Abstract base element class. More...

#include <itkFEMElementBase.h>

Inheritance diagram for itk::fem::Element:

Collaboration diagram for itk::fem::Element:

Classes
class	Node
	Class that stores information required to define a node. More...

Public Types
enum	{ InvalidDegreeOfFreedomID = 0xffffffff }

enum	{ gaussMaxOrder =10 }

typedef FEMPArray< Element >	ArrayType

typedef Self	Baseclass

typedef const Self *	ConstPointer

typedef unsigned int	DegreeOfFreedomIDType

typedef double	Float

typedef LoadType::Pointer	LoadPointer

typedef FEMLightObject	LoadType

typedef vnl_matrix< Float >	MatrixType

typedef Node::ConstPointer	NodeIDType

typedef Self *	Pointer

typedef Element	Self

typedef FEMLightObject	Superclass

typedef vnl_vector< Float >	VectorType

Public Member Functions
virtual int	ClassID () const =0

virtual Baseclass::Pointer	Clone () const =0

DegreeOfFreedomIDType	GetDegreeOfFreedom (unsigned int local_dof) const

virtual Float	GetElementDeformationEnergy (MatrixType &LocalSolution) const

virtual VectorType	GetGlobalFromLocalCoordinates (const VectorType &pt) const

virtual void	GetIntegrationPointAndWeight (unsigned int i, VectorType &pt, Float &w, unsigned int order=0) const =0

virtual void	GetLandmarkContributionMatrix (float eta, MatrixType &Le) const

virtual void	GetLoadVector (LoadPointer l, VectorType &Fe) const =0

virtual bool	GetLocalFromGlobalCoordinates (const VectorType &globalPt, VectorType &localPt) const =0

virtual void	GetMassMatrix (MatrixType &Me) const

virtual Material::ConstPointer	GetMaterial (void) const

virtual void	GetMaterialMatrix (MatrixType &D) const =0

virtual NodeIDType	GetNode (unsigned int n) const =0

virtual const VectorType &	GetNodeCoordinates (unsigned int n) const =0

virtual unsigned int	GetNumberOfDegreesOfFreedom (void) const

virtual unsigned int	GetNumberOfDegreesOfFreedomPerNode (void) const =0

virtual unsigned int	GetNumberOfIntegrationPoints (unsigned int order=0) const =0

virtual unsigned int	GetNumberOfNodes (void) const =0

virtual unsigned int	GetNumberOfSpatialDimensions () const =0

virtual void	GetStiffnessMatrix (MatrixType &Ke) const

virtual void	GetStrainDisplacementMatrix (MatrixType &B, const MatrixType &shapeDgl) const =0

virtual VectorType	GetStrainsAtPoint (const VectorType &pt, const Solution &sol, unsigned int index) const

virtual VectorType	GetStressesAtPoint (const VectorType &pt, const VectorType &e, const Solution &sol, unsigned int index) const

virtual VectorType	InterpolateSolution (const VectorType &pt, const Solution &sol, unsigned int solutionIndex=0) const

virtual Float	InterpolateSolutionN (const VectorType &pt, const Solution &sol, unsigned int f, unsigned int solutionIndex=0) const

virtual void	Jacobian (const VectorType &pt, MatrixType &J, const MatrixType *pshapeD=0) 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

virtual void	Read (std::istream &f, void *info)

virtual void	SetMaterial (Material::ConstPointer)

virtual void	SetNode (unsigned int n, NodeIDType node)=0

virtual void	ShapeFunctionDerivatives (const VectorType &pt, MatrixType &shapeD) const =0

virtual void	ShapeFunctionGlobalDerivatives (const VectorType &pt, MatrixType &shapeDgl, const MatrixType pJ=0, const MatrixType pshapeD=0) const

virtual VectorType	ShapeFunctions (const VectorType &pt) const =0

virtual void	Write (std::ostream &f) const

Static Public Member Functions
static FEMLightObject::Pointer	CreateFromStream (std::istream &f, void *info)

static void	SkipWhiteSpace (std::istream &f)

Public Attributes
int	GN

Static Public Attributes
static const Float	gaussPoint [gaussMaxOrder+1][gaussMaxOrder]

static const Float	gaussWeight [gaussMaxOrder+1][gaussMaxOrder]

static const std::string	whitespaces =" \t\n\r"

Detailed Description

Abstract base element class.

Derive this class to create new finite element classes. All derived classes must define:

Ke(): Function to calculate the element stiffness matrix in global coordinate system.
Fe(): Function to calculate the element force vector in global coordinate system.
uDOF(): Provide a pointer to storage of i-th DOF displacement in the element.
Clone(): Function that creates a duplicate of current element and returns a pointer to it.

and optionally (if required):

Read(): Reads element data from the stream f. assume that the stream position is already where the element data starts. Take care of the error checking.
Write(): Writes element data to the stream.
Draw(): Draws the element on the device context (Windows only).

The storage of element parameters (geometry...) can't be implemented here, since we don't know yet, how much memory each element needs. Instead each derived class should take care of the memory management (declare appropriate data members) for the element parameters and provide access to these parameters (like nodes, materials...).

Definition at line 73 of file itkFEMElementBase.h.

Member Typedef Documentation

typedef FEMPArray<Element> itk::fem::Element::ArrayType

Array class that holds special pointers to the Element objects

Definition at line 86 of file itkFEMElementBase.h.

typedef Self itk::fem::FEMLightObject::Baseclass

inherited

Store the base class typedef for easy access from derived classes. FEM_CLASS macro also expects this for the FEMOF...

Definition at line 62 of file itkFEMLightObject.h.

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

Const pointer or SmartPointer to an object.

Definition at line 75 of file itkFEMElementBase.h.

typedef unsigned int itk::fem::Element::DegreeOfFreedomIDType

Type that stores global ID's of degrees of freedom.

Definition at line 115 of file itkFEMElementBase.h.

typedef double itk::fem::Element::Float

Floating point type used in all Element classes.

Definition at line 81 of file itkFEMElementBase.h.

typedef LoadType::Pointer itk::fem::Element::LoadPointer

Definition at line 110 of file itkFEMElementBase.h.

typedef FEMLightObject itk::fem::Element::LoadType

Easy and consistent access to LoadElement and LoadElement::Pointer type. This is a pointer to FEMLightObject to avoid cyclic references between LoadElement and Element classes. As a consequence whenever you need to use a pointer to LoadElement class within the element's declaration or definition, ALWAYS use this typedef instead. When calling the GetLoadVector(...) function from outside, you should ALWAYS first convert the argument to Element::LoadPointer. See code of function Solver::AssembleF(...) for more info.

Definition at line 109 of file itkFEMElementBase.h.

typedef vnl_matrix<Float> itk::fem::Element::MatrixType

Class used to store the element stiffness matrix

Definition at line 91 of file itkFEMElementBase.h.

typedef Node::ConstPointer itk::fem::Element::NodeIDType

Type that is used to store IDs of a node. It is a pointer to Node objects.

Definition at line 497 of file itkFEMElementBase.h.

typedef Self* itk::fem::Element::Pointer

Pointer or SmartPointer to an object.

Definition at line 75 of file itkFEMElementBase.h.

typedef Element itk::fem::Element::Self

Standard Self typedef.

Definition at line 75 of file itkFEMElementBase.h.

typedef FEMLightObject itk::fem::Element::Superclass

Standard Superclass typedef.

Definition at line 75 of file itkFEMElementBase.h.

typedef vnl_vector<Float> itk::fem::Element::VectorType

Class to store the element load vector

Definition at line 96 of file itkFEMElementBase.h.

Member Enumeration Documentation

anonymous enum

Constant that represents an invalid DegreeOfFreedomID object. If a degree of freedom is assigned this value, this means that that no specific value was (yet) assigned to this DOF.

Enumerator
InvalidDegreeOfFreedomID

Definition at line 122 of file itkFEMElementBase.h.

anonymous enum

Maximum supported order of 1D Gauss-Legendre integration. Integration points are defined for orders from 1 to gaussMaxOrder. Number of integration points is equal to the order of integration rule.

See Also: gaussPoint

Enumerator
gaussMaxOrder

Definition at line 465 of file itkFEMElementBase.h.

Member Function Documentation

virtual int itk::fem::FEMLightObject::ClassID ( ) const

pure virtualinherited

Returns the class ID of the object. This function is used to determine the class of the object without having to use the dynamic_cast operator.

Note: Class must be registered with the FEMObjectFactory in order to create the class ID. Abstract classes don't define this function.

Referenced by itk::fem::FEMLightObject::Write().

virtual Baseclass::Pointer itk::fem::FEMLightObject::Clone ( ) const

pure virtualinherited

Duplicates the currect object. This function must be implemented by every derived class to create an exact copy of an object. The function returns a pointer to a base class.

Referenced by itk::fem::Generate2DRectilinearMesh(), and itk::fem::Generate3DRectilinearMesh().

FEMLightObject::Pointer itk::fem::FEMLightObject::CreateFromStream	(	std::istream &	f,
		void *	info
	)

staticinherited

Read object of any derived type from stream.

This static function creates an object of a class, which is derived from FEMLightObject. The class of object is first determined from the stream, then the object of that class is constructed using the FEMObjectFactory. Finally the data for this object is read from the stream, by calling the Read() member function.

Read and create object of any derived class from stream

Catch possible exceptions while reading object's data from stream

Return a pointer to a newly created object if all was OK Technically everithing should be fine here (a!=0), but we check again, just in case.

Something went wrong. Reset the stream position to where it was before reading the object.

Definition at line 77 of file itkFEMLightObject.cxx.

References itk::fem::FEMObjectFactory< FEMLightObject >::ClassName2ID(), itk::fem::FEMObjectFactory< FEMLightObject >::Create(), itk::fem::FEMLightObject::Read(), itk::fem::FEMLightObject::SkipWhiteSpace(), and itk::fem::FEMLightObject::whitespaces.

Referenced by itk::fem::Solver::Read().

DegreeOfFreedomIDType itk::fem::Element::GetDegreeOfFreedom ( unsigned int local_dof ) const

inline

Convenient way to access IDs of degrees of freedom that are stored in node objects.

Parameters

local_dof Local number of degree of freedom within an element.

Definition at line 382 of file itkFEMElementBase.h.

References itk::fem::Element::Node::GetDegreeOfFreedom(), GetNode(), GetNumberOfDegreesOfFreedom(), GetNumberOfDegreesOfFreedomPerNode(), and InvalidDegreeOfFreedomID.

Referenced by itk::fem::SolverHyperbolic::AssembleElementMatrix(), itk::fem::Solver::AssembleElementMatrix(), itk::fem::Solver::AssembleF(), itk::fem::SolverCrankNicolson::AssembleKandM(), itk::fem::Solver::AssembleLandmarkContribution(), InterpolateSolution(), and InterpolateSolutionN().

Element::Float itk::fem::Element::GetElementDeformationEnergy ( MatrixType & LocalSolution ) const

virtual

Compute the physical energy, U, of the deformation (e.g. stress / strain ).

U = u Ke u

The matrix LocalSolution contains the solution to use in the energy computation. Usually, this is the solution at the nodes.

Definition at line 268 of file itkFEMElementBase.cxx.

References GetStiffnessMatrix().

Element::VectorType itk::fem::Element::GetGlobalFromLocalCoordinates ( const VectorType & pt ) const

virtual

Transforms the given local element coordinates into global.

Parameters

pt	Point in local element coordinates.

Definition at line 488 of file itkFEMElementBase.cxx.

References GetNodeCoordinates(), GetNumberOfNodes(), GetNumberOfSpatialDimensions(), and ShapeFunctions().

Referenced by itk::fem::LoadImplementationGenericBodyLoad::Implementation().

virtual void itk::fem::Element::GetIntegrationPointAndWeight	(	unsigned int	i,
		VectorType &	pt,
		Float &	w,
		unsigned int	order = `0`
	)		const

pure virtual

Methods related to numeric integration 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()

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element3DC0LinearHexahedron.

Referenced by GetLandmarkContributionMatrix(), GetMassMatrix(), GetStiffnessMatrix(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), and itk::fem::LoadImplementationGenericBodyLoad::Implementation().

void itk::fem::Element::GetLandmarkContributionMatrix	(	float	eta,
		MatrixType &	Le
	)		const

virtual

Compute and return landmark contribution to element stiffness matrix (Le) in global coordinate system.

b             T

int (1/eta)^2 N(x) N(x) dx a

where (eta ) is the landmark weight. Implementation is similar to GetMassMatrix.

Definition at line 229 of file itkFEMElementBase.cxx.

References GetIntegrationPointAndWeight(), GetNumberOfDegreesOfFreedom(), GetNumberOfDegreesOfFreedomPerNode(), GetNumberOfIntegrationPoints(), GetNumberOfNodes(), and ShapeFunctions().

Referenced by itk::fem::SolverCrankNicolson::AssembleKandM(), and itk::fem::Solver::AssembleLandmarkContribution().

virtual void itk::fem::Element::GetLoadVector	(	LoadPointer	l,
		VectorType &	Fe
	)		const

pure virtual

Compute and return the element load vector for a given external load. The class of load object determines the type of load acting on the elemnent. Basically this is the contribution of this element on the right side of the master matrix equation, due to the specified load. Returned vector includes only nodal forces that correspond to the given Load object.

Visitor design pattern is used in the loads implementation. This function only selects and calls the proper function based on the given class of load object. The code that performs the actual conversion to the corresponding nodal loads is defined elswhere.

Note: Each derived class must implement its own version of this function. This is automated by calling the LOAD_FUNCTION() macro within the class declaration (in the public: block).

For example on how to define specific element load, see funtion LoadImplementationPoint_Bar2D.

Note: : Before a load can be applied to an element, the function that implements a load must be registered with the VisitorDispactcher class.

Parameters

l	Pointer to a load object.
Fe	Reference to vector object that will store nodal forces.

See Also: VisitorDispatcher

Referenced by itk::fem::Solver::AssembleF().

virtual bool itk::fem::Element::GetLocalFromGlobalCoordinates	(	const VectorType &	globalPt,
		VectorType &	localPt
	)		const

pure 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.

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearQuadrilateral, and itk::fem::Element3DC0LinearHexahedron.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::InterpolateVectorField().

void itk::fem::Element::GetMassMatrix ( MatrixType & Me ) const

virtual

Compute and return element mass matrix (Me) in global coordinate system.

b   T

int N(x) (rho c) N(x) dx a

where (rho c) is constant (element density), which is here assumed to be equal to one. If this is not the case, this function must be overriden in a derived class. Implementation is similar to GetStiffnessMatrix.

Definition at line 281 of file itkFEMElementBase.cxx.

References GetIntegrationPointAndWeight(), GetNumberOfDegreesOfFreedom(), GetNumberOfDegreesOfFreedomPerNode(), GetNumberOfIntegrationPoints(), GetNumberOfNodes(), Jacobian(), JacobianDeterminant(), ShapeFunctionDerivatives(), and ShapeFunctions().

Referenced by itk::fem::SolverHyperbolic::AssembleElementMatrix().

virtual Material::ConstPointer itk::fem::Element::GetMaterial ( void ) const

inlinevirtual

Return the pointer to the Material object used by the element. All derived classes, which use objects of Material class should override this method to provide access to the material from the base class.

Note: Derived Element classes don't have to use a material class, but since the majority of the final Element classes uses Material classes to specify phhysical constants that the element depends on, we provide this virtual function that enables easy access to this pointer from the base class. If the derived class does not override this function, the returned pointer is 0 by default, signaling that there is no Material object.

See Also: SetMaterial

Definition at line 404 of file itkFEMElementBase.h.

virtual void itk::fem::Element::GetMaterialMatrix ( MatrixType & D ) const

pure virtual

Compute the element material matrix.

Parameters

D	Reference to a matrix object

Referenced by GetStiffnessMatrix(), and GetStressesAtPoint().

virtual NodeIDType itk::fem::Element::GetNode ( unsigned int n ) const

pure virtual

Returns the ID (pointer) of n-th node in an element.

Implemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, and itk::fem::ElementStd< 4, 2 >.

Referenced by GetDegreeOfFreedom(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), InterpolateSolution(), InterpolateSolutionN(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::InterpolateVectorField().

virtual const VectorType& itk::fem::Element::GetNodeCoordinates ( unsigned int n ) const

pure virtual

Return a vector of global coordinates of n-th node in an element.

Parameters

n	Local number of node. Must be 0 <= n < this->GetNumberOfNodes().

Implemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, and itk::fem::ElementStd< 4, 2 >.

Referenced by GetGlobalFromLocalCoordinates(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), and Jacobian().

virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedom ( void ) const

inlinevirtual

Return the total number of degrees of freedom defined in a derived element class. By default this is equal to number of points in a cell multiplied by number of degrees of freedom at each point.

Definition at line 642 of file itkFEMElementBase.h.

References GetNumberOfDegreesOfFreedomPerNode(), and GetNumberOfNodes().

Referenced by itk::fem::SolverHyperbolic::AssembleElementMatrix(), itk::fem::Solver::AssembleElementMatrix(), itk::fem::Solver::AssembleF(), itk::fem::SolverCrankNicolson::AssembleKandM(), itk::fem::Solver::AssembleLandmarkContribution(), GetDegreeOfFreedom(), GetLandmarkContributionMatrix(), GetMassMatrix(), itk::fem::LoadImplementationGenericLandmarkLoad::Implementation(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), and itk::fem::LoadImplementationGenericBodyLoad::Implementation().

virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode ( void ) const

pure virtual

Return the number of degrees of freedom at each node. This is also equal to number of unknowns that we want to solve for at each point within an element.

Note: This function must be overriden in all derived classes.

Referenced by GetDegreeOfFreedom(), GetLandmarkContributionMatrix(), GetMassMatrix(), GetNumberOfDegreesOfFreedom(), itk::fem::LoadImplementationGenericLandmarkLoad::Implementation(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), itk::fem::LoadImplementationGenericBodyLoad::Implementation(), and InterpolateSolution().

virtual unsigned int itk::fem::Element::GetNumberOfIntegrationPoints ( unsigned int order = 0 ) const

pure 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()

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element3DC0LinearHexahedron.

Referenced by GetLandmarkContributionMatrix(), GetMassMatrix(), GetStiffnessMatrix(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), and itk::fem::LoadImplementationGenericBodyLoad::Implementation().

virtual unsigned int itk::fem::Element::GetNumberOfNodes ( void ) const

pure virtual

Return the total number of nodes in an elememnt.

Implemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, and itk::fem::ElementStd< 4, 2 >.

Referenced by GetGlobalFromLocalCoordinates(), GetLandmarkContributionMatrix(), GetMassMatrix(), GetNumberOfDegreesOfFreedom(), itk::fem::LoadImplementationGenericLandmarkLoad::Implementation(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), itk::fem::LoadImplementationGenericBodyLoad::Implementation(), InterpolateSolution(), InterpolateSolutionN(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::InterpolateVectorField().

virtual unsigned int itk::fem::Element::GetNumberOfSpatialDimensions ( ) const

pure virtual

Returns the number of dimensions of space in which the element is defined. e.g. 2 for 2D elements, 3 for 3D... This is also equal to the size vector containing nodal coordinates.

Implemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, and itk::fem::ElementStd< 4, 2 >.

Referenced by GetGlobalFromLocalCoordinates(), and Jacobian().

void itk::fem::Element::GetStiffnessMatrix ( MatrixType & Ke ) const

virtual

Compute and return element stiffnes matrix (Ke) in global coordinate system. The base class provides a general implementation which only computes

b   T

int B(x) D B(x) dx a

using the Gaussian numeric integration method. The function calls GetIntegrationPointAndWeight() / GetNumberOfIntegrationPoints() to obtain the integration points. It also calls the GetStrainDisplacementMatrix() and GetMaterialMatrix() member functions.

Parameters

Ke	Reference to the resulting stiffnes matrix.

Note: This is a very generic implementation of the stiffness matrix that is suitable for any problem/element definition. A specifc element may override this implementation with its own simple one.

Physics of a problem.

Reimplemented in itk::fem::Element1DStress< Element2DC0LinearLine >, and itk::fem::Element2DC1Beam.

Definition at line 155 of file itkFEMElementBase.cxx.

References GetIntegrationPointAndWeight(), GetMaterialMatrix(), GetNumberOfIntegrationPoints(), GetStrainDisplacementMatrix(), Jacobian(), JacobianDeterminant(), ShapeFunctionDerivatives(), and ShapeFunctionGlobalDerivatives().

Referenced by itk::fem::SolverHyperbolic::AssembleElementMatrix(), itk::fem::Solver::AssembleElementMatrix(), and GetElementDeformationEnergy().

virtual void itk::fem::Element::GetStrainDisplacementMatrix	(	MatrixType &	B,
		const MatrixType &	shapeDgl
	)		const

pure virtual

Compute the strain displacement matrix at local point.

Parameters

B	Reference to a matrix object that will contain the result
shapeDgl	Matrix that contains derivatives of shape functions w.r.t. global coordinates.

Referenced by GetStiffnessMatrix(), and GetStrainsAtPoint().

Element::VectorType itk::fem::Element::GetStrainsAtPoint	(	const VectorType &	pt,
		const Solution &	sol,
		unsigned int	index
	)		const

virtual

Definition at line 194 of file itkFEMElementBase.cxx.

References GetStrainDisplacementMatrix(), InterpolateSolution(), Jacobian(), ShapeFunctionDerivatives(), and ShapeFunctionGlobalDerivatives().

Element::VectorType itk::fem::Element::GetStressesAtPoint	(	const VectorType &	pt,
		const VectorType &	e,
		const Solution &	sol,
		unsigned int	index
	)		const

virtual

Definition at line 213 of file itkFEMElementBase.cxx.

References GetMaterialMatrix().

Element::VectorType itk::fem::Element::InterpolateSolution	(	const VectorType &	pt,
		const Solution &	sol,
		unsigned int	solutionIndex = `0`
	)		const

virtual

Return interpolated value of all unknown functions at given local point.

Parameters

pt	Point in local element coordinates.
sol	Reference to the master solution object. This object is created by the Solver object when the whole FEM problem is solved and contains the values of unknown functions at nodes (degrees of freedom).
solutionIndex	We allow more than one solution vector to be stored - this selects which to use in interpolation.

Definition at line 327 of file itkFEMElementBase.cxx.

References GetDegreeOfFreedom(), GetNode(), GetNumberOfDegreesOfFreedomPerNode(), GetNumberOfNodes(), itk::fem::Solution::GetSolutionValue(), and ShapeFunctions().

Referenced by GetStrainsAtPoint(), and itk::fem::LoadImplementationGenericLandmarkLoad::Implementation().

Element::Float itk::fem::Element::InterpolateSolutionN	(	const VectorType &	pt,
		const Solution &	sol,
		unsigned int	f,
		unsigned int	solutionIndex = `0`
	)		const

virtual

Return interpolated value of f-th unknown function at given local point.

Parameters

pt	Point in local element coordinates.
sol	Reference to the master solution object. This object is created by the Solver object when the whole FEM problem is solved and contains the values of unknown functions at nodes (degrees of freedom).
f	Number of unknown function to interpolate. Must be 0 <= f < GetNumberOfDegreesOfFreedomPerNode().
solutionIndex	We allow more than one solution vector to be stored - this selects which to use in interpolation.

Definition at line 355 of file itkFEMElementBase.cxx.

References GetDegreeOfFreedom(), GetNode(), GetNumberOfNodes(), itk::fem::Solution::GetSolutionValue(), and ShapeFunctions().

void itk::fem::Element::Jacobian	(	const VectorType &	pt,
		MatrixType &	J,
		const MatrixType *	pshapeD = `0`
	)		const

virtual

Compute the Jacobian matrix of the transformation from local to global coordinates at a given local point.

A column in this matrix corresponds to a global coordinate, while a row corresponds to different local coordinates. E.g. element at row 2, col 3 contains derivative of the third global coordinate with respect to local coordinate number 2.

In order to compute the Jacobian, we normally need the shape function derivatives. If they are known, you should pass a pointer to an object of MatrixType that contains the shape function derivatives. If they are not known, pass null pointer and they will be computed automatically.

Parameters

pt	Point in local coordinates
J	referece to matrix object, which will contain the jacobian
pshapeD	A pointer to derivatives of shape functions at point pt. If this pointer is 0, derivatives will be computed as necessary.

Geometry of a problem.

Reimplemented in itk::fem::Element2DC0LinearLine.

Definition at line 376 of file itkFEMElementBase.cxx.

References GetNodeCoordinates(), GetNumberOfSpatialDimensions(), and ShapeFunctionDerivatives().

Referenced by GetMassMatrix(), GetStiffnessMatrix(), GetStrainsAtPoint(), JacobianDeterminant(), JacobianInverse(), and ShapeFunctionGlobalDerivatives().

Element::Float itk::fem::Element::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 in itk::fem::Element2DC1Beam, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element2DC0LinearTriangular.

Definition at line 409 of file itkFEMElementBase.cxx.

References Jacobian().

Referenced by GetMassMatrix(), GetStiffnessMatrix(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), and itk::fem::LoadImplementationGenericBodyLoad::Implementation().

void itk::fem::Element::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 in itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element2DC0LinearTriangular.

Definition at line 432 of file itkFEMElementBase.cxx.

References Jacobian().

Referenced by ShapeFunctionGlobalDerivatives().

void itk::fem::FEMLightObject::Read	(	std::istream &	f,
		void *	info
	)

virtualinherited

Read an object data from input stream. Call this member to initialize the data members in the current object by reading data from provided input stream. Derived classes should first call the the parent's read function, to initialize the data from parent. Note that you must manually create the object of desired type using the FEMObjectFactory before you can call read function (this is pretty obvious). In this class only the global number is read from file. Derived classes may require some additional info in order to perform the reading. Pack this info in an object and pass a pointer to it in the info parameter. If you need runtime typechecking, use a polymorphic class and dynamic_cast operator inside the implementation of Read.

Here we just read the global number from the stream. This should be the first function called when reading object data.

Read and set the global object number

Reimplemented in itk::fem::Element::Node, itk::fem::LoadLandmark, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::LoadBCMFC, itk::fem::LoadGravConst, itk::fem::LoadBC, itk::fem::Element2DC1Beam, itk::fem::LoadElement, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::LoadTest< TClass >, itk::fem::LoadNode, itk::fem::LoadEdge, and itk::fem::MaterialLinearElasticity.

Definition at line 33 of file itkFEMLightObject.cxx.

References itk::fem::FEMLightObject::GN, and itk::fem::FEMLightObject::SkipWhiteSpace().

Referenced by itk::fem::FEMLightObject::CreateFromStream(), itk::fem::MaterialLinearElasticity::Read(), itk::fem::LoadNode::Read(), itk::fem::LoadElement::Read(), itk::fem::LoadBC::Read(), itk::fem::LoadBCMFC::Read(), and itk::fem::Element::Node::Read().

virtual void itk::fem::Element::SetMaterial ( Material::ConstPointer )

inlinevirtual

Set the pointer to the Material object used by the element. All derived classes, which use objects of Material class should override this method to provide access to the material from the base class.

See Also: GetMaterial

Definition at line 414 of file itkFEMElementBase.h.

virtual void itk::fem::Element::SetNode	(	unsigned int	n,
		NodeIDType	node
	)

pure virtual

Sets the pointe of n-th node in an element to node.

Implemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, and itk::fem::ElementStd< 4, 2 >.

virtual void itk::fem::Element::ShapeFunctionDerivatives	(	const VectorType &	pt,
		MatrixType &	shapeD
	)		const

pure 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

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element3DC0LinearHexahedron.

Referenced by GetMassMatrix(), GetStiffnessMatrix(), GetStrainsAtPoint(), Jacobian(), and ShapeFunctionGlobalDerivatives().

void itk::fem::Element::ShapeFunctionGlobalDerivatives	(	const VectorType &	pt,
		MatrixType &	shapeDgl,
		const MatrixType *	pJ = `0`,
		const MatrixType *	pshapeD = `0`
	)		const

virtual

Compute matrix of shape function derivatives with respect to global coordinates.

A column in this matrix corresponds to a specific shape function, while a row corresponds to different global coordinates.

Parameters

pt	Point in local element coordinates.
shapeDgl	Reference to a matrix object, which will be filled with values of shape function derivatives w.r.t. global (world) 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.
pshapeD	A pointer to derivatives of shape functions at point pt. If this pointer is 0, derivatives will be computed as necessary.

See Also: ShapeFunctionDerivatives

Definition at line 453 of file itkFEMElementBase.cxx.

References Jacobian(), JacobianInverse(), and ShapeFunctionDerivatives().

Referenced by GetStiffnessMatrix(), and GetStrainsAtPoint().

virtual VectorType itk::fem::Element::ShapeFunctions ( const VectorType & pt ) const

pure 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.

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element3DC0LinearHexahedron.

Referenced by itk::fem::ImageMetricLoad< TMoving, TFixed >::EvaluateMetricGivenSolution(), GetGlobalFromLocalCoordinates(), GetLandmarkContributionMatrix(), GetMassMatrix(), itk::fem::LoadImplementationGenericLandmarkLoad::Implementation(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::Implementation(), itk::fem::LoadImplementationGenericBodyLoad::Implementation(), InterpolateSolution(), InterpolateSolutionN(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::InterpolateVectorField().

void itk::fem::FEMLightObject::SkipWhiteSpace ( std::istream & f )

staticinherited

Helper function that skips all the whitespace and comments in an input stream.

Definition at line 189 of file itkFEMLightObject.cxx.

Referenced by itk::fem::FEMLightObject::CreateFromStream(), itk::fem::MaterialLinearElasticity::Read(), itk::fem::LoadEdge::Read(), itk::fem::LoadNode::Read(), itk::fem::LoadElement::Read(), itk::fem::LoadBC::Read(), itk::fem::LoadGravConst::Read(), itk::fem::FEMLightObject::Read(), itk::fem::LoadBCMFC::Read(), itk::fem::LoadLandmark::Read(), itk::fem::Element::Node::Read(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::ReadConfigFile().

void itk::fem::FEMLightObject::Write ( std::ostream & f ) const

virtualinherited

Write an object to the output stream. Call this member to write the data members in the current object to the output stream. Here we also need to know which derived class we actually are, so that we can write the class name. The class name is obtained by calling the virtual ClassID() member function and passing the result to the FEMObjectFactory.

Implementations of Write member funtion in derived classes should first call the parent's implementation of Write and finaly write whatever they need.

Here we just write the class name and GN. This should be the first function called when writing object data, so every derived class should first call the parent's write function. The Write function in base (this one) class knows which class is being written by calling the virtual ClassID() function and can write the class name properly.

Reimplemented in itk::fem::Element::Node, itk::fem::LoadLandmark, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::LoadBCMFC, itk::fem::LoadGravConst, itk::fem::LoadBC, itk::fem::Element2DC1Beam, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::LoadElement, itk::fem::LoadTest< TClass >, itk::fem::LoadNode, itk::fem::LoadEdge, and itk::fem::MaterialLinearElasticity.

Definition at line 57 of file itkFEMLightObject.cxx.

References itk::fem::FEMLightObject::ClassID(), and itk::fem::FEMLightObject::GN.

Referenced by itk::fem::MaterialLinearElasticity::Write(), itk::fem::LoadNode::Write(), itk::fem::LoadElement::Write(), itk::fem::LoadBC::Write(), itk::fem::LoadBCMFC::Write(), and itk::fem::Element::Node::Write().

Member Data Documentation

const Element::Float itk::fem::Element::gaussPoint

static

Initial value:

=
{
  { 0.0 },
  { 0.000000000000000 },
  { 0.577350269189626,-0.577350269189626 },
  { 0.774596669241483, 0.000000000000000,-0.774596669241483 },
  { 0.861136311594053, 0.339981043584856,-0.339981043584856,-0.861136311594053 },
  { 0.906179845938664, 0.538469310105683, 0.000000000000000,-0.538469310105683,-0.906179845938664},
  { 0.932469514203152, 0.661209386466264, 0.238619186083197,-0.238619186083197,-0.661209386466264,-0.932469514203152 },
  { 0.949107912342759, 0.741531185599394, 0.405845151377397, 0.000000000000000,-0.405845151377397,-0.741531185599394,-0.949107912342759 },
  { 0.960289856497536, 0.796666477413627, 0.525532409916329, 0.183434642495650,-0.183434642495650,-0.525532409916329,-0.796666477413627,-0.960289856497536 },
  { 0.968160239507626, 0.836031107326636, 0.613371432700590, 0.324253423403809, 0.000000000000000,-0.324253423403809,-0.613371432700590,-0.836031107326636,-0.968160239507626 },
  { 0.973906528517172, 0.865063366688985, 0.679409568299024, 0.433395394129247, 0.148874338981631,-0.148874338981631,-0.433395394129247,-0.679409568299024,-0.865063366688985,-0.973906528517172 }
}

Points for 1D Gauss-Legendre integration from -1 to 1. First index is order of integration, second index is the number of integration point.

Example: gaussPoint[4][2] returns third point of the 4th order integration rule. Subarray gaussPoint[0][...] does not provide useful information. It is there only to keep order index correct.

See Also: gaussWeight

Definition at line 478 of file itkFEMElementBase.h.

const Element::Float itk::fem::Element::gaussWeight

static

Initial value:

=
{
  { 0.0 },
  { 2.000000000000000 },
  { 1.000000000000000, 1.000000000000000 },
  { 0.555555555555555, 0.888888888888889, 0.555555555555555 },
  { 0.347854845137454, 0.652145154862546, 0.652145154862546, 0.347854845137454 },
  { 0.236926885056189, 0.478628670499366, 0.568888888888889, 0.478628670499366, 0.236926885056189 },
  { 0.171324492379170, 0.360761573048139, 0.467913934572691, 0.467913934572691, 0.360761573048139, 0.171324492379170 },
  { 0.129484966168869, 0.279705391489277, 0.381830050505119, 0.417959183673469, 0.381830050505119, 0.279705391489277, 0.129484966168869 },
  { 0.101228536290376, 0.222381034453374, 0.313706645877887, 0.362683783378362, 0.362683783378362, 0.313706645877887, 0.222381034453374, 0.101228536290376 },
  { 0.081274388361575, 0.180648160694858, 0.260610696402935, 0.312347077040003, 0.330239355001260, 0.312347077040003, 0.260610696402935, 0.180648160694858, 0.081274388361575 },
  { 0.066671344308688, 0.149451349150581, 0.219086362515982, 0.269266719309996, 0.295524224714753, 0.295524224714753, 0.269266719309996, 0.219086362515982, 0.149451349150581, 0.066671344308688 }
}

Weights for Gauss-Legendre integration.

See Also: gaussPoint

Definition at line 485 of file itkFEMElementBase.h.

int itk::fem::FEMLightObject::GN

inherited

Global number of an object (ID of an object) In general the ID's are required to be unique only within a specific type of derived classes (Elements, Nodes, ...) If the GN is not required, it can be ignored. (normally you need the GN when writing or reading objects to/from stream.

Definition at line 163 of file itkFEMLightObject.h.

Referenced by itk::fem::FEMLightObject::FEMLightObject(), itk::fem::Generate2DRectilinearMesh(), itk::fem::Generate3DRectilinearMesh(), itk::fem::FEMLightObject::Read(), itk::fem::LoadNode::Write(), itk::fem::LoadBC::Write(), and itk::fem::FEMLightObject::Write().

const std::string itk::fem::FEMLightObject::whitespaces =" \t\n\r"

staticinherited

Const string of all whitespace characters. This string is used by SkipWhiteSpace function.

Definition at line 133 of file itkFEMLightObject.h.

Referenced by itk::fem::FEMLightObject::CreateFromStream(), and itk::fem::MaterialLinearElasticity::Read().

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Typedef Documentation

Member Enumeration Documentation

Member Function Documentation

Member Data Documentation