class
PolytopeTransformationRepresents the transformation function of a simplex, taking reference coordinates to physical coordinates.
Let denote a polytope in a triangulation which has an associated reference element , This class represents the transformation of a reference point into a physical point :
Here, and represent the reference and physical dimensions, denotes the physical coordinates of the point, while represents the transformation taking reference coordinates , for a reference geometry .
Derived classes
- class IdentityTransformation final
- Polytope Identity transformation.
-
template<class FE>class IsoparametricTransformation
- Polytope isoparametric transformation.
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
Math::SpatialVector<Real> Rodin:: Geometry:: PolytopeTransformation:: transform(const Math::SpatialVector<Real>& rc) const
Computes the physical coordinates of the given reference point.
Parameters | |
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rc in | Reference coordinates of the point. |
Returns | A vector of size where represents the physical dimension. |
Given , computes the point:
in physical coordinates.
Math:: SpatialMatrix<Real> Rodin:: Geometry:: PolytopeTransformation:: 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. |
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Given , computes the Jacobian matrix:
for the given transformation .