Gedim::MapTetrahedron Class Reference

#include <MapTetrahedron.hpp>

Classes
struct	MapTetrahedronData

Public Member Functions
	MapTetrahedron (const Gedim::GeometryUtilities &geometryUtilities)
	~MapTetrahedron ()
MapTetrahedronData	Compute (const Eigen::MatrixXd &vertices) const

Static Public Member Functions
static Eigen::Matrix3d	Q (const Eigen::Vector3d &firstVertex, const Eigen::Vector3d &secondVertex, const Eigen::Vector3d &thirdVertex, const Eigen::Vector3d &fourthVertex)
static Eigen::Vector3d	b (const Eigen::Vector3d &firstVertex)
static Eigen::MatrixXd	F (const MapTetrahedronData &mapData, const Eigen::MatrixXd &x)
static Eigen::MatrixXd	FInv (const MapTetrahedronData &mapData, const Eigen::MatrixXd &x)
static Eigen::MatrixXd	J (const MapTetrahedronData &mapData, const Eigen::MatrixXd &x)
static Eigen::VectorXd	DetJ (const MapTetrahedronData &mapData, const Eigen::MatrixXd &x)
static double	DetJ (const MapTetrahedronData &mapData)

Constructor & Destructor Documentation

MapTetrahedron()

Gedim::MapTetrahedron::MapTetrahedron

(

const Gedim::GeometryUtilities &

geometryUtilities

)

~MapTetrahedron()

Gedim::MapTetrahedron::~MapTetrahedron ( )

inline

Member Function Documentation

b()

static Eigen::Vector3d Gedim::MapTetrahedron::b ( const Eigen::Vector3d &  firstVertex )

inlinestatic

Matrix Q for linear map x = Q * x_r + b from reference tetrahedron [0,1]x[0,1]x[0,1]/2 to tetrahedron with x points vertices the tetrahedron to map vertices, size 3 x 4 return the resulting value, size 3 x 3

Compute()

MapTetrahedron::MapTetrahedronData Gedim::MapTetrahedron::Compute

(

const Eigen::MatrixXd &

vertices

)

const

Map from the tetrahedron reference element [0,1]x[0,1]x[0,1]/2 to the polygon x = F(x_r) = Q * x_r + b

Parameters

vertices

the tetrahedron to map vertices, size 3 x 4

Returns

the map data

DetJ() [1/2]

static double Gedim::MapTetrahedron::DetJ ( const MapTetrahedronData &  mapData )

inlinestatic

Compute the determinant of the jacobian matrix of the trasformation

Parameters

mapData

the map data computed

Returns

the determinant of Jacobian matrix

DetJ() [2/2]

VectorXd Gedim::MapTetrahedron::DetJ ( const MapTetrahedronData &  mapData, const Eigen::MatrixXd &  x  )

static

Compute the determinant of the jacobian matrix of the trasformation

Parameters

mapData	the map data computed
x	points in reference tetrahedron, size 3 x numPoints

Returns

the determinant of Jacobian matrix for each points, size 1 x numPoints

F()

static Eigen::MatrixXd Gedim::MapTetrahedron::F ( const MapTetrahedronData &  mapData, const Eigen::MatrixXd &  x  )

inlinestatic

Map from the tetrahedron reference element [0,1]x[0,1]x[0,1]/2 to the polygon x = F(x_r) = Q * x_r + b

Parameters

mapData	the map data computed
x	points in reference tetrahedron, size 3 x numPoints

Returns

the mapped points, size 3 x numPoints

FInv()

static Eigen::MatrixXd Gedim::MapTetrahedron::FInv ( const MapTetrahedronData &  mapData, const Eigen::MatrixXd &  x  )

inlinestatic

J()

MatrixXd Gedim::MapTetrahedron::J ( const MapTetrahedronData &  mapData, const Eigen::MatrixXd &  x  )

static

Compute the jacobian matrix of the transformation F

Parameters

mapData	the map data computed
x	points in reference tetrahedron, size 3 x numPoints

Returns

the Q matrix for each points, size 2 x (2 * numPoints)

Q()

static Eigen::Matrix3d Gedim::MapTetrahedron::Q ( const Eigen::Vector3d &  firstVertex, const Eigen::Vector3d &  secondVertex, const Eigen::Vector3d &  thirdVertex, const Eigen::Vector3d &  fourthVertex  )

inlinestatic

Matrix Q for linear map x = Q * x_r + b from reference tetrahedron [0,1]x[0,1]x[0,1]/2 to tetrahedron with x points vertices the tetrahedron to map vertices, size 3 x 4 return the resulting value, size 3 x 3

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The documentation for this class was generated from the following files:

• MapTetrahedron.hpp
• MapTetrahedron.cpp