template<UNSIGNED_INTEGER_TYPE _Dimension>
struct caribou::geometry::Triangle< _Dimension, Quadratic >
Quadratic Triangle.
* v
* ^
* |
* 2
* |`\
* | `\
* 5 `4
* | `\
* | `\
* 0-----3----1 --> u
*
- Template Parameters
-
| _Dimension | The world coordinates dimension |
|
|
using | Base = BaseTriangle< Triangle< _Dimension, 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 > |
| |
|
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 > |
| |
|
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 > |
| |
|
|
| Triangle (const Triangle< Dimension, Linear > &linear_triangle) |
| |
|
| Triangle (WorldCoordinates &p0, WorldCoordinates &p1, WorldCoordinates &p2) |
| | Construct a quadratic triangle from three nodes.
|
| |
|
| Triangle (const WorldCoordinates &p0, const WorldCoordinates &p1, const WorldCoordinates &p2) |
| | Construct a quadratic triangle from three nodes.
|
| |
|
| 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...
|
| |
|
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...
|
| |
Public Types inherited from caribou::geometry::BaseTriangle< Derived >