Dune::Geo::ReferenceElement< Implementation > Class Template Reference

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

#include <dune/geometry/referenceelement.hh>

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

Public Types
using	ctype = typename Implementation::ctype
	The coordinate field type.
using	CoordinateField = ctype
	The coordinate field type.
using	Coordinate = typename Implementation::Coordinate
	The coordinate type.
typedef ctype	Volume
	Type used for volume.

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...
auto	subEntities (int i, int c, int cc) const
	Obtain the range of numbers of subentities with codim cc of (i,c) More...
GeometryType	type (int i, int c) const
	obtain the type of subentity (i,c) More...
GeometryType	type () const
	obtain the type of this reference element
Coordinate	position (int i, int c) const
	position of the barycenter of entity (i,c) More...
bool	checkInside (const Coordinate &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...
CoordinateField	volume () const
	obtain the volume of the reference element
Coordinate	integrationOuterNormal (int face) const
	obtain the integration outer normal of the reference element More...
	ReferenceElement ()
	Constructs an empty reference element. More...
const Implementation &	impl () const
	Returns a reference to the internal implementation object. More...
bool	operator== (const ReferenceElement &r) const
	Compares for equality with another reference element.
bool	operator!= (const ReferenceElement &r) const
	Compares for inequality with another reference element.

Static Public Attributes
static constexpr int	dimension = Implementation::dimension
	The dimension of the reference element.

Detailed Description

template<typename Implementation>
class Dune::Geo::ReferenceElement< Implementation >

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.

This class has value semantics, i.e. you can (and should) pass it around by value and not by reference and store a copy of it.

Instances of this object for a given geometry type can be retrieved from the ReferenceElements class.

Constructor & Destructor Documentation

ReferenceElement()

template<typename Implementation >

Dune::Geo::ReferenceElement< Implementation >::ReferenceElement ( )

inline

Constructs an empty reference element.

This constructor creates an empty (invalid) reference element. This element may not be used in any way except for assigning other reference elements to it. After assigning a valid reference element (obtained from ReferenceElements), it may be used without restrictions.

Member Function Documentation

checkInside()

template<typename Implementation >

bool Dune::Geo::ReferenceElement< Implementation >::checkInside ( const Coordinate &  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

geometry()

template<typename Implementation >

template<int codim>

Codim< codim >::Geometry Dune::Geo::ReferenceElement< Implementation >::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 ))

impl()

template<typename Implementation >

const Implementation & Dune::Geo::ReferenceElement< Implementation >::impl ( ) const

inline

Returns a reference to the internal implementation object.

Warning

This method may only be called on valid reference elements.

This method exposes undocumented internals that may change without notice!

integrationOuterNormal()

template<typename Implementation >

Coordinate Dune::Geo::ReferenceElement< Implementation >::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<typename Implementation >

Coordinate Dune::Geo::ReferenceElement< Implementation >::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(), and Dune::AffineGeometry< ct, mydim, cdim >::corner().

size() [1/2]

template<typename Implementation >

int Dune::Geo::ReferenceElement< Implementation >::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().

size() [2/2]

template<typename Implementation >

int Dune::Geo::ReferenceElement< Implementation >::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. If cc<c this number is zero.

Parameters

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

subEntities()

template<typename Implementation >

auto Dune::Geo::ReferenceElement< Implementation >::subEntities ( int  i, int  c, int  cc  ) const

inline

Obtain the range of numbers of subentities with codim cc of (i,c)

Denote by E the i-th subentity of codimension c of the current reference element. This method returns a range of numbers of all subentities of E with codimension cc. Notice that the sub-subentity codimension as well as the numbers in the returned range are given with respect to the reference element itself and not with respect to E. For 0<=cc<c this will return an empty range. The returned range r provide the methods r.begin(), r.end(), r.contains(std::size_t) and r.size() mimicking an immutable iterable set.

Parameters

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

Returns

An iterable range of numbers of the sub-subentities.

subEntity()

template<typename Implementation >

int Dune::Geo::ReferenceElement< Implementation >::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 cc 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<typename Implementation >

GeometryType Dune::Geo::ReferenceElement< Implementation >::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

Referenced by Dune::AffineGeometry< ct, mydim, cdim >::type().

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

• dune/geometry/affinegeometry.hh
• dune/geometry/referenceelement.hh