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 inside. The embedding of each subentity into the reference element is also provided. More...

#include <dune/geometry/affinegeometry.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 More...

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>
bool	checkInside (const FieldVector< ctype, dim-codim > &local, int i) const
	check if a local coordinate is in the reference element of the i-th subentity E with codimension c of the current reference element. More...

template<int codim>
FieldVector< ctype, dim >	global (const FieldVector< ctype, dim-codim > &local, int i, int c) const
	map a local coordinate on subentity (i,codim) into the reference element More...

template<int codim>
FieldVector< ctype, dim >	global (const FieldVector< ctype, dim-codim > &local, int i) const
	map a local coordinate on subentity (i,codim) into 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...

template<int codim>
const Codim< codim >::Mapping &	mapping (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 More...

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

const FieldVector< ctype, dim > &	volumeOuterNormal (int face) const

void	initializeTopology (unsigned int topologyId)
	initialize the reference element More...

Friends
class	ReferenceElementContainer< ctype, dim >

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 inside. 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

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::GeometryType::id(), and Dune::ReferenceElement< ctype, dim >::type().

template<class ctype, int dim>

template<int codim>

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

inline

check if a local coordinate is in the reference element of the i-th subentity E with codimension c of the current reference element.

Denote by E the i-th subentity of codimension codim of the current reference element. This method return true, if the given local coordinate is within the reference element for the entity E.

Template Parameters

codim codimension of subentity E

Parameters

[in]	local	coordinates of the point with respect to the reference element of E
[in]	i	number of subentity E (0 <= i < size( c ))

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

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 ))

template<class ctype, int dim>

template<int codim>

FieldVector< ctype, dim > Dune::ReferenceElement< ctype, dim >::global	(	const FieldVector< ctype, dim-codim > &	local,
		int	i,
		int	c
	)		const

inline

map a local coordinate on subentity (i,codim) into the reference element

Denote by E the i-th subentity of codimension codim of the current reference element. This method maps a point within the reference element of E into the current reference element.

Template Parameters

codim codimension of subentity E

Parameters

[in]	local	coordinates of the point with respect to the reference element of E
[in]	i	number of subentity E (0 <= i < size( c ))
[in]	c	codimension of subentity E

Note: The runtime argument c is redundant and must equal codim.

Deprecated:: "Use geometry< codim >( i ).global( local ) instead."

Referenced by Dune::ReferenceElement< ctype, dim >::global().

template<class ctype, int dim>

template<int codim>

FieldVector< ctype, dim > Dune::ReferenceElement< ctype, dim >::global	(	const FieldVector< ctype, dim-codim > &	local,
		int	i
	)		const

inline

map a local coordinate on subentity (i,codim) into the reference element

Denote by E the i-th subentity of codimension codim of the current reference element. This method maps a point within the reference element of E into the current reference element.

Template Parameters

codim codimension of subentity E

Parameters

[in]	local	coordinates of the point with respect to the reference element of E
[in]	i	number of subentity E (0 <= i < size( codim ))

Deprecated:: "Use geometry< codim >( i ).global( local ) instead."

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

template<class ctype, int dim>

void Dune::ReferenceElement< ctype, dim >::initializeTopology ( unsigned int topologyId )

inline

initialize the reference element

Parameters

[in] topologyId topology id for the desired reference element

Deprecated:: "initializeTopology has never been an official interface method."

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

Referenced by Dune::ReferenceElement< ctype, dim >::volumeOuterNormal().

template<class ctype, int dim>

template<int codim>

const Codim< codim >::Mapping& Dune::ReferenceElement< ctype, dim >::mapping ( 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 ))

Deprecated:: "Use geometry(i) instead."

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::AffineGeometry< ct, mydim, cdim >::corner(), Dune::RefinementImp::Simplex::RefinementIteratorSpecial< dimension, CoordType, 0 >::geometry(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::local().

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::ReferenceElement< ctype, dim >::SubEntityInfo::number(), Dune::ReferenceElement< ctype, dim >::size(), Dune::ReferenceElement< ctype, dim >::subEntity(), and Dune::ReferenceElement< ctype, dim >::type().

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().

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)