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/genericreferenceelements.hh>

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

class	SubEntityInfo
	Topological and geometric 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 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 >::Mapping &	mapping (int i) const
	obtain the embedding of subentity (i,codim) into the reference element 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

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

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

template<class Topology >
void	initializeTopology ()
	initialize the reference element More...

Detailed Description

template<class ctype, int dim>
class Dune::GenericReferenceElement< 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 GenericReferenceElements class.

Deprecated:: GenericReferenceElement was renamed to ReferenceElement. The class with the old name will be removed after Dune 2.3.

Template Parameters

ctype	field type for coordinates
dim	dimension of the reference element

Member Function Documentation

◆ checkInside() [1/2]

template<class ctype , int dim>

bool Dune::GenericReferenceElement< 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

◆ checkInside() [2/2]

template<class ctype , int dim>

template<int codim>

bool Dune::GenericReferenceElement< 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 ))

◆ global() [1/2]

template<class ctype , int dim>

template<int codim>

FieldVector< ctype, dim > Dune::GenericReferenceElement< 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 ))

Note: This method is just an alias for
mapping< codim >( i ).global( local );

◆ global() [2/2]

template<class ctype , int dim>

template<int codim>

FieldVector< ctype, dim > Dune::GenericReferenceElement< 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.; This method is just an alias for
mapping< codim >( i ).global( local );

◆ initializeTopology()

template<class ctype , int dim>

template<class Topology >

void Dune::GenericReferenceElement< ctype, dim >::initializeTopology ( )

inline

initialize the reference element

Template Parameters

Topology topology of the desired reference element

Note: The dimension of the topology must match dim.

References dune_static_assert.

◆ mapping()

template<class ctype , int dim>

template<int codim>

Codim< codim >::Mapping & Dune::GenericReferenceElement< 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::GenericGeometry::HybridMapping HybridMapping that maps the reference element of E into the current reference element.

This method can be used in a GenericGeometry to represent subentities of the current reference element.

Template Parameters

codim codimension of subentity E

Parameters

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

◆ position()

template<class ctype , int dim>

const FieldVector< ctype, dim > & Dune::GenericReferenceElement< 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

◆ size() [1/2]

template<class ctype , int dim>

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

inline

number of subentities of codimension c

Parameters

[in] c codimension whose size is desired

◆ size() [2/2]

template<class ctype , int dim>

int Dune::GenericReferenceElement< 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)

◆ subEntity()

template<class ctype , int dim>

int Dune::GenericReferenceElement< 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)

◆ type()

template<class ctype , int dim>

const GeometryType & Dune::GenericReferenceElement< ctype, dim >::type	(	int	i,
		int	c
	)		const

inline

obtain the type of subentity (i,c)

Denote by E the i-th subentity of codimension c of the current reference element. This method returns the GeometryType of E.

Parameters

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

◆ volumeOuterNormal()

template<class ctype , int dim>

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

inline

obtain the volume outer normal of the reference element

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

Parameters

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

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

dune/geometry/genericreferenceelements.hh

DUNE Distributed and Unified Numerics Environment

Dune Core Modules (2.3.1)

Classes

Public Member Functions

Detailed Description

Member Function Documentation

◆ checkInside() [1/2]

◆ checkInside() [2/2]

◆ global() [1/2]

◆ global() [2/2]

◆ initializeTopology()

◆ mapping()

◆ position()

◆ size() [1/2]

◆ size() [2/2]

◆ subEntity()

◆ type()

◆ volumeOuterNormal()