Detailed Description
template<UNSIGNED_INTEGER_TYPE _Dimension>
struct caribou::geometry::Triangle< _Dimension, Linear >
Linear Triangle.
* v * ^ * | * 2 * |`\ * | `\ * | `\ * | `\ * | `\ * 0----------1 --> u *
- Template Parameters
-
_Dimension The world coordinates dimension
#include <Triangle.h>
Inheritance diagram for caribou::geometry::Triangle< _Dimension, Linear >:
Public Types | |
| using | Base = BaseTriangle< Triangle< _Dimension, Linear > > |
| 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::BaseTriangle< 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 > |
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::BaseTriangle< 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< Triangle< _Dimension, Linear > > |
| struct | BaseTriangle< Triangle< _Dimension, Linear > > |
Additional Inherited Members | |
| Public Member Functions inherited from caribou::geometry::BaseTriangle< Derived > | |
| BaseTriangle ()=default | |
| Default empty constructor. | |
| template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) > | |
| BaseTriangle (Eigen::EigenBase< EigenType > &nodes) | |
| Constructor from an Eigen matrix containing the positions of the triangle's nodes. | |
| template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) > | |
| BaseTriangle (const Eigen::EigenBase< EigenType > &nodes) | |
| Constructor from an Eigen matrix containing the positions of the triangle's nodes. | |
| template<typename ... Nodes> | |
| BaseTriangle (const WorldCoordinates &first_node, Nodes &&...remaining_nodes) | |
| Constructor from a serie of nodes. | |
| auto | normal () const noexcept -> WorldCoordinates |
| Get the vector normal to the triangle's surface. More... | |
| auto | edges () const |
| Get the list of node indices of the edges. 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... | |
| Protected Attributes inherited from caribou::geometry::BaseTriangle< Derived > | |
| Matrix< NumberOfNodesAtCompileTime, Dimension > | p_nodes |
The documentation for this struct was generated from the following file:
- /home/jnbrunet/sources/caribou/src/Geometry/Triangle.h
