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caribou::geometry::BaseRectangularQuad< Derived > Struct Template Reference
Inheritance diagram for caribou::geometry::BaseRectangularQuad< Derived >:
caribou::geometry::Element< Derived >

Public Types

using Base = Element< Derived >
using LocalCoordinates = typename Base::LocalCoordinates
using WorldCoordinates = typename Base::WorldCoordinates
using GaussNode = typename Base::GaussNode
using Vector = typename Base::template Vector< Dim >
using Matrix = typename Base::template Matrix< Rows, Cols >
using Size = Vector< CanonicalDimension >
using Rotation = Matrix< Dimension, Dimension >
- Public Types inherited from caribou::geometry::Element< Derived >
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

 BaseRectangularQuad ()
 Default empty constructor.
 BaseRectangularQuad (WorldCoordinates center)
 Constructor by specifying the center point.
 BaseRectangularQuad (WorldCoordinates center, Size H)
 Constructor by specifying the center point and the size (hx, hy, hz)
 BaseRectangularQuad (WorldCoordinates center, Rotation R)
 Constructor by specifying the center point and the rotation.
 BaseRectangularQuad (WorldCoordinates center, Size H, Rotation R)
 Constructor by specifying the center point, the size (hx, hy, hz) and the rotation.
auto edges () const
 Get the list of node indices of the edges. More...
auto rotation () const -> const Rotation &
 Get the rotation frame of the quad.
auto size () const -> const Size &
 Get the size (hx, hy) of the quad.
auto T (const LocalCoordinates &coordinates) const -> WorldCoordinates
 Compute the transformation of a local position {u,v} to its world position {x,y[ ,z]}.
- 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

WorldCoordinates p_center
 Position of the center point of the quad.
Size p_H
 Size of the quad {hx, hy}.
Rotation p_R
 Rotation matrix (a.k.a. the local coordinates frame) at the center of the quad.


struct Element< Derived >

Member Function Documentation

◆ edges()

template<typename Derived >
auto caribou::geometry::BaseRectangularQuad< Derived >::edges ( ) const

Get the list of node indices of the edges.

See also

The documentation for this struct was generated from the following file: