dune-geometry
2.4
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Implementation of the Geometry interface for affine geometries. More...
#include <dune/geometry/affinegeometry.hh>
Public Types | |
typedef ct | ctype |
Type used for coordinates. More... | |
typedef FieldVector< ctype, mydimension > | LocalCoordinate |
Type for local coordinate vector. More... | |
typedef FieldVector< ctype, coorddimension > | GlobalCoordinate |
Type for coordinate vector in world space. More... | |
typedef FieldMatrix< ctype, mydimension, coorddimension > | JacobianTransposed |
Type for the transposed Jacobian matrix. More... | |
typedef FieldMatrix< ctype, coorddimension, mydimension > | JacobianInverseTransposed |
Type for the transposed inverse Jacobian matrix. More... | |
Public Member Functions | |
AffineGeometry (const ReferenceElement &refElement, const GlobalCoordinate &origin, const JacobianTransposed &jt) | |
Create affine geometry from reference element, one vertex, and the Jacobian matrix. More... | |
AffineGeometry (Dune::GeometryType gt, const GlobalCoordinate &origin, const JacobianTransposed &jt) | |
Create affine geometry from GeometryType, one vertex, and the Jacobian matrix. More... | |
template<class CoordVector > | |
AffineGeometry (const ReferenceElement &refElement, const CoordVector &coordVector) | |
Create affine geometry from reference element and a vector of vertex coordinates. More... | |
template<class CoordVector > | |
AffineGeometry (Dune::GeometryType gt, const CoordVector &coordVector) | |
Create affine geometry from GeometryType and a vector of vertex coordinates. More... | |
bool | affine () const |
Always true: this is an affine geometry. More... | |
Dune::GeometryType | type () const |
Obtain the type of the reference element. More... | |
int | corners () const |
Obtain number of corners of the corresponding reference element. More... | |
GlobalCoordinate | corner (int i) const |
Obtain coordinates of the i-th corner. More... | |
GlobalCoordinate | center () const |
Obtain the centroid of the mapping's image. More... | |
GlobalCoordinate | global (const LocalCoordinate &local) const |
Evaluate the mapping. More... | |
LocalCoordinate | local (const GlobalCoordinate &global) const |
Evaluate the inverse mapping. More... | |
ctype | integrationElement (const LocalCoordinate &local) const |
Obtain the integration element. More... | |
ctype | volume () const |
Obtain the volume of the element. More... | |
const JacobianTransposed & | jacobianTransposed (const LocalCoordinate &local) const |
Obtain the transposed of the Jacobian. More... | |
const JacobianInverseTransposed & | jacobianInverseTransposed (const LocalCoordinate &local) const |
Obtain the transposed of the Jacobian's inverse. More... | |
Static Public Attributes | |
static const int | mydimension = mydim |
Dimension of the geometry. More... | |
static const int | coorddimension = cdim |
Dimension of the world space. More... | |
Implementation of the Geometry interface for affine geometries.
ct | Type used for coordinates |
mydim | Dimension of the geometry |
cdim | Dimension of the world space |
typedef ct Dune::AffineGeometry< ct, mydim, cdim >::ctype |
Type used for coordinates.
typedef FieldVector< ctype, coorddimension > Dune::AffineGeometry< ct, mydim, cdim >::GlobalCoordinate |
Type for coordinate vector in world space.
typedef FieldMatrix< ctype, coorddimension, mydimension > Dune::AffineGeometry< ct, mydim, cdim >::JacobianInverseTransposed |
Type for the transposed inverse Jacobian matrix.
typedef FieldMatrix< ctype, mydimension, coorddimension > Dune::AffineGeometry< ct, mydim, cdim >::JacobianTransposed |
Type for the transposed Jacobian matrix.
typedef FieldVector< ctype, mydimension > Dune::AffineGeometry< ct, mydim, cdim >::LocalCoordinate |
Type for local coordinate vector.
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Create affine geometry from reference element, one vertex, and the Jacobian matrix.
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Create affine geometry from GeometryType, one vertex, and the Jacobian matrix.
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Create affine geometry from reference element and a vector of vertex coordinates.
References Dune::AffineGeometry< ct, mydim, cdim >::mydimension.
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Create affine geometry from GeometryType and a vector of vertex coordinates.
References Dune::AffineGeometry< ct, mydim, cdim >::mydimension.
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Always true: this is an affine geometry.
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Obtain the centroid of the mapping's image.
References Dune::AffineGeometry< ct, mydim, cdim >::global(), and Dune::ReferenceElement< ctype, dim >::position().
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Obtain coordinates of the i-th corner.
References Dune::AffineGeometry< ct, mydim, cdim >::global(), and Dune::ReferenceElement< ctype, dim >::position().
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Obtain number of corners of the corresponding reference element.
References Dune::ReferenceElement< ctype, dim >::size().
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Evaluate the mapping.
[in] | local | local coordinate to map |
Referenced by Dune::AffineGeometry< ct, mydim, cdim >::center(), and Dune::AffineGeometry< ct, mydim, cdim >::corner().
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Obtain the integration element.
If the Jacobian of the mapping is denoted by $J(x)$, the integration integration element is given by
[in] | local | local coordinate to evaluate the integration element in |
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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:
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Obtain the transposed of the Jacobian.
[in] | local | local coordinate to evaluate Jacobian in |
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Evaluate the inverse mapping.
[in] | global | global coordinate to map |
The returned local coordinate y minimizes
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.
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Obtain the type of the reference element.
References Dune::ReferenceElement< ctype, dim >::type().
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Obtain the volume of the element.
References Dune::ReferenceElement< ctype, dim >::volume().
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Dimension of the world space.
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Dimension of the geometry.
Referenced by Dune::AffineGeometry< ct, mydim, cdim >::AffineGeometry().