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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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| 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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template<typename Derived >
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.
This function will return a matrix of the form: | ux vx wx | | uy vy wy | | uz vz wz |
Where (ux, uy, uz), (vx, vy, vz) and (wx, wy, wz) are orthogonal unitary vectors representing the u, v and w frames in the current element. If the element is orthogonal and not rotated, this matrix is the Identity matrix. If it is orthogonal but rotated, rotating the element by the transposed of this frame should align the u,v ,w axis to the x,y,z world frame (identity matrix).
- Warning
- If the element isn't orthogonal, the frame extracted by this function will be a rough approximation that could be far from the real solution, especially for strongly deformed or inverted elements.
Public Types inherited from caribou::geometry::Element< Derived >