basix::cell Namespace Reference

Information about reference cells. More...

Enumerations
enum class	type : int {   point = 0 , interval = 1 , triangle = 2 , tetrahedron = 3 ,   quadrilateral = 4 , hexahedron = 5 , prism = 6 , pyramid = 7 }
	Cell type.

Functions
template<std::floating_point T>
std::pair< std::vector< T >, std::array< std::size_t, 2 > >	geometry (cell::type celltype)
std::vector< std::vector< std::vector< int > > >	topology (cell::type celltype)
std::vector< std::vector< std::vector< std::vector< int > > > >	sub_entity_connectivity (cell::type celltype)
template<std::floating_point T>
std::pair< std::vector< T >, std::array< std::size_t, 2 > >	sub_entity_geometry (cell::type celltype, int dim, int index)
int	num_sub_entities (cell::type celltype, int dim)
int	topological_dimension (cell::type celltype)
cell::type	sub_entity_type (cell::type celltype, int dim, int index)
template<std::floating_point T>
T	volume (cell::type cell_type)
template<std::floating_point T>
std::pair< std::vector< T >, std::array< std::size_t, 2 > >	facet_outward_normals (cell::type cell_type)
template<std::floating_point T>
std::pair< std::vector< T >, std::array< std::size_t, 2 > >	facet_normals (cell::type cell_type)
std::vector< bool >	facet_orientations (cell::type cell_type)
template<std::floating_point T>
std::vector< T >	facet_reference_volumes (cell::type cell_type)
std::vector< std::vector< cell::type > >	subentity_types (cell::type cell_type)
template<std::floating_point T>
std::pair< std::vector< T >, std::array< std::size_t, 3 > >	facet_jacobians (cell::type cell_type)

Detailed Description

Information about reference cells.

This namespace include functions that can be used to obtain geometric and topological information about reference cells

Function Documentation

geometry()

template<std::floating_point T>

std::pair< std::vector< T >, std::array< std::size_t, 2 > > basix::cell::geometry

(

cell::type

celltype

)

Cell geometry

Parameters

celltype

Cell Type

Returns

(0) Vertex point data of the cell and (1) the shape of the data array. The points are stored in row-major format and the shape is is (npoints, gdim)

topology()

std::vector< std::vector< std::vector< int > > > basix::cell::topology

(

cell::type

celltype

)

Cell topology

Parameters

celltype

Cell Type

Returns

List of topology (vertex indices) for each dimension (0..tdim)

sub_entity_connectivity()

std::vector< std::vector< std::vector< std::vector< int > > > > basix::cell::sub_entity_connectivity

(

cell::type

celltype

)

Get the numbers of entities connected to each subentity of the cell.

Returns a vector of the form: output[dim][entity_n][connected_dim] = [connected_entity_n0, connected_entity_n1, ...] This indicates that the entity of dimension dim and number entity_n is connected to the entities of dimension connected_dim and numbers connected_entity_n0, connected_entity_n1, ...

Parameters

celltype

Cell Type

Returns

List of topology (vertex indices) for each dimension (0..tdim)

sub_entity_geometry()

template<std::floating_point T>

std::pair< std::vector< T >, std::array< std::size_t, 2 > > basix::cell::sub_entity_geometry	(	cell::type	celltype,
		int	dim,
		int	index
	)

Sub-entity of a cell, given by topological dimension and index

Parameters

celltype	The cell::type
dim	Dimension of sub-entity
index	Local index of sub-entity

Returns

Set of vertex points of the sub-entity. Shape is (npoints, gdim)

num_sub_entities()

int basix::cell::num_sub_entities	(	cell::type	celltype,
		int	dim
	)

Number of sub-entities of a cell by topological dimension

Parameters

celltype	The cell::type
dim	Dimension of sub-entity

Returns

The number of sub-entities of the given dimension

topological_dimension()

int basix::cell::topological_dimension

(

cell::type

celltype

)

Get the topological dimension for a given cell type

Parameters

celltype

Cell type

Returns

the topological dimension

sub_entity_type()

cell::type basix::cell::sub_entity_type	(	cell::type	celltype,
		int	dim,
		int	index
	)

Get the cell type of a sub-entity of given dimension and index

Parameters

celltype	Type of cell
dim	Topological dimension of sub-entity
index	Index of sub-entity

Returns

cell type of sub-entity

volume()

template<std::floating_point T>

T basix::cell::volume

(

cell::type

cell_type

)

Get the volume of a reference cell

Parameters

cell_type

Type of cell

Returns

The volume of the cell

facet_outward_normals()

template<std::floating_point T>

std::pair< std::vector< T >, std::array< std::size_t, 2 > > basix::cell::facet_outward_normals

(

cell::type

cell_type

)

Get the (outward) normals to the facets of a reference cell

Parameters

cell_type

Type of cell

Returns

The outward normals. Shape is (nfacets, gdim)

facet_normals()

template<std::floating_point T>

std::pair< std::vector< T >, std::array< std::size_t, 2 > > basix::cell::facet_normals

(

cell::type

cell_type

)

Get the normals to the facets of a reference cell oriented using the low-to-high ordering of the facet

Parameters

cell_type

Type of cell

Returns

The normals. Shape is (nfacets, gdim)

facet_orientations()

std::vector< bool > basix::cell::facet_orientations

(

cell::type

cell_type

)

Get an array of bools indicating whether or not the facet normals are outward pointing

Parameters

cell_type

Type of cell

Returns

The orientations

facet_reference_volumes()

template<std::floating_point T>

std::vector< T > basix::cell::facet_reference_volumes

(

cell::type

cell_type

)

Get the reference volumes of the facets of a reference cell

Parameters

cell_type

Type of cell

Returns

The volumes of the references associated with each facet

subentity_types()

std::vector< std::vector< cell::type > > basix::cell::subentity_types

(

cell::type

cell_type

)

Get the types of the subentities of a reference cell

Parameters

cell_type

Type of cell

Returns

The subentity types. Indices are (tdim, entity)

facet_jacobians()

template<std::floating_point T>

std::pair< std::vector< T >, std::array< std::size_t, 3 > > basix::cell::facet_jacobians

(

cell::type

cell_type

)

Get the jacobians of the facets of a reference cell

Parameters

cell_type

Type of cell

Returns

The jacobians of the facets. Shape is (nfacets, gdim, gdim - 1)