Linear Tetrahedron.
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using | Base = BaseTetrahedron< Tetrahedron< Linear > > |
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using | LocalCoordinates = typename Base::LocalCoordinates |
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using | WorldCoordinates = typename Base::WorldCoordinates |
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using | GaussNode = typename Base::GaussNode |
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template<UNSIGNED_INTEGER_TYPE Dim> |
| using | Vector = typename Base::template Vector< Dim > |
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template<UNSIGNED_INTEGER_TYPE Rows, UNSIGNED_INTEGER_TYPE Cols> |
| using | Matrix = typename Base::template Matrix< Rows, Cols > |
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using | Base = Element< Derived > |
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using | LocalCoordinates = typename Base::LocalCoordinates |
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using | WorldCoordinates = typename Base::WorldCoordinates |
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using | GaussNode = typename Base::GaussNode |
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template<UNSIGNED_INTEGER_TYPE Dim> |
| using | Vector = typename Base::template Vector< Dim > |
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template<UNSIGNED_INTEGER_TYPE Rows, UNSIGNED_INTEGER_TYPE Cols> |
| using | Matrix = typename Base::template Matrix< Rows, Cols > |
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using | Scalar = FLOATING_POINT_TYPE |
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using | Vector = Eigen::Matrix< Scalar, Dim, 1 > |
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using | Matrix = Eigen::Matrix< Scalar, Rows, Cols, Options > |
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using | MatrixI = Eigen::Matrix< Scalar, Rows, Cols, Options > |
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using | LocalCoordinates = Vector< CanonicalDimension > |
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using | WorldCoordinates = Vector< Dimension > |
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| auto | edges () const |
| | Get the list of node indices of the edges. More...
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| BaseTetrahedron ()=default |
| | Default empty constructor.
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template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) > |
| | BaseTetrahedron (Eigen::EigenBase< EigenType > &nodes) |
| | Constructor from an Eigen matrix containing the positions of the tetra's nodes.
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template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) > |
| | BaseTetrahedron (const Eigen::EigenBase< EigenType > &nodes) |
| | Constructor from an Eigen matrix containing the positions of the tetra's nodes.
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template<typename ... Nodes> |
| | BaseTetrahedron (const WorldCoordinates &first_node, Nodes &&...remaining_nodes) |
| | Constructor from a serie of nodes.
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| auto | faces () const |
| | Get the list of node indices of the faces. More...
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| auto | frame () const -> Matrix< 3, 3 > |
| | Extract the orthogonal frame of the element by computing the cross product of the unit vectors from the position of the first node to its projection on opposite faces. More...
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auto | number_of_nodes () const -> UNSIGNED_INTEGER_TYPE |
| | Get the number of nodes in the element.
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auto | number_of_gauss_nodes () const -> UNSIGNED_INTEGER_TYPE |
| | Get the number of gauss nodes in the element.
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auto | node (const UNSIGNED_INTEGER_TYPE &index) const |
| | Get the Node at given index.
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auto | nodes () const |
| | Get the set of nodes.
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auto | gauss_node (const UNSIGNED_INTEGER_TYPE &index) const -> const GaussNode & |
| | Get the gauss node at given index.
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auto | gauss_nodes () const -> const std::vector< GaussNode > & |
| | Get the set of gauss nodes.
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| auto | number_of_boundary_elements () const |
| | Get the number of boundary elements (ex. More...
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| auto | boundary_elements_node_indices () const -> const auto & |
| | Get the list of node indices of the boundary elements. More...
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| auto | boundary_element (const UNSIGNED_INTEGER_TYPE &boundary_id) const |
| | Construct and return the given boundary element. More...
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| auto | L (const LocalCoordinates &xi) const -> Vector< NumberOfNodesAtCompileTime > |
| | Get the Lagrange polynomial values evaluated at local coordinates xi w.r.t each element's interpolation nodes. More...
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| auto | dL (const LocalCoordinates &xi) const -> Matrix< NumberOfNodesAtCompileTime, CanonicalDimension > |
| | Get the Lagrange polynomial derivatives w.r.t the local frame {dL/du} evaluated at local coordinates {u} w.r.t each segment's interpolation nodes. More...
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auto | center () const -> WorldCoordinates |
| | Get the position at the center of the element.
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auto | world_coordinates (const LocalCoordinates &coordinates) const -> WorldCoordinates |
| | Get the world coordinates of a point from its local coordinates.
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| auto | local_coordinates (const WorldCoordinates &coordinates) const -> LocalCoordinates |
| | Get the local coordinates of a point from its world coordinates by doing a set of Newton-Raphson iterations. More...
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| auto | local_coordinates (const WorldCoordinates &coordinates, const LocalCoordinates &starting_point, const FLOATING_POINT_TYPE &residual_tolerance, const UNSIGNED_INTEGER_TYPE &maximum_number_of_iterations) const -> LocalCoordinates |
| | Get the local coordinates of a point from its world coordinates by doing a set of Newton-Raphson iterations. More...
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| auto | contains_local (const LocalCoordinates &xi, const FLOATING_POINT_TYPE &eps=1e-10) const -> bool |
| | Return true if the element contains the point located at the given local coordinates. More...
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| auto | interpolate (const LocalCoordinates &coordinates, const Eigen::MatrixBase< MatrixType > &values) const |
| | Interpolate a value at local coordinates from the given interpolation node values. More...
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| auto | jacobian (const LocalCoordinates &coordinates) const -> Matrix< Dimension, CanonicalDimension > |
| | Compute the Jacobian matrix of the transformation T(xi)-> x evaluated at local coordinates xi. More...
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Public Types inherited from caribou::geometry::BaseTetrahedron< Derived >