template<class FE>
IsoparametricTransformation class
Polytope isoparametric transformation.
Base classes
- class PolytopeTransformation
- Represents the transformation function of a simplex, taking reference coordinates to physical coordinates.
Constructors, destructors, conversion operators
-
IsoparametricTransformation(const Math::
PointMatrix& pm, const FE& fe)
Public functions
- auto transform(const Math::SpatialVector<Real>& rc) const -> Math::SpatialVector<Real>
- Computes the physical coordinates of the given reference point.
-
auto jacobian(const Math::SpatialVector<Real>& rc) const -> Math::
SpatialMatrix<Real> - Computes the Jacobian matrix of the transformation.
- auto inverse(const Math::SpatialVector<Real>& pc) const -> Math::SpatialVector<Real>
- Computes the reference coordinates of the given physical point.
Function documentation
template<class FE>
Rodin:: Geometry:: IsoparametricTransformation<FE>:: IsoparametricTransformation(const Math:: PointMatrix& pm,
const FE& fe)
pm : sdim x dof
template<class FE>
Math::SpatialVector<Real> Rodin:: Geometry:: IsoparametricTransformation<FE>:: transform(const Math::SpatialVector<Real>& rc) const
Computes the physical coordinates of the given reference point.
Parameters | |
---|---|
rc in | Reference coordinates of the point. |
Returns | A vector of size where represents the physical dimension. |
Given , computes the point:
in physical coordinates.
template<class FE>
Math:: SpatialMatrix<Real> Rodin:: Geometry:: IsoparametricTransformation<FE>:: jacobian(const Math::SpatialVector<Real>& rc) const
Computes the Jacobian matrix of the transformation.
Returns | A matrix of dimensions where represents the reference dimension and represents the physical dimension. |
---|
Given , computes the Jacobian matrix:
for the given transformation .
template<class FE>
Math::SpatialVector<Real> Rodin:: Geometry:: IsoparametricTransformation<FE>:: inverse(const Math::SpatialVector<Real>& pc) const
Computes the reference coordinates of the given physical point.
Parameters | |
---|---|
pc in | Physical coordinates of the point. |
Given , computes the point:
in reference coordinates.