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itk::fem::Element2DC0LinearTriangular Class Reference

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

#include <itkFEMElement2DC0LinearTriangular.h>

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List of all members.

Public Types

typedef Element2DC0LinearTriangular Self
typedef TemplatedParentClass Superclass
typedef SelfPointer
typedef const SelfConstPointer
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 const Self* itk::fem::Element2DC0LinearTriangular::ConstPointer
 

Const pointer or SmartPointer to an object.

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 Self* itk::fem::Element2DC0LinearTriangular::Pointer
 

Pointer or SmartPointer to an object.

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 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:
Generated at Sun Apr 1 03:18:21 2007 for ITK by doxygen 1.3.8 written by Dimitri van Heesch, © 1997-2000