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.
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int | size (int c) const |
| number of subentities of codimension c More...
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int | size (int i, int c, int cc) const |
| number of subentities of codimension cc of subentity (i,c) More...
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int | subEntity (int i, int c, int ii, int cc) const |
| obtain number of ii-th subentity with codim cc of (i,c) More...
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const FieldVector< ctype, dim > & | position (int i, int c) const |
| position of the barycenter of entity (i,c) More...
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bool | checkInside (const FieldVector< ctype, dim > &local) const |
| check if a coordinate is in the reference element More...
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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...
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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...
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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...
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template<int codim> |
Codim< codim >::Mapping & | mapping (int i) const |
| obtain the embedding of subentity (i,codim) into the reference element More...
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const GeometryType & | type (int i, int c) const |
| obtain the type of subentity (i,c) More...
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const GeometryType & | type () const |
| obtain the type of this reference element More...
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unsigned int | topologyId (int i, int c) const |
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ctype | volume () const |
| obtain the volume of the reference element More...
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const FieldVector< ctype, dim > & | volumeOuterNormal (int face) const |
| obtain the volume outer normal of the reference element More...
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template<class Topology > |
void | initializeTopology () |
| initialize the reference element More...
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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.
- Template Parameters
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ctype | field type for coordinates |
dim | dimension of the reference element |
template<class ctype , int dim>
template<int codim>
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
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codim | codimension of subentity E |
- Parameters
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[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::GenericReferenceElement< ctype, dim >::checkInside().
template<class ctype , int dim>
template<int codim>
FieldVector< ctype, dim > Dune::GenericReferenceElement< ctype, dim >::global |
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const FieldVector< ctype, dim-codim > & |
local, |
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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
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codim | codimension of subentity E |
- Parameters
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[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.
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This method is just an alias for
mapping< codim >( i ).
global( local );
Referenced by Dune::GenericReferenceElement< ctype, dim >::global().
template<class ctype , int dim>
template<int codim>
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
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codim | codimension of subentity E |
- Parameters
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[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 );
References Dune::GenericReferenceElement< ctype, dim >::global().
template<class ctype , int dim>
template<int codim>
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
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codim | codimension of subentity E |
- Parameters
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[in] | i | number of subentity E (0 <= i < size( codim )) |
template<class ctype , int dim>
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
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[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) |
template<class ctype , int dim>
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
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[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) |