/usr/include/dune/geometry/referenceelements.hh is in libdune-geometry-dev 2.5.0-1.
This file is owned by root:root, with mode 0o644.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_GEOMETRY_REFERENCEELEMENTS_HH
#define DUNE_GEOMETRY_REFERENCEELEMENTS_HH
#include <cassert>
#include <algorithm>
#include <limits>
#include <tuple>
#include <utility>
#include <vector>
#include <dune/common/array.hh>
#include <dune/common/forloop.hh>
#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>
#include <dune/common/typetraits.hh>
#include <dune/common/visibility.hh>
#include <dune/common/unused.hh>
#include <dune/geometry/affinegeometry.hh>
#include <dune/geometry/type.hh>
namespace Dune
{
// Internal Forward Declarations
// -----------------------------
template< class ctype, int dim >
class ReferenceElementContainer;
template< class ctype, int dim >
struct ReferenceElements;
namespace Impl
{
/** \brief Compute the number of subentities of a given codimension */
unsigned int size ( unsigned int topologyId, int dim, int codim );
/** \brief Compute the topology id of a given subentity
*
* \param topologyId Topology id of entity
* \param dim Dimension of entity
* \param codim Codimension of the subentity that we are interested in
* \param i Number of the subentity that we are interested in
*/
unsigned int subTopologyId ( unsigned int topologyId, int dim, int codim, unsigned int i );
// subTopologyNumbering
// --------------------
void subTopologyNumbering ( unsigned int topologyId, int dim, int codim, unsigned int i, int subcodim,
unsigned int *beginOut, unsigned int *endOut );
// checkInside
// -----------
template< class ct, int cdim >
inline bool
checkInside ( unsigned int topologyId, int dim, const FieldVector< ct, cdim > &x, ct tolerance, ct factor = ct( 1 ) )
{
assert( (dim >= 0) && (dim <= cdim) );
assert( topologyId < numTopologies( dim ) );
if( dim > 0 )
{
const ct baseFactor = (isPrism( topologyId, dim ) ? factor : factor - x[ dim-1 ]);
if( (x[ dim-1 ] > -tolerance) && (factor - x[ dim-1 ] > -tolerance) )
return checkInside< ct, cdim >( baseTopologyId( topologyId, dim ), dim-1, x, tolerance, baseFactor );
else
return false;
}
else
return true;
}
// referenceCorners
// ----------------
template< class ct, int cdim >
inline unsigned int
referenceCorners ( unsigned int topologyId, int dim, FieldVector< ct, cdim > *corners )
{
assert( (dim >= 0) && (dim <= cdim) );
assert( topologyId < numTopologies( dim ) );
if( dim > 0 )
{
const unsigned int nBaseCorners
= referenceCorners( baseTopologyId( topologyId, dim ), dim-1, corners );
assert( nBaseCorners == size( baseTopologyId( topologyId, dim ), dim-1, dim-1 ) );
if( isPrism( topologyId, dim ) )
{
std::copy( corners, corners + nBaseCorners, corners + nBaseCorners );
for( unsigned int i = 0; i < nBaseCorners; ++i )
corners[ i+nBaseCorners ][ dim-1 ] = ct( 1 );
return 2*nBaseCorners;
}
else
{
corners[ nBaseCorners ] = FieldVector< ct, cdim >( ct( 0 ) );
corners[ nBaseCorners ][ dim-1 ] = ct( 1 );
return nBaseCorners+1;
}
}
else
{
*corners = FieldVector< ct, cdim >( ct( 0 ) );
return 1;
}
}
// referenceVolume
// ---------------
unsigned long referenceVolumeInverse ( unsigned int topologyId, int dim );
template< class ct >
inline ct referenceVolume ( unsigned int topologyId, int dim )
{
return ct( 1 ) / ct( referenceVolumeInverse( topologyId, dim ) );
}
// referenceOrigins
// ----------------
template< class ct, int cdim >
inline unsigned int
referenceOrigins ( unsigned int topologyId, int dim, int codim, FieldVector< ct, cdim > *origins )
{
assert( (dim >= 0) && (dim <= cdim) );
assert( topologyId < numTopologies( dim ) );
assert( (codim >= 0) && (codim <= dim) );
if( codim > 0 )
{
const unsigned int baseId = baseTopologyId( topologyId, dim );
if( isPrism( topologyId, dim ) )
{
const unsigned int n = (codim < dim ? referenceOrigins( baseId, dim-1, codim, origins ) : 0);
const unsigned int m = referenceOrigins( baseId, dim-1, codim-1, origins+n );
for( unsigned int i = 0; i < m; ++i )
{
origins[ n+m+i ] = origins[ n+i ];
origins[ n+m+i ][ dim-1 ] = ct( 1 );
}
return n+2*m;
}
else
{
const unsigned int m = referenceOrigins( baseId, dim-1, codim-1, origins );
if( codim == dim )
{
origins[ m ] = FieldVector< ct, cdim >( ct( 0 ) );
origins[ m ][ dim-1 ] = ct( 1 );
return m+1;
}
else
return m+referenceOrigins( baseId, dim-1, codim, origins+m );
}
}
else
{
origins[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
return 1;
}
}
// referenceEmbeddings
// -------------------
template< class ct, int cdim, int mydim >
inline unsigned int
referenceEmbeddings ( unsigned int topologyId, int dim, int codim,
FieldVector< ct, cdim > *origins,
FieldMatrix< ct, mydim, cdim > *jacobianTransposeds )
{
assert( (0 <= codim) && (codim <= dim) && (dim <= cdim) );
assert( (dim - codim <= mydim) && (mydim <= cdim) );
assert( topologyId < numTopologies( dim ) );
if( codim > 0 )
{
const unsigned int baseId = baseTopologyId( topologyId, dim );
if( isPrism( topologyId, dim ) )
{
const unsigned int n = (codim < dim ? referenceEmbeddings( baseId, dim-1, codim, origins, jacobianTransposeds ) : 0);
for( unsigned int i = 0; i < n; ++i )
jacobianTransposeds[ i ][ dim-codim-1 ][ dim-1 ] = ct( 1 );
const unsigned int m = referenceEmbeddings( baseId, dim-1, codim-1, origins+n, jacobianTransposeds+n );
std::copy( origins+n, origins+n+m, origins+n+m );
std::copy( jacobianTransposeds+n, jacobianTransposeds+n+m, jacobianTransposeds+n+m );
for( unsigned int i = 0; i < m; ++i )
origins[ n+m+i ][ dim-1 ] = ct( 1 );
return n+2*m;
}
else
{
const unsigned int m = referenceEmbeddings( baseId, dim-1, codim-1, origins, jacobianTransposeds );
if( codim == dim )
{
origins[ m ] = FieldVector< ct, cdim >( ct( 0 ) );
origins[ m ][ dim-1 ] = ct( 1 );
jacobianTransposeds[ m ] = FieldMatrix< ct, mydim, cdim >( ct( 0 ) );
return m+1;
}
else
{
const unsigned int n = referenceEmbeddings( baseId, dim-1, codim, origins+m, jacobianTransposeds+m );
for( unsigned int i = 0; i < n; ++i )
{
for( int k = 0; k < dim-1; ++k )
jacobianTransposeds[ m+i ][ dim-codim-1 ][ k ] = -origins[ m+i ][ k ];
jacobianTransposeds[ m+i ][ dim-codim-1 ][ dim-1 ] = ct( 1 );
}
return m+n;
}
}
}
else
{
origins[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
jacobianTransposeds[ 0 ] = FieldMatrix< ct, mydim, cdim >( ct( 0 ) );
for( int k = 0; k < dim; ++k )
jacobianTransposeds[ 0 ][ k ][ k ] = ct( 1 );
return 1;
}
}
// referenceIntegrationOuterNormals
// --------------------------------
template< class ct, int cdim >
inline unsigned int
referenceIntegrationOuterNormals ( unsigned int topologyId, int dim,
const FieldVector< ct, cdim > *origins,
FieldVector< ct, cdim > *normals )
{
assert( (dim > 0) && (dim <= cdim) );
assert( topologyId < numTopologies( dim ) );
if( dim > 1 )
{
const unsigned int baseId = baseTopologyId( topologyId, dim );
if( isPrism( topologyId, dim ) )
{
const unsigned int numBaseFaces
= referenceIntegrationOuterNormals( baseId, dim-1, origins, normals );
for( unsigned int i = 0; i < 2; ++i )
{
normals[ numBaseFaces+i ] = FieldVector< ct, cdim >( ct( 0 ) );
normals[ numBaseFaces+i ][ dim-1 ] = ct( 2*int( i )-1 );
}
return numBaseFaces+2;
}
else
{
normals[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
normals[ 0 ][ dim-1 ] = ct( -1 );
const unsigned int numBaseFaces
= referenceIntegrationOuterNormals( baseId, dim-1, origins+1, normals+1 );
for( unsigned int i = 1; i <= numBaseFaces; ++i )
normals[ i ][ dim-1 ] = normals[ i ]*origins[ i ];
return numBaseFaces+1;
}
}
else
{
for( unsigned int i = 0; i < 2; ++i )
{
normals[ i ] = FieldVector< ct, cdim >( ct( 0 ) );
normals[ i ][ 0 ] = ct( 2*int( i )-1 );
}
return 2;
}
}
template< class ct, int cdim >
inline unsigned int
referenceIntegrationOuterNormals ( unsigned int topologyId, int dim,
FieldVector< ct, cdim > *normals )
{
assert( (dim > 0) && (dim <= cdim) );
FieldVector< ct, cdim > *origins
= new FieldVector< ct, cdim >[ size( topologyId, dim, 1 ) ];
referenceOrigins( topologyId, dim, 1, origins );
const unsigned int numFaces
= referenceIntegrationOuterNormals( topologyId, dim, origins, normals );
assert( numFaces == size( topologyId, dim, 1 ) );
delete[] origins;
return numFaces;
}
} // namespace Impl
// ReferenceElement
// ----------------
/** \class ReferenceElement
* \ingroup GeometryReferenceElements
* \brief 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.
* \tparam ctype field type for coordinates
* \tparam dim dimension of the reference element
*
*/
template< class ctype, int dim >
class ReferenceElement
{
typedef ReferenceElement< ctype, dim > This;
friend class ReferenceElementContainer< ctype, dim >;
struct SubEntityInfo;
// make copy constructor private
ReferenceElement ( const This & );
ReferenceElement () {}
template< int codim > struct CreateGeometries;
public:
/** \brief Collection of types depending on the codimension */
template< int codim >
struct Codim
{
//! type of geometry embedding a subentity into the reference element
typedef AffineGeometry< ctype, dim-codim, dim > Geometry;
};
/** \brief number of subentities of codimension c
*
* \param[in] c codimension whose size is desired
*/
int size ( int c ) const
{
assert( (c >= 0) && (c <= dim) );
return info_[ c ].size();
}
/** \brief 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.
*
* \param[in] i number of subentity E (0 <= i < size( c ))
* \param[in] c codimension of subentity E
* \param[in] cc codimension whose size is desired (c <= cc <= dim)
*/
int size ( int i, int c, int cc ) const
{
assert( (i >= 0) && (i < size( c )) );
return info_[ c ][ i ].size( cc );
}
/** \brief 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.
*
* \param[in] i number of subentity E (0 <= i < size( c ))
* \param[in] c codimension of subentity E
* \param[in] ii number of subentity S (with respect to E)
* \param[in] cc codimension of subentity S (c <= cc <= dim)
*/
int subEntity ( int i, int c, int ii, int cc ) const
{
assert( (i >= 0) && (i < size( c )) );
return info_[ c ][ i ].number( ii, cc );
}
/** \brief 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.
*
* \param[in] i number of subentity E (0 <= i < size( c ))
* \param[in] c codimension of subentity E
*/
const GeometryType &type ( int i, int c ) const
{
assert( (i >= 0) && (i < size( c )) );
return info_[ c ][ i ].type();
}
/** \brief obtain the type of this reference element */
const GeometryType &type () const { return type( 0, 0 ); }
/** \brief 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.
*
* \param[in] i number of subentity E (0 <= i < size( c ))
* \param[in] c codimension of subentity E
*/
const FieldVector< ctype, dim > &position( int i, int c ) const
{
assert( (c >= 0) && (c <= dim) );
return baryCenters_[ c ][ i ];
}
/** \brief check if a coordinate is in the reference element
*
* This method returns true if the given local coordinate is within this
* reference element.
*
* \param[in] local coordinates of the point
*/
bool checkInside ( const FieldVector< ctype, dim > &local ) const
{
const ctype tolerance = ctype( 64 ) * std::numeric_limits< ctype >::epsilon();
return Impl::template checkInside< ctype, dim >( type().id(), dim, local, tolerance );
}
/** \brief 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 \ref Dune::AffineGeometry
* that maps the reference element of E into the current reference element.
*
* \tparam codim codimension of subentity E
*
* \param[in] i number of subentity E (0 <= i < size( codim ))
*/
template< int codim >
typename Codim< codim >::Geometry geometry ( int i ) const
{
return std::get< codim >( geometries_ )[ i ];
}
/** \brief obtain the volume of the reference element */
ctype volume () const
{
return volume_;
}
/** \brief 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.
*
* \param[in] face index of the face, whose normal is desired
*/
const FieldVector< ctype, dim > &integrationOuterNormal ( int face ) const
{
assert( (face >= 0) && (face < int( integrationNormals_.size() )) );
return integrationNormals_[ face ];
}
private:
void initialize ( unsigned int topologyId )
{
assert( topologyId < Impl::numTopologies( dim ) );
// set up subentities
for( int codim = 0; codim <= dim; ++codim )
{
const unsigned int size = Impl::size( topologyId, dim, codim );
info_[ codim ].resize( size );
for( unsigned int i = 0; i < size; ++i )
info_[ codim ][ i ].initialize( topologyId, codim, i );
}
// compute corners
const unsigned int numVertices = size( dim );
baryCenters_[ dim ].resize( numVertices );
Impl::referenceCorners( topologyId, dim, &(baryCenters_[ dim ][ 0 ]) );
// compute barycenters
for( int codim = 0; codim < dim; ++codim )
{
baryCenters_[ codim ].resize( size(codim) );
for( int i = 0; i < size( codim ); ++i )
{
baryCenters_[ codim ][ i ] = FieldVector< ctype, dim >( ctype( 0 ) );
const unsigned int numCorners = size( i, codim, dim );
for( unsigned int j = 0; j < numCorners; ++j )
baryCenters_[ codim ][ i ] += baryCenters_[ dim ][ subEntity( i, codim, j, dim ) ];
baryCenters_[ codim ][ i ] *= ctype( 1 ) / ctype( numCorners );
}
}
// compute reference element volume
volume_ = Impl::template referenceVolume< ctype >( topologyId, dim );
// compute integration outer normals
if( dim > 0 )
{
integrationNormals_.resize( size( 1 ) );
Impl::referenceIntegrationOuterNormals( topologyId, dim, &(integrationNormals_[ 0 ]) );
}
// set up geometries
Dune::ForLoop< CreateGeometries, 0, dim >::apply( *this, geometries_ );
}
template< int... codim >
static std::tuple< std::vector< typename Codim< codim >::Geometry >... >
makeGeometryTable ( std::integer_sequence< int, codim... > );
/** \brief Type to store all subentities of all codimensions */
typedef decltype( makeGeometryTable( std::make_integer_sequence< int, dim+1 >() ) ) GeometryTable;
/** \brief The reference element volume */
ctype volume_;
std::vector< FieldVector< ctype, dim > > baryCenters_[ dim+1 ];
std::vector< FieldVector< ctype, dim > > integrationNormals_;
/** \brief Stores all subentities of all codimensions */
GeometryTable geometries_;
std::vector< SubEntityInfo > info_[ dim+1 ];
};
/** \brief topological information about the subentities of a reference element */
template< class ctype, int dim >
struct ReferenceElement< ctype, dim >::SubEntityInfo
{
SubEntityInfo ()
: numbering_( nullptr )
{
std::fill( offset_.begin(), offset_.end(), 0 );
}
SubEntityInfo ( const SubEntityInfo &other )
: offset_( other.offset_ ),
type_( other.type_ )
{
numbering_ = allocate();
std::copy( other.numbering_, other.numbering_ + capacity(), numbering_ );
}
~SubEntityInfo () { deallocate( numbering_ ); }
const SubEntityInfo &operator= ( const SubEntityInfo &other )
{
type_ = other.type_;
offset_ = other.offset_;
deallocate( numbering_ );
numbering_ = allocate();
std::copy( other.numbering_, other.numbering_ + capacity(), numbering_ );
return *this;
}
int size ( int cc ) const
{
assert( (cc >= codim()) && (cc <= dim) );
return (offset_[ cc+1 ] - offset_[ cc ]);
}
int number ( int ii, int cc ) const
{
assert( (ii >= 0) && (ii < size( cc )) );
return numbering_[ offset_[ cc ] + ii ];
}
const GeometryType &type () const { return type_; }
void initialize ( unsigned int topologyId, int codim, unsigned int i )
{
const unsigned int subId = Impl::subTopologyId( topologyId, dim, codim, i );
type_ = GeometryType( subId, dim-codim );
// compute offsets
for( int cc = 0; cc <= codim; ++cc )
offset_[ cc ] = 0;
for( int cc = codim; cc <= dim; ++cc )
offset_[ cc+1 ] = offset_[ cc ] + Impl::size( subId, dim-codim, cc-codim );
// compute subnumbering
deallocate( numbering_ );
numbering_ = allocate();
for( int cc = codim; cc <= dim; ++cc )
Impl::subTopologyNumbering( topologyId, dim, codim, i, cc-codim, numbering_+offset_[ cc ], numbering_+offset_[ cc+1 ] );
}
protected:
int codim () const { return dim - type().dim(); }
unsigned int *allocate () { return (capacity() != 0 ? new unsigned int[ capacity() ] : nullptr); }
void deallocate ( unsigned int *ptr ) { delete[] ptr; }
unsigned int capacity () const { return offset_[ dim+1 ]; }
private:
unsigned int *numbering_;
std::array< unsigned int, dim+2 > offset_;
GeometryType type_;
};
template< class ctype, int dim >
template< int codim >
struct ReferenceElement< ctype, dim >::CreateGeometries
{
template< int cc >
static const ReferenceElement< ctype, dim-cc > &
subRefElement( const ReferenceElement< ctype, dim > &refElement, int i, std::integral_constant< int, cc > )
{
return ReferenceElements< ctype, dim-cc >::general( refElement.type( i, cc ) );
}
static const ReferenceElement< ctype, dim > &
subRefElement( const ReferenceElement< ctype, dim > &refElement, int i, std::integral_constant< int, 0 > )
{
DUNE_UNUSED_PARAMETER(i);
return refElement;
}
static void apply ( const ReferenceElement< ctype, dim > &refElement, GeometryTable &geometries )
{
const int size = refElement.size( codim );
std::vector< FieldVector< ctype, dim > > origins( size );
std::vector< FieldMatrix< ctype, dim - codim, dim > > jacobianTransposeds( size );
Impl::referenceEmbeddings( refElement.type().id(), dim, codim, &(origins[ 0 ]), &(jacobianTransposeds[ 0 ]) );
std::get< codim >( geometries ).reserve( size );
for( int i = 0; i < size; ++i )
{
typename Codim< codim >::Geometry geometry( subRefElement( refElement, i, std::integral_constant< int, codim >() ), origins[ i ], jacobianTransposeds[ i ] );
std::get< codim >( geometries ).push_back( geometry );
}
}
};
// ReferenceElementContainer
// -------------------------
template< class ctype, int dim >
class ReferenceElementContainer
{
static const unsigned int numTopologies = (1u << dim);
public:
typedef ReferenceElement< ctype, dim > value_type;
typedef const value_type *const_iterator;
ReferenceElementContainer ()
{
for( unsigned int topologyId = 0; topologyId < numTopologies; ++topologyId )
values_[ topologyId ].initialize( topologyId );
}
const value_type &operator() ( const GeometryType &type ) const
{
assert( type.dim() == dim );
return values_[ type.id() ];
}
const value_type &simplex () const
{
return values_[ Impl::SimplexTopology< dim >::type::id ];
}
const value_type &cube () const
{
return values_[ Impl::CubeTopology< dim >::type::id ];
}
const value_type &pyramid () const
{
return values_[ Impl::PyramidTopology< dim >::type::id ];
}
const value_type &prism () const
{
return values_[ Impl::PrismTopology< dim >::type::id ];
}
const_iterator begin () const { return values_; }
const_iterator end () const { return values_ + numTopologies; }
private:
value_type values_[ numTopologies ];
};
// ReferenceElements
// ------------------------
/** \brief Class providing access to the singletons of the
* reference elements
*
* Special methods are available for
* simplex and cube elements of any dimension.
* The method general can be used to obtain the reference element
* for a given geometry type.
*
* \ingroup GeometryReferenceElements
*/
template< class ctype, int dim >
struct ReferenceElements
{
typedef typename ReferenceElementContainer< ctype, dim >::const_iterator Iterator;
//! get general reference elements
static const ReferenceElement< ctype, dim > &
general ( const GeometryType &type )
{
return container() ( type );
}
//! get simplex reference elements
static const ReferenceElement< ctype, dim > &simplex ()
{
return container().simplex();
}
//! get hypercube reference elements
static const ReferenceElement< ctype, dim > &cube ()
{
return container().cube();
}
static Iterator begin () { return container().begin(); }
static Iterator end () { return container().end(); }
private:
DUNE_EXPORT static const ReferenceElementContainer< ctype, dim > &container ()
{
static ReferenceElementContainer< ctype, dim > container;
return container;
}
};
} // namespace Dune
#endif // #ifndef DUNE_GEOMETRY_REFERENCEELEMENTS_HH
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