Implementation of the Geometry interface for affine geometries. More...

#include <dune/geometry/affinegeometry.hh>

Public Types
typedef ct	ctype
	Type used for coordinates.

typedef FieldVector< ctype, mydimension >	LocalCoordinate
	Type for local coordinate vector.

typedef FieldVector< ctype, coorddimension >	GlobalCoordinate
	Type for coordinate vector in world space.

typedef ctype	Volume
	Type used for volume.

typedef FieldMatrix< ctype, mydimension, coorddimension >	JacobianTransposed
	Type for the transposed Jacobian matrix.

typedef FieldMatrix< ctype, coorddimension, mydimension >	JacobianInverseTransposed
	Type for the transposed inverse Jacobian matrix.

typedef FieldMatrix< ctype, coorddimension, mydimension >	Jacobian
	Type for the Jacobian matrix.

typedef FieldMatrix< ctype, mydimension, coorddimension >	JacobianInverse
	Type for the inverse Jacobian matrix.

Public Member Functions
	AffineGeometry ()=default
	Constructs an empty geometry.

	AffineGeometry (const ReferenceElement &refElement, const GlobalCoordinate &origin, const JacobianTransposed &jt)
	Create affine geometry from reference element, one vertex, and the Jacobian matrix.

	AffineGeometry (Dune::GeometryType gt, const GlobalCoordinate &origin, const JacobianTransposed &jt)
	Create affine geometry from GeometryType, one vertex, and the Jacobian matrix.

template<class CoordVector >
	AffineGeometry (const ReferenceElement &refElement, const CoordVector &coordVector)
	Create affine geometry from reference element and a vector of vertex coordinates.

template<class CoordVector >
	AffineGeometry (Dune::GeometryType gt, const CoordVector &coordVector)
	Create affine geometry from GeometryType and a vector of vertex coordinates.

bool	affine () const
	Always true: this is an affine geometry.

Dune::GeometryType	type () const
	Obtain the type of the reference element.

int	corners () const
	Obtain number of corners of the corresponding reference element.

GlobalCoordinate	corner (int i) const
	Obtain coordinates of the i-th corner.

GlobalCoordinate	center () const
	Obtain the centroid of the mapping's image.

GlobalCoordinate	global (const LocalCoordinate &local) const
	Evaluate the mapping.

LocalCoordinate	local (const GlobalCoordinate &global) const
	Evaluate the inverse mapping.

ctype	integrationElement (const LocalCoordinate &local) const
	Obtain the integration element.

Volume	volume () const
	Obtain the volume of the element.

const JacobianTransposed &	jacobianTransposed (const LocalCoordinate &local) const
	Obtain the transposed of the Jacobian.

const JacobianInverseTransposed &	jacobianInverseTransposed (const LocalCoordinate &local) const
	Obtain the transposed of the Jacobian's inverse.

Jacobian	jacobian (const LocalCoordinate &local) const
	Obtain the Jacobian.

JacobianInverse	jacobianInverse (const LocalCoordinate &local) const
	Obtain the Jacobian's inverse.

Static Public Attributes
static const int	mydimension = mydim
	Dimension of the geometry.

static const int	coorddimension = cdim
	Dimension of the world space.

Detailed Description

template<class ct, int mydim, int cdim>
class Dune::AffineGeometry< ct, mydim, cdim >

Implementation of the Geometry interface for affine geometries.

Template Parameters

ct	Type used for coordinates
mydim	Dimension of the geometry
cdim	Dimension of the world space

Member Typedef Documentation

◆ ctype

template<class ct , int mydim, int cdim>

typedef ct Dune::AffineGeometry< ct, mydim, cdim >::ctype

Type used for coordinates.

◆ GlobalCoordinate

template<class ct , int mydim, int cdim>

typedef FieldVector< ctype, coorddimension > Dune::AffineGeometry< ct, mydim, cdim >::GlobalCoordinate

Type for coordinate vector in world space.

◆ Jacobian

template<class ct , int mydim, int cdim>

typedef FieldMatrix< ctype, coorddimension, mydimension > Dune::AffineGeometry< ct, mydim, cdim >::Jacobian

Type for the Jacobian matrix.

◆ JacobianInverse

template<class ct , int mydim, int cdim>

typedef FieldMatrix< ctype, mydimension, coorddimension > Dune::AffineGeometry< ct, mydim, cdim >::JacobianInverse

Type for the inverse Jacobian matrix.

◆ JacobianInverseTransposed

template<class ct , int mydim, int cdim>

typedef FieldMatrix< ctype, coorddimension, mydimension > Dune::AffineGeometry< ct, mydim, cdim >::JacobianInverseTransposed

Type for the transposed inverse Jacobian matrix.

◆ JacobianTransposed

template<class ct , int mydim, int cdim>

typedef FieldMatrix< ctype, mydimension, coorddimension > Dune::AffineGeometry< ct, mydim, cdim >::JacobianTransposed

Type for the transposed Jacobian matrix.

◆ LocalCoordinate

template<class ct , int mydim, int cdim>

typedef FieldVector< ctype, mydimension > Dune::AffineGeometry< ct, mydim, cdim >::LocalCoordinate

Type for local coordinate vector.

◆ Volume

template<class ct , int mydim, int cdim>

typedef ctype Dune::AffineGeometry< ct, mydim, cdim >::Volume

Type used for volume.

Constructor & Destructor Documentation

◆ AffineGeometry() [1/5]

template<class ct , int mydim, int cdim>

Dune::AffineGeometry< ct, mydim, cdim >::AffineGeometry ( )

default

Constructs an empty geometry.

This constructor creates an empty (invalid) affine geometry. It may not be used in any way except for assigning other affine geometries to it. After assigning a valid geometry, it may be used without restrictions.

◆ AffineGeometry() [2/5]

template<class ct , int mydim, int cdim>

Dune::AffineGeometry< ct, mydim, cdim >::AffineGeometry	(	const ReferenceElement &	refElement,
		const GlobalCoordinate &	origin,
		const JacobianTransposed &	jt
	)

inline

Create affine geometry from reference element, one vertex, and the Jacobian matrix.

◆ AffineGeometry() [3/5]

template<class ct , int mydim, int cdim>

Dune::AffineGeometry< ct, mydim, cdim >::AffineGeometry	(	Dune::GeometryType	gt,
		const GlobalCoordinate &	origin,
		const JacobianTransposed &	jt
	)

inline

Create affine geometry from GeometryType, one vertex, and the Jacobian matrix.

◆ AffineGeometry() [4/5]

template<class ct , int mydim, int cdim>

template<class CoordVector >

Dune::AffineGeometry< ct, mydim, cdim >::AffineGeometry	(	const ReferenceElement &	refElement,
		const CoordVector &	coordVector
	)

inline

Create affine geometry from reference element and a vector of vertex coordinates.

◆ AffineGeometry() [5/5]

template<class ct , int mydim, int cdim>

template<class CoordVector >

Dune::AffineGeometry< ct, mydim, cdim >::AffineGeometry	(	Dune::GeometryType	gt,
		const CoordVector &	coordVector
	)

inline

Create affine geometry from GeometryType and a vector of vertex coordinates.

Member Function Documentation

◆ affine()

template<class ct , int mydim, int cdim>

bool Dune::AffineGeometry< ct, mydim, cdim >::affine ( ) const

inline

Always true: this is an affine geometry.

◆ center()

template<class ct , int mydim, int cdim>

GlobalCoordinate Dune::AffineGeometry< ct, mydim, cdim >::center ( ) const

inline

Obtain the centroid of the mapping's image.

◆ corner()

template<class ct , int mydim, int cdim>

GlobalCoordinate Dune::AffineGeometry< ct, mydim, cdim >::corner ( int i ) const

inline

Obtain coordinates of the i-th corner.

◆ corners()

template<class ct , int mydim, int cdim>

int Dune::AffineGeometry< ct, mydim, cdim >::corners ( ) const

inline

Obtain number of corners of the corresponding reference element.

◆ global()

template<class ct , int mydim, int cdim>

GlobalCoordinate Dune::AffineGeometry< ct, mydim, cdim >::global ( const LocalCoordinate & local ) const

inline

Evaluate the mapping.

Parameters

[in] local local coordinate to map

Returns: corresponding global coordinate

◆ integrationElement()

template<class ct , int mydim, int cdim>

ctype Dune::AffineGeometry< ct, mydim, cdim >::integrationElement ( const LocalCoordinate & local ) const

inline

Obtain the integration element.

If the Jacobian of the mapping is denoted by $J(x)$, the integration integration element $\mu(x)$ is given by

$\mu(x) = \sqrt{|\det (J^T(x) J(x))|}.$

Parameters

[in] local local coordinate to evaluate the integration element in

Returns: the integration element $\mu(x)$ .

◆ jacobian()

template<class ct , int mydim, int cdim>

Jacobian Dune::AffineGeometry< ct, mydim, cdim >::jacobian ( const LocalCoordinate & local ) const

inline

Obtain the Jacobian.

Parameters

[in] local local coordinate to evaluate Jacobian in

Returns: a copy of the transposed of the Jacobian

◆ jacobianInverse()

template<class ct , int mydim, int cdim>

JacobianInverse Dune::AffineGeometry< ct, mydim, cdim >::jacobianInverse ( const LocalCoordinate & local ) const

inline

Obtain the Jacobian's inverse.

The Jacobian's inverse is defined as a pseudo-inverse. If we denote the Jacobian by , the following condition holds:

$J^{-1}(x) J(x) = I.$

◆ jacobianInverseTransposed()

template<class ct , int mydim, int cdim>

const JacobianInverseTransposed & Dune::AffineGeometry< ct, mydim, cdim >::jacobianInverseTransposed ( const LocalCoordinate & local ) const

inline

Obtain the transposed of the Jacobian's inverse.

The Jacobian's inverse is defined as a pseudo-inverse. If we denote the Jacobian by , the following condition holds:

$J^{-1}(x) J(x) = I.$

◆ jacobianTransposed()

template<class ct , int mydim, int cdim>

const JacobianTransposed & Dune::AffineGeometry< ct, mydim, cdim >::jacobianTransposed ( const LocalCoordinate & local ) const

inline

Obtain the transposed of the Jacobian.

Parameters

[in] local local coordinate to evaluate Jacobian in

Returns: a reference to the transposed of the Jacobian

◆ local()

template<class ct , int mydim, int cdim>

LocalCoordinate Dune::AffineGeometry< ct, mydim, cdim >::local ( const GlobalCoordinate & global ) const

inline

Evaluate the inverse mapping.

Parameters

[in] global global coordinate to map

Returns: corresponding local coordinate

The returned local coordinate y minimizes

(global( y ) - x).two_norm()

Dune::AffineGeometry::global

GlobalCoordinate global(const LocalCoordinate &local) const

Evaluate the mapping.

Definition affinegeometry.hh:603

on the entire affine hull of the reference element. This degenerates to the inverse map if the argument y is in the range of the map.

◆ type()

template<class ct , int mydim, int cdim>

Dune::GeometryType Dune::AffineGeometry< ct, mydim, cdim >::type ( ) const

inline

Obtain the type of the reference element.

◆ volume()

template<class ct , int mydim, int cdim>

Volume Dune::AffineGeometry< ct, mydim, cdim >::volume ( ) const

inline

Obtain the volume of the element.

Member Data Documentation

◆ coorddimension

template<class ct , int mydim, int cdim>

const int Dune::AffineGeometry< ct, mydim, cdim >::coorddimension = cdim

static

Dimension of the world space.

◆ mydimension

template<class ct , int mydim, int cdim>

const int Dune::AffineGeometry< ct, mydim, cdim >::mydimension = mydim

static

Dimension of the geometry.

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

affinegeometry.hh

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ ctype

◆ GlobalCoordinate

◆ Jacobian

◆ JacobianInverse

◆ JacobianInverseTransposed

◆ JacobianTransposed

◆ LocalCoordinate

◆ Volume

Constructor & Destructor Documentation

◆ AffineGeometry() [1/5]

◆ AffineGeometry() [2/5]

◆ AffineGeometry() [3/5]

◆ AffineGeometry() [4/5]

◆ AffineGeometry() [5/5]

Member Function Documentation

◆ affine()

◆ center()

◆ corner()

◆ corners()

◆ global()

◆ integrationElement()

◆ jacobian()

◆ jacobianInverse()

◆ jacobianInverseTransposed()

◆ jacobianTransposed()

◆ local()

◆ type()

◆ volume()

Member Data Documentation

◆ coorddimension

◆ mydimension