Inheritance diagram for caribou::geometry::BaseQuad< 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
	BaseQuad ()=default
	Default empty constructor.

template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) >
	BaseQuad (Eigen::EigenBase< EigenType > &nodes)
	Constructor from an Eigen matrix containing the positions of the quad's nodes.

template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) >
	BaseQuad (const Eigen::EigenBase< EigenType > &nodes)
	Constructor from an Eigen matrix containing the positions of the quad's nodes.

template<typename ... Nodes>
	BaseQuad (const WorldCoordinates &first_node, Nodes &&...remaining_nodes)
	Constructor from a serie of nodes.

auto	edges () const
	Get the list of node indices of the edges. More...

auto	frame () const -> Matrix< Dimension, Dimension >
	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< Dimension, Dimension >
	Extract the frame positioned at the given position (in local coordinates) on the quad by computing the cross product of the unit vectors from the given position its projection on opposite 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...

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

◆ edges()

template<typename Derived >

auto caribou::geometry::BaseQuad< Derived >::edges ( ) const

inline

Get the list of node indices of the edges.

See also: Element::boundary_elements_node_indices

◆ frame() [1/2]

template<typename Derived >

auto caribou::geometry::BaseQuad< Derived >::frame ( ) const -> Matrix<Dimension, Dimension>

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: BaseQuad::frame(const LocalCoordinates & local_point)

Warning: If the quad 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 quads.

◆ frame() [2/2]

template<typename Derived >

auto caribou::geometry::BaseQuad< Derived >::frame ( const LocalCoordinates & local_point ) const -> Matrix<Dimension, Dimension>

inline

Extract the frame positioned at the given position (in local coordinates) on the quad by computing the cross product of the unit vectors from the given position its projection on opposite edges.

This function will return a matrix of the form:

2D 3D

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 quad. If the quad is rectangular and not rotated, this matrix is the Identity matrix. If it is rectangular but rotated, rotating the quad 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 quad 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 quads.

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

/home/jnbrunet/sources/caribou/src/Geometry/BaseQuad.h

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Member Function Documentation

◆ edges()

◆ frame() [1/2]

◆ frame() [2/2]