Detailed Description
Quadratic Hexahedron (20 nodes)
* v * ^ * | * 3-----10---2 * |\ | |\ * | 19 | | 18 * 11 \ | 9 \ * | 7----14+---6 * | | +-- |-- | ---> u * 0---+-8-\--1 | * \ 15 \ \ 13 * 16 | \ 17| * \| w \| * 4----12----5 u *
#include <Hexahedron.h>
Inheritance diagram for caribou::geometry::Hexahedron< Quadratic >:
Public Types | |
| using | Base = BaseHexahedron< Hexahedron< Quadratic > > |
| 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::BaseHexahedron< Derived > | |
| 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 | |
| Hexahedron (const Hexahedron< Linear > &linear_Hexahedron) | |
| Hexahedron (WorldCoordinates &p0, WorldCoordinates &p1, WorldCoordinates &p2, WorldCoordinates &p3, WorldCoordinates &p4, WorldCoordinates &p5, WorldCoordinates &p6, WorldCoordinates &p7) | |
| Construct a quadratic Hexahedron from eight nodes. | |
| Hexahedron (const WorldCoordinates &p0, const WorldCoordinates &p1, const WorldCoordinates &p2, const WorldCoordinates &p3, const WorldCoordinates &p4, const WorldCoordinates &p5, const WorldCoordinates &p6, const WorldCoordinates &p7) | |
| Construct a quadratic Hexahedron from eight nodes. | |
| auto | edges () const |
| Get the list of node indices of the edges. More... | |
| Public Member Functions inherited from caribou::geometry::BaseHexahedron< Derived > | |
| 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 constexpr FLOATING_POINT_TYPE | canonical_nodes [NumberOfNodesAtCompileTime][CanonicalDimension] |
| Static Public Attributes inherited from caribou::geometry::BaseHexahedron< Derived > | |
| 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 |
Friends | |
| struct | Element< Hexahedron< Quadratic > > |
| struct | BaseHexahedron< Hexahedron< Quadratic > > |
Additional Inherited Members | |
| Protected Attributes inherited from caribou::geometry::BaseHexahedron< Derived > | |
| Matrix< NumberOfNodesAtCompileTime, Dimension > | p_nodes |
Member Function Documentation
◆ edges()
|
inline |
Get the list of node indices of the edges.
Member Data Documentation
◆ canonical_nodes
|
staticconstexpr |
Initial value:
= {
{-1, -1, -1},
{+1, -1, -1},
{+1, +1, -1},
{-1, +1, -1},
{-1, -1, +1},
{+1, -1, +1},
{+1, +1, +1},
{-1, +1, +1},
{ 0, -1, -1},
{+1, 0, -1},
{ 0, +1, -1},
{-1, 0, -1},
{ 0, -1, +1},
{+1, 0, +1},
{ 0, +1, +1},
{-1, 0, +1},
{-1, -1, 0},
{+1, -1, 0},
{+1, +1, 0},
{-1, +1, 0},
}
The documentation for this struct was generated from the following file:
- /home/jnbrunet/sources/caribou/src/Geometry/Hexahedron.h
