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itk::fem::Element2DC0LinearTriangular Class Reference

3-noded, linear, C0 continuous finite element in 2D space. More...

#include <itkFEMElement2DC0LinearTriangular.h>

Inheritance diagram for itk::fem::Element2DC0LinearTriangular:

[legend]Collaboration diagram for itk::fem::Element2DC0LinearTriangular:

[legend]List of all members.


Public Types
typedef Element2DC0LinearTriangular	Self
typedef TemplatedParentClass	Superclass
typedef Self *	Pointer
typedef const Self *	ConstPointer
enum	{ DefaultIntegrationOrder = 1 }
Public Member Functions
virtual void	GetIntegrationPointAndWeight (unsigned int i, VectorType &pt, Float &w, unsigned int order) const
virtual unsigned int	GetNumberOfIntegrationPoints (unsigned int order) const
virtual VectorType	ShapeFunctions (const VectorType &pt) const
virtual void	ShapeFunctionDerivatives (const VectorType &pt, MatrixType &shapeD) const
virtual bool	GetLocalFromGlobalCoordinates (const VectorType &globalPt, VectorType &localPt) const
virtual Float	JacobianDeterminant (const VectorType &pt, const MatrixType *pJ=0) const
virtual void	JacobianInverse (const VectorType &pt, MatrixType &invJ, const MatrixType *pJ=0) const
Static Public Attributes
const Float	trigGaussRuleInfo [6][7][4]
const unsigned int	Nip [6]

Detailed Description

3-noded, linear, C0 continuous finite element in 2D space.

Definition at line 33 of file itkFEMElement2DC0LinearTriangular.h.

Member Typedef Documentation

typedef Element2DC0LinearTriangular itk::fem::Element2DC0LinearTriangular::Self

Standard Self typedef.
Reimplemented from itk::fem::ElementStd< 3, 2 >.
Reimplemented in itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, and itk::fem::Element2DStress< Element2DC0LinearTriangular >.
Definition at line 36 of file itkFEMElement2DC0LinearTriangular.h.

typedef TemplatedParentClass itk::fem::Element2DC0LinearTriangular::Superclass

Standard Superclass typedef.
Reimplemented from itk::fem::ElementStd< 3, 2 >.
Reimplemented in itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, and itk::fem::Element2DStress< Element2DC0LinearTriangular >.
Definition at line 36 of file itkFEMElement2DC0LinearTriangular.h.

Member Enumeration Documentation

anonymous enum

Enumeration values:

DefaultIntegrationOrder

Definition at line 45 of file itkFEMElement2DC0LinearTriangular.h.

Member Function Documentation

virtual void itk::fem::Element2DC0LinearTriangular::GetIntegrationPointAndWeight ( unsigned int i,

VectorType & pt,

Float & w,

unsigned int order

) const [virtual]

Computes the vector representing the i-th integration point in local element coordinates for a Gauss-Legendre numerical integration over the element domain. It also computes the weight at this integration point.
Optionally you can also specify the order of integration. If order is not specified, it defaults to 0, which means that the derived element should use the optimal integration order specific for that element.

Note:
This function must be implemented in derived element classes, and is expected to provide valid integration points for up to gaussMaxOrder-th order of integration.

Parameters:

i Integration point number 0<=i<GetNumberOfIntegrationPoints()

pt Reference to object of class VectorType that will hold the integration point.

w Reference to Float variable that will hold the weight.

order Order of integration.

See also:
GetNumberOfIntegrationPoints()

Implements itk::fem::Element.

virtual bool itk::fem::Element2DC0LinearTriangular::GetLocalFromGlobalCoordinates ( const VectorType & globalPt,

VectorType & localPt

) const [virtual]

Transforms the given global element coordinates into local. Returns false if the point is outside.

Parameters:

globalPt Reference to vector containing a point in global (world) coordinates.

localPt Reference to the vector that will store the local coordinate.

Implements itk::fem::Element.

virtual unsigned int itk::fem::Element2DC0LinearTriangular::GetNumberOfIntegrationPoints ( unsigned int order ) const [virtual]

Returns total number of integration points, for given order of Gauss-Legendre numerical integration rule.

Note:
This function must be implemented in derived element classes, and is expected to provide valid number of integration points for up to gaussMaxOrder-th order of integration.

See also:
GetIntegrationPointAndWeight()

Implements itk::fem::Element.

virtual Float itk::fem::Element2DC0LinearTriangular::JacobianDeterminant ( const VectorType & pt,

const MatrixType * pJ = 0

) const [virtual]

Compute the determinant of the Jacobian matrix at a given point with respect to the local coordinate system.

Parameters:

pt Point in local element coordinates.

pJ Optional pointer to Jacobian matrix computed at point pt. If this is set to 0, the Jacobian will be computed as necessary.

Reimplemented from itk::fem::Element.

virtual void itk::fem::Element2DC0LinearTriangular::JacobianInverse ( const VectorType & pt,

MatrixType & invJ,

const MatrixType * pJ = 0

) const [virtual]

Compute the inverse of the Jacobian matrix at a given point with respect to the local coordinate system.

Parameters:

pt Point in local element coordinates.

invJ Reference to the object of MatrixType that will store the computed inverse if Jacobian.

pJ Optional pointer to Jacobian matrix computed at point pt. If this is set to 0, the Jacobian will be computed as necessary.

Reimplemented from itk::fem::Element.

virtual void itk::fem::Element2DC0LinearTriangular::ShapeFunctionDerivatives ( const VectorType & pt,

MatrixType & shapeD

) const [virtual]

Compute the matrix of values of the shape functions derivatives with respect to local coordinates of this element at a given point.
A column in this matrix corresponds to a specific shape function, while a row corresponds to different local coordinates. E.g. element at row 2, col 3 contains derivative of shape function number 3 with respect to local coordinate number 2.

Parameters:

pt Point in local element coordinates.

shapeD Reference to a matrix object, which will be filled with values of shape function derivatives.

See also:
ShapeFunctionGlobalDerivatives

Implements itk::fem::Element.

virtual VectorType itk::fem::Element2DC0LinearTriangular::ShapeFunctions ( const VectorType & pt ) const [virtual]

Returns a vector containing the values of all shape functions that define the geometry of a finite element at a given local point within an element.

Parameters:

pt Point in local element coordinates.

Implements itk::fem::Element.

Member Data Documentation

const unsigned int itk::fem::Element2DC0LinearTriangular::Nip[6] [static]

Array that holds number of integration point for each order of numerical integration.
Definition at line 86 of file itkFEMElement2DC0LinearTriangular.h.

const Float itk::fem::Element2DC0LinearTriangular::trigGaussRuleInfo[6][7][4] [static]

Constants for integration rules.
Definition at line 80 of file itkFEMElement2DC0LinearTriangular.h.

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

itkFEMElement2DC0LinearTriangular.h

Generated at Thu May 25 02:49:17 2006 for ITK by

itk::fem::Element2DC0LinearTriangular Class Reference

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

Member Enumeration Documentation

Member Function Documentation

Member Data Documentation