Detailed Description

Quadratic Rectangular 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 <RectangularHexahedron.h>

Inheritance diagram for caribou::geometry::RectangularHexahedron< Quadratic >:

Public Types
using	Base = BaseRectangularHexahedron< RectangularHexahedron< 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::BaseRectangularHexahedron< 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 >

using	Size = Vector< 3 >

using	Rotation = Matrix< 3, 3 >

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
template<UNSIGNED_INTEGER_TYPE Order>
	RectangularHexahedron (const Hexahedron< Order > &hexa)

template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) >
	RectangularHexahedron (Eigen::EigenBase< EigenType > &nodes)
	Constructor from an Eigen matrix containing the positions of an quadratic hexa nodes.

template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==NumberOfNodesAtCompileTime) >
	RectangularHexahedron (const Eigen::EigenBase< EigenType > &nodes)
	Constructor from an Eigen matrix containing the positions of an quadratic hexa nodes.

template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==8) >
	RectangularHexahedron (Eigen::EigenBase< EigenType > &nodes)
	Constructor from an Eigen matrix containing the positions of a linear hexa nodes.

template<typename EigenType , REQUIRES(EigenType::RowsAtCompileTime==8) >
	RectangularHexahedron (const Eigen::EigenBase< EigenType > &nodes)
	Constructor from an Eigen matrix containing the positions of a linear hexa nodes.

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

Public Member Functions inherited from caribou::geometry::BaseRectangularHexahedron< Derived >
	BaseRectangularHexahedron ()
	Default empty constructor.

	BaseRectangularHexahedron (WorldCoordinates center)
	Constructor by specifying the center point.

	BaseRectangularHexahedron (WorldCoordinates center, Size H)
	Constructor by specifying the center point and the size (hx, hy, hz)

	BaseRectangularHexahedron (WorldCoordinates center, Rotation R)
	Constructor by specifying the center point and the rotation.

	BaseRectangularHexahedron (WorldCoordinates center, Size H, Rotation R)
	Constructor by specifying the center point, the size (hx, hy, hz) and the rotation.

auto	faces () const
	Get the list of node indices of the faces. 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	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.

auto	contains (const WorldCoordinates &coordinates) const -> bool
	Returns true if the given world coordinates are within the hexahedron's boundaries, false otherwise.

auto	intersects (const Segment< _3D, Linear > &segment, const FLOATING_POINT_TYPE eps=EPSILON) const -> bool
	Test if the cube intersects the given 3D segment (in world coordinates) More...

auto	intersects (const Triangle< _3D, Linear > &t, const FLOATING_POINT_TYPE eps=1e-10) const -> bool
	Test if the cube intersects the given 3D triangle (in world coordinates) 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 auto	canonical_nodes = Hexahedron<Quadratic>::canonical_nodes

Static Public Attributes inherited from caribou::geometry::BaseRectangularHexahedron< 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< RectangularHexahedron< Quadratic > >

struct	BaseRectangularHexahedron< RectangularHexahedron< Quadratic > >

Additional Inherited Members
Protected Attributes inherited from caribou::geometry::BaseRectangularHexahedron< Derived >
WorldCoordinates	p_center
	Position of the center point of the hexahedron.

Size	p_H
	Size of the hexahedron {hx, hy, hz}.

Rotation	p_R
	Rotation matrix (a.k.a. the local coordinates frame) at the center of the hexahedron.

Member Function Documentation

◆ edges()

auto caribou::geometry::RectangularHexahedron< Quadratic >::edges ( ) const

inline

Get the list of node indices of the edges.

See also: Element::boundary_elements_node_indices

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

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

Detailed Description

Public Types

Public Member Functions

Static Public Attributes

Friends

Additional Inherited Members

Member Function Documentation

◆ edges()