itk::fem::Element2DC0QuadraticTriangular Class Reference

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

#include <itkFEMElement2DC0QuadraticTriangular.h>

Inheritance diagram for itk::fem::Element2DC0QuadraticTriangular:

[legend]Collaboration diagram for itk::fem::Element2DC0QuadraticTriangular:

[legend]List of all members.

Public Types
typedef Element2DC0QuadraticTriangular	Self
typedef TemplatedParentClass	Superclass
typedef Self *	Pointer
typedef const Self *	ConstPointer
enum	{ DefaultIntegrationOrder = 2 }
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 &, VectorType &) 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

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Detailed Description

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

Definition at line 33 of file itkFEMElement2DC0QuadraticTriangular.h.

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Member Typedef Documentation

typedef const Self* itk::fem::Element2DC0QuadraticTriangular::ConstPointer

Const pointer or SmartPointer to an object. Reimplemented from itk::fem::ElementStd< 6, 2 >. Reimplemented in itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, and itk::fem::Element2DStress< Element2DC0QuadraticTriangular >. Definition at line 36 of file itkFEMElement2DC0QuadraticTriangular.h.

typedef Self* itk::fem::Element2DC0QuadraticTriangular::Pointer

Pointer or SmartPointer to an object. Reimplemented from itk::fem::ElementStd< 6, 2 >. Reimplemented in itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, and itk::fem::Element2DStress< Element2DC0QuadraticTriangular >. Definition at line 36 of file itkFEMElement2DC0QuadraticTriangular.h.

typedef Element2DC0QuadraticTriangular itk::fem::Element2DC0QuadraticTriangular::Self

Standard Self typedef. Reimplemented from itk::fem::ElementStd< 6, 2 >. Reimplemented in itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, and itk::fem::Element2DStress< Element2DC0QuadraticTriangular >. Definition at line 36 of file itkFEMElement2DC0QuadraticTriangular.h.

typedef TemplatedParentClass itk::fem::Element2DC0QuadraticTriangular::Superclass

Standard Superclass typedef. Reimplemented from itk::fem::ElementStd< 6, 2 >. Reimplemented in itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, and itk::fem::Element2DStress< Element2DC0QuadraticTriangular >. Definition at line 36 of file itkFEMElement2DC0QuadraticTriangular.h.

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Member Enumeration Documentation

anonymous enum

Enumeration values: DefaultIntegrationOrder  Definition at line 46 of file itkFEMElement2DC0QuadraticTriangular.h.

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Member Function Documentation

virtual void itk::fem::Element2DC0QuadraticTriangular::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::Element2DC0QuadraticTriangular::GetLocalFromGlobalCoordinates (  const VectorType &  , VectorType &  )  const [inline, 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. Definition at line 64 of file itkFEMElement2DC0QuadraticTriangular.h.

virtual unsigned int itk::fem::Element2DC0QuadraticTriangular::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::Element2DC0QuadraticTriangular::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::Element2DC0QuadraticTriangular::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::Element2DC0QuadraticTriangular::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::Element2DC0QuadraticTriangular::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.

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

• itkFEMElement2DC0QuadraticTriangular.h

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