>neighbor(neighbor)>face(face_no)>child(subface_no)==cell>face(neighbor)
. This case in 3d and how it can happen is discussed in the introduction of the step30 tutorial program.
This function is impossible for dim==1
.
Definition at line 2358 of file tria_accessor.cc.
unsigned int CellAccessor< dim, spacedim >::neighbor_face_no  (  const unsigned int  neighbor  )  const 
This function is a generalization of the neighbor_of_neighbor
and the neighbor_of_coarser_neighbor
functions. It checks whether the neighbor is coarser or not and calls the respective function. In both cases, only the face_no is returned.

static 
Compatibility interface with DoFCellAccessor. Always returns false
.
bool CellAccessor< dim, spacedim >::has_periodic_neighbor  (  const unsigned int  i  )  const 
If the cell has a periodic neighbor at its ith
face, this function returns true, otherwise, the returned value is false.
Definition at line 2534 of file tria_accessor.cc.
TriaIterator< CellAccessor< dim, spacedim > > CellAccessor< dim, spacedim >::periodic_neighbor  (  const unsigned int  i  )  const 
For a cell with its ith
face at a periodic boundary, see the entry for periodic boundaries, this function returns an iterator to the cell on the other side of the periodic boundary. If there is no periodic boundary at the ith
face, an exception will be thrown. In order to avoid running into an exception, check the result of has_periodic_neighbor() for the ith
face prior to using this function. The behavior of periodic_neighbor() is similar to neighbor(), in the sense that the returned cell has at most the same level of refinement as the current cell. On distributed meshes, by calling Triangulation::add_periodicity(), we can make sure that the element on the other side of the periodic boundary exists in this rank as a ghost cell or a locally owned cell.
Definition at line 2562 of file tria_accessor.cc.
TriaIterator< CellAccessor< dim, spacedim > > CellAccessor< dim, spacedim >::neighbor_or_periodic_neighbor  (  const unsigned int  i  )  const 
For a cell whose ith
face is not at a boundary, this function returns the same result as neighbor(). If the ith
face is at a periodic boundary this function returns the same result as periodic_neighbor(). If neither of the aforementioned conditions are met, i.e. the ith
face is on a nonperiodic boundary, an exception will be thrown.
Definition at line 2589 of file tria_accessor.cc.
TriaIterator< CellAccessor< dim, spacedim > > CellAccessor< dim, spacedim >::periodic_neighbor_child_on_subface  (  const unsigned int  face_no, 
const unsigned int  subface_no  
)  const 
Return an iterator to the periodic neighbor of the cell at a given face and subface number. The general guidelines for using this function is similar to the function neighbor_child_on_subface(). The implementation of this function is consistent with periodic_neighbor_of_coarser_periodic_neighbor(). For instance, assume that we are sitting on a cell named cell1
, whose neighbor behind the ith
face is one level coarser. Let us name this coarser neighbor cell2
. Then, by calling periodic_neighbor_of_coarser_periodic_neighbor(), from cell1
, we get a face_num
and a subface_num
. Now, if we call periodic_neighbor_child_on_subface() from cell2, with the above face_num and subface_num, we get an iterator to cell1
.
Definition at line 2606 of file tria_accessor.cc.
std::pair< unsigned int, unsigned int > CellAccessor< dim, spacedim >::periodic_neighbor_of_coarser_periodic_neighbor  (  const unsigned  face_no  )  const 
This function is a generalization of periodic_neighbor_of_periodic_neighbor() for those cells which have a coarser periodic neighbor. The returned pair of numbers can be used in periodic_neighbor_child_on_subface() to get back to the current cell. In other words, the following assertion should be true, for a cell with coarser periodic neighbor: cell>periodic_neighbor(i)>periodic_neighbor_child_on_subface(face_no, subface_no)==cell
Definition at line 2658 of file tria_accessor.cc.
int CellAccessor< dim, spacedim >::periodic_neighbor_index  (  const unsigned int  i  )  const 
This function returns the index of the periodic neighbor at the ith
face of the current cell. If there is no periodic neighbor at the given face, the returned value is 1.
Definition at line 2719 of file tria_accessor.cc.
int CellAccessor< dim, spacedim >::periodic_neighbor_level  (  const unsigned int  i  )  const 
This function returns the level of the periodic neighbor at the ith
face of the current cell. If there is no periodic neighbor at the given face, the returned value is 1.
Definition at line 2729 of file tria_accessor.cc.
unsigned int CellAccessor< dim, spacedim >::periodic_neighbor_of_periodic_neighbor  (  const unsigned int  i  )  const 
For a cell with a periodic neighbor at its ith
face, this function returns the face number of that periodic neighbor such that the current cell is the periodic neighbor of that neighbor. In other words the following assertion holds for those cells which have a periodic neighbor with the same or a higher level of refinement as the current cell: {cell>periodic_neighbor(i)>
periodic_neighbor(cell>periodic_neighbor_of_periodic_neighbor(i))==cell} For the cells with a coarser periodic neighbor, one should use periodic_neighbor_of_coarser_periodic_neighbor() and periodic_neighbor_child_on_subface() to get back to the current cell.
Definition at line 2739 of file tria_accessor.cc.
unsigned int CellAccessor< dim, spacedim >::periodic_neighbor_face_no  (  const unsigned int  i  )  const 
If a cell has a periodic neighbor at its ith
face, this function returns the face number of the periodic neighbor, which is connected to the ith
face of this cell.
Definition at line 2749 of file tria_accessor.cc.
bool CellAccessor< dim, spacedim >::periodic_neighbor_is_coarser  (  const unsigned int  i  )  const 
This function returns true if the element on the other side of the periodic boundary is coarser and returns false otherwise. The implementation allows this function to work in the case of anisotropic refinement.
Definition at line 2780 of file tria_accessor.cc.
bool CellAccessor< dim, spacedim >::at_boundary  (  const unsigned int  i  )  const 
Return whether the ith
vertex or face (depending on the dimension) is part of the boundary. This is true, if the ith
neighbor does not exist.
Definition at line 2835 of file tria_accessor.cc.
bool CellAccessor< dim, spacedim >::at_boundary  (  )  const 
Return whether the cell is at the boundary. Being at the boundary is defined by one face being on the boundary. Note that this does not catch cases where only one vertex of a quad or of a hex is at the boundary, or where only one line of a hex is at the boundary while the interiors of all faces are in the interior of the domain. For the latter case, the has_boundary_lines
function is the right one to ask.
Definition at line 1952 of file tria_accessor.cc.
bool CellAccessor< dim, spacedim >::has_boundary_lines  (  )  const 
This is a slight variation to the at_boundary
function: for 1 and 2 dimensions, it is equivalent, for three dimensions it returns whether at least one of the 12 lines of the hexahedron is at a boundary. This, of course, includes the case where a whole face is at the boundary, but also some other cases.
Definition at line 2847 of file tria_accessor.cc.
RefinementCase<dim> CellAccessor< dim, spacedim >::refine_flag_set  (  )  const 
Return the RefinementCase<dim>
this cell was flagged to be refined with. The return value of this function can be compared to a bool to check if this cell is flagged for any kind of refinement. For example, if you have previously called cell>set_refine_flag() for a cell, then you will enter the 'if' block in the following snippet:
void CellAccessor< dim, spacedim >::set_refine_flag  (  const RefinementCase< dim >  ref_case = RefinementCase< dim >::isotropic_refinement  )  const 
Flag the cell pointed to for refinement. This function is only allowed for active cells. Keeping the default value for ref_case
will mark this cell for isotropic refinement.
If you choose anisotropic refinement, for example by passing as argument one of the flags RefinementCase::cut_x, RefinementCase::cut_y, RefinementCase::cut_z, or a combination of these, then keep in mind that refining in x, y, or zdirection happens with regard to the local coordinate system of the cell. In other words, these flags determine which edges and faces of the cell will be cut into new edges and faces. On the other hand, this process is independent of how the cell is oriented within the global coordinate system, and you should not assume any particular orientation of the cell's local coordinate system within the global coordinate system of the space it lives in.
void CellAccessor< dim, spacedim >::clear_refine_flag  (  )  const 
Clear the refinement flag.
bool CellAccessor< dim, spacedim >::flag_for_face_refinement  (  const unsigned int  face_no, 
const RefinementCase< dim  1 > &  face_refinement_case = RefinementCase< dim  1 >::isotropic_refinement 

)  const 
Modify the refinement flag of the cell to ensure (at least) the given refinement case face_refinement_case
at face face_no
, taking into account orientation, flip and rotation of the face. Return, whether the refinement flag had to be modified. This function is only allowed for active cells.
bool CellAccessor< dim, spacedim >::flag_for_line_refinement  (  const unsigned int  line_no  )  const 
Modify the refinement flag of the cell to ensure that line face_no
will be refined. Return, whether the refinement flag had to be modified. This function is only allowed for active cells.
::internal::SubfaceCase<dim> CellAccessor< dim, spacedim >::subface_case  (  const unsigned int  face_no  )  const 
Return the SubfaceCase of face face_no
. Note that this is not identical to asking cell>face(face_no)>refinement_case()
since the latter returns a RefinementCase<dim1> and thus only considers one (anisotropic) refinement, whereas this function considers the complete refinement situation including possible refinement of the face's children. This function may only be called for active cells in 2d and 3d.
bool CellAccessor< dim, spacedim >::coarsen_flag_set  (  )  const 
Return whether the coarsen flag is set or not.
void CellAccessor< dim, spacedim >::set_coarsen_flag  (  )  const 
Flag the cell pointed to for coarsening. This function is only allowed for active cells.
void CellAccessor< dim, spacedim >::clear_coarsen_flag  (  )  const 
Clear the coarsen flag.
types::material_id CellAccessor< dim, spacedim >::material_id  (  )  const 
Return the material id of this cell.
For a typical use of this function, see the step28 tutorial program.
See the glossary for more information.
Definition at line 1965 of file tria_accessor.cc.
void CellAccessor< dim, spacedim >::set_material_id  (  const types::material_id  new_material_id  )  const 
Set the material id of this cell.
For a typical use of this function, see the step28 tutorial program.
See the glossary for more information.
Definition at line 1977 of file tria_accessor.cc.
void CellAccessor< dim, spacedim >::recursively_set_material_id  (  const types::material_id  new_material_id  )  const 
Set the material id of this cell and all its children (and grand children, and so on) to the given value.
See the glossary for more information.
Definition at line 1991 of file tria_accessor.cc.
types::subdomain_id CellAccessor< dim, spacedim >::subdomain_id  (  )  const 
Return the subdomain id of this cell.
See the glossary for more information.
void CellAccessor< dim, spacedim >::set_subdomain_id  (  const types::subdomain_id  new_subdomain_id  )  const 
Set the subdomain id of this cell.
See the glossary for more information. This function should not be called if you use a parallel::distributed::Triangulation object.
Definition at line 2005 of file tria_accessor.cc.
types::subdomain_id CellAccessor< dim, spacedim >::level_subdomain_id  (  )  const 
Get the level subdomain id of this cell. This is used for parallel multigrid where not only the global mesh (consisting of the active cells) is partitioned among processors, but also the individual levels of the hierarchy of recursively refined cells that make up the mesh. In other words, the level subdomain id is a property that is also defined for nonactive cells if a multigrid hierarchy is used.
Definition at line 2019 of file tria_accessor.cc.
void CellAccessor< dim, spacedim >::set_level_subdomain_id  (  const types::subdomain_id  new_level_subdomain_id  )  const 
Set the level subdomain id of this cell. This is used for parallel multigrid.
Definition at line 2030 of file tria_accessor.cc.
void CellAccessor< dim, spacedim >::recursively_set_subdomain_id  (  const types::subdomain_id  new_subdomain_id  )  const 
Set the subdomain id of this cell (if it is active) or all its terminal children (and grandchildren, and so on, as long as they have no children of their own) to the given value. Since the subdomain id is a concept that is only defined for cells that are active (i.e., have no children of their own), this function only sets the subdomain ids for all children and grand children of this cell that are actually active, skipping intermediate child cells.
See the glossary for more information. This function should not be called if you use a parallel::distributed::Triangulation object since there the subdomain id is implicitly defined by which processor you're on.
Definition at line 2182 of file tria_accessor.cc.

inline 
Return globally unique cell index for a nonartificial active cell. The value is identical to active_cell_index() in the context of a serial triangulation.
In the context of parallel triangulations, locallyowned cells are enumerated contiguously within each subdomain of the mesh.
If a celldata vector has been set up with parallel::TriangulationBase::global_active_cell_index_partitioner(), the returned index can be used to access the correct vector entry.
Definition at line 2132 of file tria_accessor.cc.

inline 
Return a globally unique index for a nonartificial level cell.
Definition at line 2158 of file tria_accessor.cc.
bool CellAccessor< dim, spacedim >::direction_flag  (  )  const 
Return the orientation of this cell.
For the meaning of this flag, see GlossDirectionFlag.
Definition at line 2041 of file tria_accessor.cc.
unsigned int CellAccessor< dim, spacedim >::active_cell_index  (  )  const 
Return the how manyth active cell the current cell is (assuming the current cell is indeed active). This is useful, for example, if you are accessing the elements of a vector with as many entries as there are active cells. Such vectors are used for estimating the error on each cell of a triangulation, for specifying refinement criteria passed to the functions in GridRefinement, and for generating cellwise output.
The function throws an exception if the current cell is not active.
Definition at line 2099 of file tria_accessor.cc.
int CellAccessor< dim, spacedim >::parent_index  (  )  const 
Return the index of the parent of this cell within the level of the triangulation to which the parent cell belongs. The level of the parent is of course one lower than that of the present cell. If the parent does not exist (i.e., if the object is at the coarsest level of the mesh hierarchy), an exception is generated.
Definition at line 2084 of file tria_accessor.cc.
TriaIterator< CellAccessor< dim, spacedim > > CellAccessor< dim, spacedim >::parent  (  )  const 
Return an iterator to the parent. If the parent does not exist (i.e., if the object is at the coarsest level of the mesh hierarchy), an exception is generated.
Definition at line 2168 of file tria_accessor.cc.
bool CellAccessor< dim, spacedim >::active  (  )  const 
Test that the cell has no children (this is the criterion for whether a cell is called "active").
See the glossary for more information.
bool CellAccessor< dim, spacedim >::is_active  (  )  const 
Test that the cell has no children (this is the criterion for whether a cell is called "active").
See the glossary for more information.
bool CellAccessor< dim, spacedim >::is_locally_owned  (  )  const 
Return whether this cell is owned by the current processor or is owned by another processor. The function always returns true if applied to an object of type Triangulation, but may yield false if the triangulation is of type parallel::distributed::Triangulation.
See the glossary and the Parallel computing with multiple processors using distributed memory module for more information.
!is_ghost() && !is_artificial()
.bool CellAccessor< dim, spacedim >::is_locally_owned_on_level  (  )  const 
Return true if either the Triangulation is not distributed or if level_subdomain_id() is equal to the id of the current processor.
bool CellAccessor< dim, spacedim >::is_ghost  (  )  const 
Return whether this cell exists in the global mesh but (i) is owned by another processor, i.e. has a subdomain_id different from the one the current processor owns and (ii) is adjacent to a cell owned by the current processor.
This function only makes sense if the triangulation used is of kind parallel::distributed::Triangulation. In all other cases, the returned value is always false.
See the glossary and the Parallel computing with multiple processors using distributed memory module for more information.
!is_locally_owned() && !is_artificial()
.bool CellAccessor< dim, spacedim >::is_artificial  (  )  const 
Return whether this cell is artificial, i.e. it isn't one of the cells owned by the current processor, and it also doesn't border on one. As a consequence, it exists in the mesh to ensure that each processor has all coarse mesh cells and that the 2:1 ratio of neighboring cells is maintained, but it is not one of the cells we should work on on the current processor. In particular, there is no guarantee that this cell isn't, in fact, further refined on one of the other processors.
This function only makes sense if the triangulation used is of kind parallel::distributed::Triangulation. In all other cases, the returned value is always false.
See the glossary and the Parallel computing with multiple processors using distributed memory module for more information.
!is_ghost() && !is_locally_owned()
.bool CellAccessor< dim, spacedim >::point_inside  (  const Point< spacedim > &  p  )  const 
Test whether the point p
is inside this cell. Points on the boundary are counted as being inside the cell.
Note that this function assumes that the mapping between unit cell and real cell is (bi, tri)linear, i.e. that faces in 2d and edges in 3d are straight lines. If you have higher order transformations, results may be different as to whether a point is in or outside the cell in real space.
In case of codim>0, the point is first projected to the manifold where the cell is embedded and then check if this projection is inside the cell.
void CellAccessor< dim, spacedim >::set_neighbor  (  const unsigned int  i, 
const TriaIterator< CellAccessor< dim, spacedim >> &  pointer  
)  const 
Set the neighbor i
of this cell to the cell pointed to by pointer
.
This function shouldn't really be public (but needs to for various reasons in order not to make a long list of functions friends): it modifies internal data structures and may leave things. Do not use it from application codes.
Definition at line 2196 of file tria_accessor.cc.
CellId CellAccessor< dim, spacedim >::id  (  )  const 
Return a unique ID for the current cell. This ID is constructed from the path in the hierarchy from the coarse father cell and works correctly in parallel computations using objects of type parallel::distributed::Triangulation. This function is therefore useful in providing a unique identifier for cells (active or not) that also works for parallel triangulations. See the documentation of the CellId class for more information.
Definition at line 2226 of file tria_accessor.cc.
double CellAccessor< dim, spacedim >::diameter  (  const Mapping< dim, spacedim > &  mapping  )  const 
The same as TriaAccessor::diameter() but also taking a Mapping class.

protected 
This function assumes that the neighbor is not coarser than the current cell. In this case it returns the neighbor_of_neighbor() value. If, however, the neighbor is coarser this function returns an invalid_unsigned_int
.
This function is not for public use. Use the function neighbor_of_neighbor() instead which throws an exception if called for a coarser neighbor. If neighbor is indeed coarser (you get to know this by e.g. the neighbor_is_coarser() function) then the neighbor_of_coarser_neighbor() function should be call. If you'd like to know only the face_no
which is required to get back from the neighbor to the present cell then simply use the neighbor_face_no() function which can be used for coarser as well as noncoarser neighbors.
Definition at line 2267 of file tria_accessor.cc.

protected 
As for any codim>0 we can use a similar code and c++ does not allow partial templates. we use this auxiliary function that is then called from point_inside.
Definition at line 1913 of file tria_accessor.cc.

private 
Set the active cell index of a cell. This is done at the end of refinement.
Definition at line 2110 of file tria_accessor.cc.

private 
Set global active cell index for a cell.
Definition at line 2121 of file tria_accessor.cc.

private 
Set global level cell index for a level cell.
Definition at line 2147 of file tria_accessor.cc.

private 
Set the parent of a cell.
Definition at line 2072 of file tria_accessor.cc.

private 
Set the orientation of this cell.
For the meaning of this flag, see GlossDirectionFlag.
Definition at line 2055 of file tria_accessor.cc.
bool CellAccessor< 1 >::point_inside  (  const Point< 1 > &  p  )  const 
Definition at line 1778 of file tria_accessor.cc.
bool CellAccessor< 2 >::point_inside  (  const Point< 2 > &  p  )  const 
Definition at line 1791 of file tria_accessor.cc.
bool CellAccessor< 3 >::point_inside  (  const Point< 3 > &  p  )  const 
Definition at line 1853 of file tria_accessor.cc.
bool CellAccessor< 1, 2 >::point_inside  (  const Point< 2 > &  p  )  const 
Definition at line 1927 of file tria_accessor.cc.
bool CellAccessor< 1, 3 >::point_inside  (  const Point< 3 > &  p  )  const 
Definition at line 1935 of file tria_accessor.cc.
bool CellAccessor< 2, 3 >::point_inside  (  const Point< 3 > &  p  )  const 
Definition at line 1943 of file tria_accessor.cc.

inherited 
Test for the element being used or not. The return value is true
for all iterators that are either normal iterators or active iterators, only raw iterators can return false
. Since raw iterators are only used in the interiors of the library, you will not usually need this function.

inherited 
Pointer to the ith
vertex bounding this object. Throw an exception if dim=1
.

inherited 
Return the global index of ith vertex of the current object. The convention regarding the numbering of vertices is laid down in the documentation of the GeometryInfo class.
Note that the returned value is only the index of the geometrical vertex. It has nothing to do with possible degrees of freedom associated with it. For this, see the DoFAccessor::vertex_dof_index
functions.

inherited 
Return a reference to the ith
vertex. The reference is not const, i.e., it is possible to call this function on the left hand side of an assignment, thereby moving the vertex of a cell within the triangulation. Of course, doing so requires that you ensure that the new location of the vertex remains useful – for example, avoiding inverted or otherwise distorted (see also this glossary entry).

inherited 
Pointer to the ith
line bounding this object.

inherited 
Line index of the ith
line bounding this object.
Implemented only for structdim>1
, otherwise an exception generated.

inherited 
Pointer to the ith
quad bounding this object.

inherited 
Quad index of the ith
quad bounding this object.
Implemented only for structdim>2
, otherwise an exception generated.

inherited 
Return whether the face with index face
has its normal pointing in the standard direction (true
) or whether it is the opposite (false
). Which is the standard direction is documented with the GeometryInfo class. 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.
This function is really only for internal use in the library unless you absolutely know what this is all about.

inherited 
Return whether the face with index face
is rotated by 180 degrees (true
) or not (false
). In 1d and 2d, this is always false
, but in 3d it may be different, see the respective discussion in the documentation of the GeometryInfo class.
This function is really only for internal use in the library unless you absolutely know what this is all about.

inherited 
Return whether the face with index face
is rotated by 90 degrees (true
) or not (false
). In 1d and 2d, this is always false
, but in 3d it may be different, see the respective discussion in the documentation of the GeometryInfo class.
This function is really only for internal use in the library unless you absolutely know what this is all about.

inherited 
Return whether the line with index line
is oriented in standard direction. 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.
This function is really only for internal use in the library unless you absolutely know what this is all about.
This function queries ReferenceCell::standard_vs_true_line_orientation().

inherited 
Test whether the object has children.

inherited 
Return the number of immediate children of this object. The number of children of an unrefined cell is zero.

inherited 

inherited 
Compute and return the number of active descendants of this objects. For example, if all of the eight children of a hex are further refined isotropically exactly once, the returned number will be 64, not 80.
If the present cell is not refined, one is returned.
If one considers a triangulation as a forest where the root of each tree are the coarse mesh cells and nodes have descendants (the children of a cell), then this function returns the number of terminal nodes in the subtree originating from the current object; consequently, if the current object is not further refined, the answer is one.

inherited 
Return the number of times that this object is refined. Note that not all its children are refined that often (which is why we prepend max_
), the returned number is rather the maximum number of refinement in any branch of children of this object.
For example, if this object is refined, and one of its children is refined exactly one more time, then max_refinement_depth
should return 2.
If this object is not refined (i.e. it is active), then the return value is zero.

inherited 
Return the child number of child
on the current cell. This is the inverse function of TriaAccessor::child().

inherited 
Return an iterator to that object that is identical to the ith child for isotropic refinement. If the current object is refined isotropically, then the returned object is the ith child. If the current object is refined anisotropically, the returned child may in fact be a grandchild of the object, or may not exist at all (in which case an exception is generated).

inherited 
Return the RefinementCase of this cell.

inherited 
Index of the ith
child. The level of the child is one higher than that of the present cell, if the children of a cell are accessed. The children of faces have no level. If the child does not exist, 1 is returned.

inherited 
Index of the ith
isotropic child. See the isotropic_child() function for a definition of this concept. If the child does not exist, 1 is returned.

inherited 
Return the boundary indicator of this object.
If the return value is the special value numbers::internal_face_boundary_id, then this object is in the interior of the domain.

inherited 
Set the boundary indicator of the current object. The same applies as for the boundary_id() function.
This function only sets the boundary object of the current object itself, not the indicators of the ones that bound it. For example, in 3d, if this function is called on a face, then the boundary indicator of the 4 edges that bound the face remain unchanged. If you want to set the boundary indicators of face and edges at the same time, use the set_all_boundary_ids() function. You can see the result of not using the correct function in the results section of step49.

inherited 
Do as set_boundary_id() but also set the boundary indicators of the objects that bound the current object. For example, in 3d, if set_boundary_id() is called on a face, then the boundary indicator of the 4 edges that bound the face remain unchanged. In contrast, if you call the current function, the boundary indicators of face and edges are all set to the given value.
This function is useful if you set boundary indicators of faces in 3d (in 2d, the function does the same as set_boundary_id()) and you do so because you want a curved boundary object to represent the part of the boundary that corresponds to the current face. In that case, the Triangulation class needs to figure out where to put new vertices upon mesh refinement, and higher order Mapping objects also need to figure out where new interpolation points for a curved boundary approximation should be. In either case, the two classes first determine where interpolation points on the edges of a boundary face should be, asking the boundary object, before asking the boundary object for the interpolation points corresponding to the interior of the boundary face. For this to work properly, it is not sufficient to have set the boundary indicator for the face alone, but you also need to set the boundary indicators of the edges that bound the face. This function does all of this at once. You can see the result of not using the correct function in the results section of step49.

inherited 
Return a constant reference to the manifold object used for this object.
As explained in the Manifold description for triangulations module, the process involved in finding the appropriate manifold description involves querying both the manifold or boundary indicators. See there for more information.

inherited 
Return the manifold indicator of this object.
If the return value is the special value numbers::flat_manifold_id, then this object is associated with a standard Cartesian Manifold Description.

inherited 
Set the manifold indicator. The same applies as for the manifold_id()
function.
Note that it only sets the manifold object of the current object itself, not the indicators of the ones that bound it, nor of its children. For example, in 3d, if this function is called on a face, then the manifold indicator of the 4 edges that bound the face remain unchanged. If you want to set the manifold indicators of face, edges and all children at the same time, use the set_all_manifold_ids() function.

inherited 
Do as set_manifold_id() but also set the manifold indicators of the objects that bound the current object. For example, in 3d, if set_manifold_id() is called on a face, then the manifold indicator of the 4 edges that bound the face remain unchanged. On the other hand, the manifold indicators of face and edges are all set at the same time using the current function.

inherited 
Definition at line 1693 of file tria_accessor.cc.

inherited 
Read the user flag. See GlossUserFlags for more information.

inherited 
Set the user flag. See GlossUserFlags for more information.

inherited 
Clear the user flag. See GlossUserFlags for more information.

inherited 
Set the user flag for this and all descendants. See GlossUserFlags for more information.

inherited 
Clear the user flag for this and all descendants. See GlossUserFlags for more information.

inherited 
Reset the user data to zero, independent if pointer or index. See GlossUserData for more information.

inherited 
Set the user pointer to p
.
See GlossUserData for more information.

inherited 
Reset the user pointer to a nullptr
pointer. See GlossUserData for more information.

inherited 
Access the value of the user pointer. It is in the responsibility of the user to make sure that the pointer points to something useful. You should use the new style cast operator to maintain a minimum of type safety, e.g.
A a=static_cast<A>(cell>user_pointer());
.See GlossUserData for more information.

inherited 
Set the user pointer of this object and all its children to the given value. This is useful for example if all cells of a certain subdomain, or all faces of a certain part of the boundary should have user pointers pointing to objects describing this part of the domain or boundary.
Note that the user pointer is not inherited under mesh refinement, so after mesh refinement there might be cells or faces that don't have user pointers pointing to the describing object. In this case, simply loop over all the elements of the coarsest level that has this information, and use this function to recursively set the user pointer of all finer levels of the triangulation.
See GlossUserData for more information.

inherited 
Clear the user pointer of this object and all of its descendants. The same holds as said for the recursively_set_user_pointer() function. See GlossUserData for more information.

inherited 
Set the user index to p
.

inherited 
Reset the user index to 0. See GlossUserData for more information.

inherited 
Access the value of the user index.
See GlossUserData for more information.

inherited 
Set the user index of this object and all its children.
Note that the user index is not inherited under mesh refinement, so after mesh refinement there might be cells or faces that don't have the expected user indices. In this case, simply loop over all the elements of the coarsest level that has this information, and use this function to recursively set the user index of all finer levels of the triangulation.
See GlossUserData for more information.

inherited 
Clear the user index of this object and all of its descendants. The same holds as said for the recursively_set_user_index() function.
See GlossUserData for more information.

inherited 
Diameter of the object.
The diameter of an object is computed to be the largest diagonal of the current object. If this object is a quadrilateral, then there are two such diagonal, and if it is a hexahedron, then there are four diagonals that connect "opposite" points. For triangles and tetrahedra, the function simply returns the length of the longest edge.
The situation is more difficult for wedges and pyramids: For wedges, we return the length of the longest diagonal of the three quadrilateral faces or the longest edge length of the two triangular faces. For pyramids, the same principle is applied.
In all of these cases, this definition of "diameter" is not necessarily the true diameter in the sense of the largest distance between points inside the object. Indeed, one can often construct objects for which it is not, though these are generally quite deformed compared to the reference shape. Furthermore, for objects that may use higher order mappings, one may have bulging faces that also create trouble for computing an exact representation of the diameter of the object. That said, the definition used above is completely sufficient for most computations.

inherited 
Return a pair of Point and double corresponding to the center and the radius of a reasonably small enclosing ball of the object.
The function implements Ritter's O(n) algorithm to get a reasonably small enclosing ball around the vertices of the object. The initial guess for the enclosing ball is taken to be the ball which contains the largest diagonal of the object as its diameter. Starting from such an initial guess, the algorithm tests whether all the vertices of the object (except the vertices of the largest diagonal) are geometrically within the ball. If any vertex (v) is found to be geometrically outside the ball, a new iterate of the ball is constructed by shifting its center and increasing the radius so as to geometrically enclose both the previous ball and the vertex (v). The algorithm terminates when all the vertices are geometrically inside the ball.
If a vertex (v) is geometrically inside a particular iterate of the ball, then it will continue to be so in the subsequent iterates of the ball (this is true by construction).
see this and [Ritter 1990]

inherited 
Return the smallest bounding box that encloses the object.
Notice that this method is not aware of any mapping you may be using to do your computations. If you are using a mapping object that modifies the position of the vertices, like MappingQEulerian, or MappingFEField, then you should call the function Mapping::get_bounding_box() instead.
Definition at line 1587 of file tria_accessor.cc.

inherited 
Length of an object in the direction of the given axis, specified in the local coordinate system. See the documentation of GeometryInfo for the meaning and enumeration of the local axes.
Note that the "length" of an object can be interpreted in a variety of ways. Here, we choose it as the maximal length of any of the edges of the object that are parallel to the chosen axis on the reference cell.
Definition at line 1609 of file tria_accessor.cc.

inherited 
Definition at line 1620 of file tria_accessor.cc.

inherited 
Definition at line 1631 of file tria_accessor.cc.

inherited 
Lines along xaxis, see GeometryInfo
Lines along yaxis
Definition at line 1642 of file tria_accessor.cc.

inherited 
Lines along xaxis, see GeometryInfo
Lines along yaxis
Definition at line 1656 of file tria_accessor.cc.

inherited 
Lines along xaxis, see GeometryInfo
Lines along yaxis
Lines along zaxis
Definition at line 1671 of file tria_accessor.cc.

inherited 
Return the minimal distance between any two vertices.

inherited 
Return a point belonging to the Manifold<dim,spacedim> where this object lives, given its parametric coordinates on the reference structdim
cell. This function queries the underlying manifold object, and can be used to obtain the exact geometrical location of arbitrary points on this object.
Notice that the argument coordinates
are the coordinates on the reference cell, given in reference coordinates. In other words, the argument provides a weighting between the different vertices. For example, for lines, calling this function with argument Point<1>(.5), is equivalent to asking the line for its center.
Definition at line 1714 of file tria_accessor.cc.

inherited 
This function computes a fast approximate transformation from the real to the unit cell by inversion of an affine approximation of the \(d\)linear function from the reference \(d\)dimensional cell.
The affine approximation of the unit to real cell mapping is found by a least squares fit of an affine function to the \(2^d\) vertices of the present object. For any valid mesh cell whose geometry is not degenerate, this operation results in a unique affine mapping. Thus, this function will return a finite result for all given input points, even in cases where the actual transformation by an actual bi/trilinear or higher order mapping might be singular. Besides only approximating the mapping from the vertex points, this function also ignores the attached manifold descriptions. The result is only exact in case the transformation from the unit to the real cell is indeed affine, such as in one dimension or for Cartesian and affine (parallelogram) meshes in 2D/3D.
For exact transformations to the unit cell, use Mapping::transform_real_to_unit_cell().
Definition at line 1736 of file tria_accessor.cc.

inherited 
Center of the object. The center of an object is defined to be the average of the locations of the vertices, which is also where a \(Q_1\) mapping would map the center of the reference cell. However, you can also ask this function to instead return the average of the vertices as computed by the underlying Manifold object associated with the current object, by setting to true the optional parameter respect_manifold
. Manifolds would then typically pull back the coordinates of the vertices to a reference domain (not necessarily the reference cell), compute the average there, and then push forward the coordinates of the averaged point to the physical space again; the resulting point is guaranteed to lie within the manifold, even if the manifold is curved.
When the object uses a different manifold description as its surrounding, like when part of the bounding objects of this TriaAccessor use a nonflat manifold description but the object itself is flat, the result given by the TriaAccessor::center() function may not be accurate enough, even when parameter respect_manifold
is set to true. If you find this to be case, than you can further refine the computation of the center by setting to true the second additional parameter interpolate_from_surrounding
. This computes the location of the center by a socalled transfinite interpolation from the center of all the bounding objects. For a 2D object, it puts a weight of 1/2
on each of the four surrounding lines and a weight 1/4
on the four vertices. This corresponds to a linear interpolation between the descriptions of the four faces, subtracting the contribution of the vertices that is added twice when coming through both lines adjacent to the vertex. In 3D, the weights for faces are 1/2
, the weights for lines are 1/4
, and the weights for vertices are 1/8
. For further information, also confer to the TransfiniteInterpolationManifold class that is able to not only apply this beneficial description to a single cell but all children of a coarse cell.
Definition at line 1755 of file tria_accessor.cc.

inherited 
Return the barycenter (also called centroid) of the object. The barycenter for an object \(K\) of dimension \(d\) in \(D\) space dimensions is given by the \(D\)dimensional vector \(\mathbf x_K\) defined by
\[ \mathbf x_K = \frac{1}{K} \int_K \mathbf x \; \textrm{d}x \]
where the measure of the object is given by
\[ K = \int_K \mathbf 1 \; \textrm{d}x. \]
This function assumes that \(K\) is mapped by a \(d\)linear function from the reference \(d\)dimensional cell. Then the integrals above can be pulled back to the reference cell and evaluated exactly (if through lengthy and, compared to the center() function, expensive computations).
Definition at line 1565 of file tria_accessor.cc.

inherited 
Compute the dimdimensional measure of the object. For a dimdimensional cell in dimdimensional space, this equals its volume. On the other hand, for a 2d cell in 3d space, or if the current object pointed to is a 2d face of a 3d cell in 3d space, then the function computes the area the object occupies. For a onedimensional object, return its length.
The function only computes the measure of cells, faces or edges assumed to be represented by (bi/tri)linear mappings. In other words, it only takes into account the locations of the vertices that bound the current object but not how the interior of the object may actually be mapped. In most simple cases, this is exactly what you want. However, for objects that are not "straight", e.g. 2d cells embedded in 3d space as part of a triangulation of a curved domain, twodimensional faces of 3d cells that are not just parallelograms, or for faces that are at the boundary of a domain that is not just bounded by straight line segments or planes, this function only computes the dimdimensional measure of a (bi/tri)linear interpolation of the "real" object as defined by the manifold or boundary object describing the real geometry of the object in question. If you want to consider the "real" geometry, you will need to compute the measure by integrating a function equal to one over the object, which after applying quadrature equals the summing the JxW values returned by the FEValues or FEFaceValues object you will want to use for the integral.
Definition at line 1576 of file tria_accessor.cc.

inherited 
Return true if the current object is a translation of the given argument.

inherited 
Reference cell type of the current object.

inherited 
Number of vertices.

inherited 
Number of lines.

inherited 
Number of faces.

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

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

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

protectedinherited 
Copy operator. Since this is only called from iterators, do not return anything, since the iterator will return itself.
This method is protected, since it is only to be called from the iterator class.

protectedinherited 
Comparison operator for accessors. This operator is used when comparing iterators into objects of a triangulation, for example when putting them into a std::map
.
If structure_dimension is less than dimension, we simply compare the index of such an object because faces and edges do not have levels. If structure_dimension equals dimension, we compare the level first, and the index only if levels are equal.

protectedinherited 
Compare for equality.

protectedinherited 
Compare for inequality.

protectedinherited 
This operator advances the iterator to the next element.
For dim=1
only: The next element is next on this level if there are more. If the present element is the last on this level, the first on the next level is accessed.

protectedinherited 
This operator moves the iterator to the previous element.
For dim=1
only: The previous element is previous on this level if index>0
. If the present element is the first on this level, the last on the previous level is accessed.

protectedinherited 
Access to the other objects of a Triangulation with same dimension.

inherited 
For cells, this function returns the level within the mesh hierarchy at which this cell is located. For all other objects, the function returns zero.
(level, index)
where the former is the cell's refinement level and the latter is the index of the cell within this refinement level (the former being what this function returns). Consequently, there may be multiple cells on different refinement levels but with the same index within their level. Contrary to this, if the current object corresponds to a face or edge, then the object is uniquely identified solely by its index as faces and edges do not have a refinement level. For these objects, the current function always returns zero as the level.

inherited 
Return the index of the element presently pointed to on the present level.
Within a Triangulation object, cells are uniquely identified by a pair (level, index)
where the former is the cell's refinement level and the latter is the index of the cell within this refinement level (the latter being what this function returns). Consequently, there may be multiple cells on different refinement levels but with the same index within their level. Contrary to this, if the current object corresponds to a face or edge, then the object is uniquely identified solely by its index as faces and edges do not have a refinement level.

inherited 
Return the state of the iterator. For the different states an accessor can be in, refer to the TriaRawIterator documentation.

inherited 
Return a reference to the triangulation which the object pointed to by this class belongs to.
Using directive for backwardscompatibility.
Definition at line 3838 of file tria_accessor.h.

friend 
Definition at line 3841 of file tria_accessor.h.

friend 
Definition at line 3843 of file tria_accessor.h.

friend 
Definition at line 3845 of file tria_accessor.h.

staticinherited 
Dimension of the space the object represented by this accessor lives in. For example, if this accessor represents a quad that is part of a two dimensional surface in fourdimensional space, then this value is four.
Definition at line 309 of file tria_accessor.h.

staticinherited 
Dimensionality of the object that the thing represented by this accessor is part of. For example, if this accessor represents a line that is part of a hexahedron, then this value will be three.
Definition at line 316 of file tria_accessor.h.

staticinherited 
Dimensionality of the current object represented by this accessor. For example, if it is line (irrespective of whether it is part of a quad or hex, and what dimension we are in), then this value equals 1.
Definition at line 323 of file tria_accessor.h.

protectedinherited 
The level if this is a cell (structdim==dim
). Else, contains zero.
Definition at line 521 of file tria_accessor.h.

protectedinherited 
Used to store the index of the element presently pointed to on the level presently used.
Definition at line 527 of file tria_accessor.h.

protectedinherited 
Pointer to the triangulation which we act on.
Definition at line 532 of file tria_accessor.h.