Detailed Description
template<typename Derived>
struct caribou::geometry::BaseHexahedron< Derived >
Base class for hexahedral elements.
- Template Parameters
-
Derived Derived hexahedral type (usually a leaf type, which is a type that is used by the user, eg Hexahedron).
#include <BaseHexahedron.h>
Inheritance diagram for caribou::geometry::BaseHexahedron< Derived >:
Public Types | |
| using | Base = Element< Derived > |
| using | LocalCoordinates = typename Base::LocalCoordinates |
| using | WorldCoordinates = typename Base::WorldCoordinates |
| using | GaussNode = typename Base::GaussNode |
| template<UNSIGNED_INTEGER_TYPE Dim> | |
| using | Vector = typename Base::template Vector< Dim > |
| template<UNSIGNED_INTEGER_TYPE Rows, UNSIGNED_INTEGER_TYPE Cols> | |
| using | Matrix = typename Base::template Matrix< Rows, Cols > |
 Public Types inherited from caribou::geometry::Element< Derived > | |
| using | Scalar = FLOATING_POINT_TYPE |
| using | Vector = Eigen::Matrix< Scalar, Dim, 1 > |
| using | Matrix = Eigen::Matrix< Scalar, Rows, Cols, Options > |
| using | MatrixI = Eigen::Matrix< Scalar, Rows, Cols, Options > |
| using | LocalCoordinates = Vector< CanonicalDimension > |
| using | WorldCoordinates = Vector< Dimension > |
Public Member Functions | |
| BaseHexahedron ()=default | |
| Default empty constructor. | |
| template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) > | |
| BaseHexahedron (Eigen::EigenBase< EigenType > &nodes) | |
| Constructor from an Eigen matrix containing the positions of the hexahedron's nodes. | |
| template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) > | |
| BaseHexahedron (const Eigen::EigenBase< EigenType > &nodes) | |
| Constructor from an Eigen matrix containing the positions of the hexahedron's nodes. | |
| template<typename ... Nodes> | |
| BaseHexahedron (const WorldCoordinates &first_node, Nodes &&...remaining_nodes) | |
| Constructor from a serie of nodes. | |
| auto | faces () const |
| Get the list of node indices of the faces. More... | |
| auto | frame () const -> Matrix< 3, 3 > |
| Extract the orthogonal frame of the element by computing the cross product of the unit vectors from the center position to its projection on opposite faces. More... | |
| auto | frame (const LocalCoordinates &local_point) const -> Matrix< 3, 3 > |
| Extract the frame positioned at the given position (in local coordinates) on the hexa by computing the cross product of the unit vectors from the given position its projection on opposite faces. More... | |
| Public Member Functions inherited from caribou::geometry::Element< Derived > | |
| auto | number_of_nodes () const -> UNSIGNED_INTEGER_TYPE |
| Get the number of nodes in the element. | |
| auto | number_of_gauss_nodes () const -> UNSIGNED_INTEGER_TYPE |
| Get the number of gauss nodes in the element. | |
| auto | node (const UNSIGNED_INTEGER_TYPE &index) const |
| Get the Node at given index. | |
| auto | nodes () const |
| Get the set of nodes. | |
| auto | gauss_node (const UNSIGNED_INTEGER_TYPE &index) const -> const GaussNode & |
| Get the gauss node at given index. | |
| auto | gauss_nodes () const -> const std::vector< GaussNode > & |
| Get the set of gauss nodes. | |
| auto | number_of_boundary_elements () const |
| Get the number of boundary elements (ex. More... | |
| auto | boundary_elements_node_indices () const -> const auto & |
| Get the list of node indices of the boundary elements. More... | |
| auto | boundary_element (const UNSIGNED_INTEGER_TYPE &boundary_id) const |
| Construct and return the given boundary element. More... | |
| 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... | |
| 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... | |
| auto | center () const -> WorldCoordinates |
| Get the position at the center of the element. | |
| auto | world_coordinates (const LocalCoordinates &coordinates) const -> WorldCoordinates |
| Get the world coordinates of a point from its local coordinates. | |
| 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... | |
| 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... | |
| 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... | |
| auto | interpolate (const LocalCoordinates &coordinates, const Eigen::MatrixBase< MatrixType > &values) const |
| Interpolate a value at local coordinates from the given interpolation node values. More... | |
| 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... | |
Static Public Attributes | |
| static constexpr auto | CanonicalDimension = Base::CanonicalDimension |
| static constexpr auto | Dimension = Base::Dimension |
| static constexpr auto | NumberOfNodesAtCompileTime = Base::NumberOfNodesAtCompileTime |
| static constexpr auto | NumberOfGaussNodesAtCompileTime = Base::NumberOfGaussNodesAtCompileTime |
| Static Public Attributes inherited from caribou::geometry::Element< Derived > | |
| static constexpr auto | CanonicalDimension |
| static constexpr auto | Dimension |
| static constexpr auto | NumberOfNodesAtCompileTime |
| static constexpr auto | NumberOfGaussNodesAtCompileTime |
Protected Attributes | |
| Matrix< NumberOfNodesAtCompileTime, Dimension > | p_nodes |
Friends | |
| struct | Element< Derived > |
Member Function Documentation
◆ faces()
template<typename Derived >
|
inline |
Get the list of node indices of the faces.
◆ frame() [1/2]
template<typename Derived >
|
inline |
Extract the orthogonal frame of the element by computing the cross product of the unit vectors from the center position to its projection on opposite faces.
- See also
- BaseHexahedron::frame(const LocalCoordinates & local_point)
- Warning
- If the hexahedron isn't rectangular, 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 hexahedrons.
◆ frame() [2/2]
template<typename Derived >
|
inline |
Extract the frame positioned at the given position (in local coordinates) on the hexa by computing the cross product of the unit vectors from the given position 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 hexa. If the hexa is rectangular and not rotated, this matrix is the Identity matrix. If it is rectangular but rotated, rotating the hexa 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 hexahedron isn't rectangular, 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 hexahedrons.
The documentation for this struct was generated from the following file:
- /home/jnbrunet/sources/caribou/src/Geometry/BaseHexahedron.h
