This class provides access to geometric and topological properties of a reference element. More...

#include <dune/geometry/referenceelements.hh>

Classes
struct	Codim
	Collection of types depending on the codimension. More...

struct	SubEntityInfo
	topological information about the subentities of a reference element More...

Public Member Functions
int	size (int c) const
	number of subentities of codimension c More...

int	size (int i, int c, int cc) const
	number of subentities of codimension cc of subentity (i,c) More...

int	subEntity (int i, int c, int ii, int cc) const
	obtain number of ii-th subentity with codim cc of (i,c) More...

const GeometryType &	type (int i, int c) const
	obtain the type of subentity (i,c) More...

const GeometryType &	type () const
	obtain the type of this reference element

const FieldVector< ctype, dim > &	position (int i, int c) const
	position of the barycenter of entity (i,c) More...

bool	checkInside (const FieldVector< ctype, dim > &local) const
	check if a coordinate is in the reference element More...

template<int codim>
Codim< codim >::Geometry	geometry (int i) const
	obtain the embedding of subentity (i,codim) into the reference element More...

ctype	volume () const
	obtain the volume of the reference element

const FieldVector< ctype, dim > &	integrationOuterNormal (int face) const
	obtain the integration outer normal of the reference element More...

Detailed Description

template<class ctype, int dim>
class Dune::ReferenceElement< ctype, dim >

This class provides access to geometric and topological properties of a reference element.

This includes its type, the number of subentities, the volume, and a method for checking if a point is contained in the reference element. The embedding of each subentity into the reference element is also provided.

A singleton of this class for a given geometry type can be accessed through the ReferenceElements class.

Template Parameters

ctype	field type for coordinates
dim	dimension of the reference element

Member Function Documentation

◆ checkInside()

template<class ctype , int dim>

bool Dune::ReferenceElement< ctype, dim >::checkInside ( const FieldVector< ctype, dim > & local ) const

inline

check if a coordinate is in the reference element

This method returns true if the given local coordinate is within this reference element.

Parameters

[in] local coordinates of the point

References Dune::ReferenceElement< ctype, dim >::type().

◆ geometry()

template<class ctype , int dim>

template<int codim>

Codim< codim >::Geometry Dune::ReferenceElement< ctype, dim >::geometry ( int i ) const

inline

obtain the embedding of subentity (i,codim) into the reference element

Denote by E the i-th subentity of codimension codim of the current reference element. This method returns a Dune::AffineGeometry that maps the reference element of E into the current reference element.

Template Parameters

codim codimension of subentity E

Parameters

[in] i number of subentity E (0 <= i < size( codim ))

◆ integrationOuterNormal()

template<class ctype , int dim>

const FieldVector< ctype, dim > & Dune::ReferenceElement< ctype, dim >::integrationOuterNormal ( int face ) const

inline

obtain the integration outer normal of the reference element

The integration outer normal is the outer normal whose length coincides with the face's integration element.

Parameters

[in] face index of the face, whose normal is desired

◆ position()

template<class ctype , int dim>

const FieldVector< ctype, dim > & Dune::ReferenceElement< ctype, dim >::position	(	int	i,
		int	c
	)		const

inline

position of the barycenter of entity (i,c)

Denote by E the i-th subentity of codimension c of the current reference element. This method returns the coordinates of the center of gravity of E within the current reference element.

Parameters

[in]	i	number of subentity E (0 <= i < size( c ))
[in]	c	codimension of subentity E

Referenced by Dune::AffineGeometry< ct, mydim, cdim >::center(), Dune::GeometryDefaultImplementation< mydim, cdim, GridImp, GeometryImp >::center(), Dune::AffineGeometry< ct, mydim, cdim >::corner(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::LocalCoordinate(), and Dune::GeometryDefaultImplementation< mydim, cdim, GridImp, GeometryImp >::volume().

◆ size() [1/2]

template<class ctype , int dim>

int Dune::ReferenceElement< ctype, dim >::size ( int c ) const

inline

number of subentities of codimension c

Parameters

[in] c codimension whose size is desired

Referenced by Dune::AffineGeometry< ct, mydim, cdim >::corners(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::corners(), Dune::GeneralVertexOrder< dim, Index_ >::end(), Dune::GeneralVertexOrder< dim, Index_ >::getReduced(), Dune::GeoGrid::EntityBase< codim, Grid, true >::partitionType(), Dune::ReferenceElement< ctype, dim >::size(), Dune::ReferenceElement< ctype, dim >::subEntity(), testElementDim(), Dune::ReferenceElement< ctype, dim >::type(), Dune::GeometryDefaultImplementation< mydim, cdim, GridImp, GeometryImp >::volume(), and Dune::AmiraMeshWriter< GridView >::writeSurfaceGrid().

◆ size() [2/2]

template<class ctype , int dim>

int Dune::ReferenceElement< ctype, dim >::size	(	int	i,
		int	c,
		int	cc
	)		const

inline

number of subentities of codimension cc of subentity (i,c)

Denote by E the i-th subentity of codimension c of the current reference element. This method returns the number of subentities of codimension cc of the current reference element, that are also a subentity of E.

Parameters

[in]	i	number of subentity E (0 <= i < size( c ))
[in]	c	codimension of subentity E
[in]	cc	codimension whose size is desired (c <= cc <= dim)

References Dune::ReferenceElement< ctype, dim >::size().

◆ subEntity()

template<class ctype , int dim>

int Dune::ReferenceElement< ctype, dim >::subEntity	(	int	i,
		int	c,
		int	ii,
		int	cc
	)		const

inline

obtain number of ii-th subentity with codim cc of (i,c)

Denote by E the i-th subentity of codimension c of the current reference element. And denote by S the ii-th subentity of codimension (cc-c) of E. Then, S is a also a subentity of codimension c of the current reference element. This method returns the number of S with respect to the current reference element.

Parameters

[in]	i	number of subentity E (0 <= i < size( c ))
[in]	c	codimension of subentity E
[in]	ii	number of subentity S (with respect to E)
[in]	cc	codimension of subentity S (c <= cc <= dim)