itk::fem Namespace Reference

Detailed Description

Contains finite element modeling (FEM) classes and support routines.

Classes

class Element

Abstract base element class. More...

class Element1DStress

Class that is used to define linear elasticity problem in 1D space. More...

class Element2DC0LinearLine

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

class Element2DC0LinearLineStress

2-noded finite element class in 2D space for linear elasticity problem. More...

class Element2DC0LinearQuadrilateral

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

class Element2DC0LinearQuadrilateralMembrane

4-noded finite element class in 2D space for linear elasticity problem More...

class Element2DC0LinearQuadrilateralStrain

4-noded finite element class in 2D space for linear elasticity problem More...

class Element2DC0LinearQuadrilateralStress

4-noded finite element class in 2D space for linear elasticity problem More...

class Element2DC0LinearTriangular

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

class Element2DC0LinearTriangularMembrane

3-noded finite element class in 2D space for linear elasticity problem. More...

class Element2DC0LinearTriangularStrain

3-noded finite element class in 2D space for linear elasticity problem. More...

class Element2DC0LinearTriangularStress

3-noded finite element class in 2D space for linear elasticity problem. More...

class Element2DC0QuadraticTriangular

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

class Element2DC0QuadraticTriangularStrain

3-noded finite element class in 2D space for linear elasticity problem. More...

class Element2DC0QuadraticTriangularStress

3-noded finite element class in 2D space for linear elasticity problem. More...

class Element2DC1Beam

1D Beam (spring that also bends) finite element in 2D space. More...

class Element2DMembrane

Class that is used to define a membrane energy problem in 2D space. More...

class Element2DStrain

Class that is used to define linear elasticity problem in 2D space. More...

class Element2DStress

Class that is used to define linear elasticity problem in 2D space. More...

class Element3DC0LinearHexahedron

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

class Element3DC0LinearHexahedronMembrane

8-noded finite element class in 3D space for linear elasticity problem More...

class Element3DC0LinearHexahedronStrain

8-noded finite element class in 3D space for linear elasticity problem More...

class Element3DC0LinearTetrahedron

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

class Element3DC0LinearTetrahedronMembrane

4-noded finite element class in 3D space for linear elasticity problem More...

class Element3DC0LinearTetrahedronStrain

4-noded finite element class in 3D space for linear elasticity problem More...

class Element3DMembrane

Class that is used to define a membrane energy problem in 3D space. More...

class Element3DStrain

Class that is used to define linear elasticity problem in 3D space. More...

class ElementStd

Implements standard node management in the element classes. More...

class FEMException

Base class for all exception's that can occur within FEM classes. More...

class FEMExceptionIO

Base class for all IO exception's that can occur within FEM classe. More...

class FEMExceptionItpackSolver

handles errors that occur in itpack solving routines More...

class FEMExceptionItpackSparseMatrixSbagn

handles errors that occur when unfinalizing the matrix More...

class FEMExceptionItpackSparseMatrixSbsij

handles errors that occur when building the matrix More...

class FEMExceptionLinearSystem

class FEMExceptionLinearSystemBounds

class FEMExceptionObjectNotFound

Object not found exception. More...

class FEMExceptionSolution

Base class for all exceptions that can occur when solving FEM problem. More...

class FEMExceptionWrongClass

Bad object exception. More...

class FEMInitialization

FEM Library initialization and housekeeping. More...

class FEMLightObject

Base class for all classes that define the FEM system. More...

class FEMObjectFactory

Create objects of derived classes by specifying a class ID. More...

class FEMP

Pointer used to store polymorphic elements in STL arrays. More...

class FEMPArray

Array for FEMP objects. More...

class FEMRegistrationFilter

FEM Image registration filter. The image registration problem is modeled here with the finite element method. Image registration is, in general, an ill-posed problem. Thus, we use an optimization scheme where the optimization criterion is given by a regularized variational energy. The variational energy arises from modeling the image as a physical body on which external forces act. The body is allowed to deform so as to minimize the applied force. The resistance of the physical body to deformation, determined by the physics associated with the body, serves to regularize the solution. The forces applied to the body are, generally, highly non-linear and so the body is allowed to deform slowly and incrementally. The direction it deforms follows the gradient of the potential energy (the force) we define. The potential energies we may choose from are given by the itk image-to-image metrics. The choices and the associated direction of descent are : Mean Squares (minimize), Normalized Cross-Correlation (maximize) Mutual Information (maximize). Note that we have to set the direction (SetDescentDirection) when we choose a metric. The forces driving the problem may also be given by user-supplied landmarks. The corners of the image, in this example, are always pinned. This example is designed for 2D or 3D images. A rectilinear mesh is generated automatically given the correct element type (Quadrilateral or Hexahedral). Our specific Solver for this example uses trapezoidal time stepping. This is a method for solving a second-order PDE in time. The solution is penalized by the zeroth (mass matrix) and first derivatives (stiffness matrix) of the shape functions. There is an option to perform a line search on the energy after each iteration. Optimal parameter settings require experimentation. The following approach tends to work well : Choose the relative size of density to elasticity (e.g. Rho / E ~= 1.) such that the image deforms locally and slowly. This also affects the stability of the solution. Choose the time step to control the size of the deformation at each step. Choose enough iterations to allow the solution to converge (this may be automated). More...

class FiniteDifferenceFunctionLoad

General image pair load that uses the itkFiniteDifferenceFunctions. More...

class GaussIntegrate

Use the Gauss-Legendre formula to perform integration. More...

class ImageMetricLoad

General image pair load that uses the itkImageToImageMetrics. More...

class ImageMetricLoadImplementation

class INITClass

Class that is used in FEM_CLASS_INIT macro. More...

class ItpackSparseMatrix

a compressed row sparse matrix representation that makes use of itpack to dynamically assemble the matrix More...

class LinearSystemWrapper

Defines all functions required by Solver class to allocate, assemble and solve a linear system of equation. More...

class LinearSystemWrapperDenseVNL

LinearSystemWrapper class that uses VNL numeric library functions to define a sparse linear system of equations. More...

class LinearSystemWrapperItpack

LinearSystemWrapper class that uses Itpack numeric library functions to define and solve a sparse linear system of equations. More...

class LinearSystemWrapperVNL

LinearSystemWrapper class that uses VNL numeric library functions to define a sparse linear system of equations. More...

class Load

General abstract load base class. More...

class LoadBC

Generic essential (Dirichlet) boundary conditions. More...

class LoadBCMFC

Generic linear multi freedom displacement constraint in global coordinate system. More...

class LoadEdge

A generic load that can be applied to an edge of the element. More...

class LoadElement

Virtual element load base class. More...

class LoadGrav

Abstract gravity load class. More...

class LoadGravConst

Constant gravity load class. More...

class LoadImplementationGenericBodyLoad

Class that holds a templated generic body load implementation. More...

class LoadImplementationGenericLandmarkLoad

Class that holds a templated generic landmark load implementation. More...

class LoadImplementationTest

Example implementation of templated LoadTest class. More...

class LoadLandmark

This load is derived from the motion of a specific landmark. More...

class LoadNode

This load is applied on a specific point within the system. More...

class LoadPoint

This load is applied on a point in an element. More...

class LoadTest

Example to show how to define templated load classes. More...

class Material

Base class for storing all the implicit material and other properties required to fully define the element class. More...

class MaterialLinearElasticity

Linear elasticity material class. More...

class ReadInfoType

Helper class for storing additional information that is required when reading FEM objects from stream. More...

class Solution

Provides functions to access the values of the solution vector. More...

class Solver

Main FEM solver. More...

class SolverHyperbolic

Solver class suitable for hyperbolic problems. More...

class VisitorDispatcher

This class provides the functionality needed to apply the correct visitor function to object of some class. The specific visitor function is choosen, based on a given pointer to some object. More...

class VisitorDispatcherTemplateHelper

typedef void(* LoadImplementationFunctionPointer )(ConstPointer, Element::LoadPointer, Element::VectorType &)

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

Typedefs

typedef FEMObjectFactory
< FEMLightObject > FEMOF

typedef Element::Node Node

typedef void(* c_void_cast )()

Functions

void Generate2DRectilinearMesh (itk::fem::Element::ConstPointer e0, Solver &S, vnl_vector< double > &orig, vnl_vector< double > &size, vnl_vector< double > &Nel)

void Generate3DRectilinearMesh (itk::fem::Element::ConstPointer e0, Solver &S, vnl_vector< double > &orig, vnl_vector< double > &size, vnl_vector< double > &Nel)

static INITClass Initializer_ElementNode (Element::Node::CLID())

Variables

static FEMInitialization FEMInitialization_var

Typedef Documentation

typedef void(* itk::fem::c_void_cast)()

Definition at line 214 of file itkFEMObjectFactory.h.

typedef FEMObjectFactory<FEMLightObject> itk::fem::FEMOF

Short alias for FEMObjectFactory<FEMLightObject>

Definition at line 173 of file itkFEMLightObject.h.

typedef void(* itk::fem::LoadImplementationFunctionPointer)(ConstPointer, Element::LoadPointer, Element::VectorType &)

Pointer type that specifies functions that can handle loads on this element

Definition at line 70 of file itkFEMElementBase.h.

typedef Element::Node itk::fem::Node

Definition at line 685 of file itkFEMElementBase.h.

Function Documentation

void itk::fem::Generate2DRectilinearMesh	(	itk::fem::Element::ConstPointer	e0,
		Solver &	S,
		vnl_vector< double > &	orig,
		vnl_vector< double > &	size,
		vnl_vector< double > &	Nel
	)

Use this function to generate 2D meshes in Solver.

Generate2DRectilinearMesh This function uses the generic quadrilateral elements to build meshes that can be used with specific elements for solving membrane or linear elasticity problems.

See other functions if you need to constuct the mesh from other types of elements.

Note:: All elements will be created by copying the existing element which is passed to the function. Only number and node pointers will be changed in copied element. Make sure that this element has material class and any other properties defined before generating a mesh.

See also:: Generate3DRectilinearMesh Generate a rectangular mesh of quadrilateral elements

void itk::fem::Generate3DRectilinearMesh	(	itk::fem::Element::ConstPointer	e0,
		Solver &	S,
		vnl_vector< double > &	orig,
		vnl_vector< double > &	size,
		vnl_vector< double > &	Nel
	)

Use this function to generate 3D meshes in Solver.

Generate3DRectilinearMesh Generate a rectangular mesh of hexahedron elements.

See also:: Generate2DRectilinearMesh

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

Pointer type that specifies functions that can handle loads on this element

Definition at line 71 of file itkFEMElementBase.h.

static INITClass itk::fem::Initializer_ElementNode ( Element::Node:: CLID() ) [static]

Variable Documentation

FEMInitialization itk::fem::FEMInitialization_var [static]

Definition at line 55 of file itkFEMInitialization.h.


Classes
class	Element
	Abstract base element class. More...
class	Element1DStress
	Class that is used to define linear elasticity problem in 1D space. More...
class	Element2DC0LinearLine
	2-noded, linear, C0 continuous line element in 2D space. More...
class	Element2DC0LinearLineStress
	2-noded finite element class in 2D space for linear elasticity problem. More...
class	Element2DC0LinearQuadrilateral
	4-noded, linear, C0 continuous finite element in 2D space. More...
class	Element2DC0LinearQuadrilateralMembrane
	4-noded finite element class in 2D space for linear elasticity problem More...
class	Element2DC0LinearQuadrilateralStrain
	4-noded finite element class in 2D space for linear elasticity problem More...
class	Element2DC0LinearQuadrilateralStress
	4-noded finite element class in 2D space for linear elasticity problem More...
class	Element2DC0LinearTriangular
	3-noded, linear, C0 continuous finite element in 2D space. More...
class	Element2DC0LinearTriangularMembrane
	3-noded finite element class in 2D space for linear elasticity problem. More...
class	Element2DC0LinearTriangularStrain
	3-noded finite element class in 2D space for linear elasticity problem. More...
class	Element2DC0LinearTriangularStress
	3-noded finite element class in 2D space for linear elasticity problem. More...
class	Element2DC0QuadraticTriangular
	3-noded, quadratic, C0 continuous finite element in 2D space. More...
class	Element2DC0QuadraticTriangularStrain
	3-noded finite element class in 2D space for linear elasticity problem. More...
class	Element2DC0QuadraticTriangularStress
	3-noded finite element class in 2D space for linear elasticity problem. More...
class	Element2DC1Beam
	1D Beam (spring that also bends) finite element in 2D space. More...
class	Element2DMembrane
	Class that is used to define a membrane energy problem in 2D space. More...
class	Element2DStrain
	Class that is used to define linear elasticity problem in 2D space. More...
class	Element2DStress
	Class that is used to define linear elasticity problem in 2D space. More...
class	Element3DC0LinearHexahedron
	8-noded, linear, C0 continuous finite element in 3D space. More...
class	Element3DC0LinearHexahedronMembrane
	8-noded finite element class in 3D space for linear elasticity problem More...
class	Element3DC0LinearHexahedronStrain
	8-noded finite element class in 3D space for linear elasticity problem More...
class	Element3DC0LinearTetrahedron
	4-noded, linear, C0 continuous finite element in 3D space. More...
class	Element3DC0LinearTetrahedronMembrane
	4-noded finite element class in 3D space for linear elasticity problem More...
class	Element3DC0LinearTetrahedronStrain
	4-noded finite element class in 3D space for linear elasticity problem More...
class	Element3DMembrane
	Class that is used to define a membrane energy problem in 3D space. More...
class	Element3DStrain
	Class that is used to define linear elasticity problem in 3D space. More...
class	ElementStd
	Implements standard node management in the element classes. More...
class	FEMException
	Base class for all exception's that can occur within FEM classes. More...
class	FEMExceptionIO
	Base class for all IO exception's that can occur within FEM classe. More...
class	FEMExceptionItpackSolver
	handles errors that occur in itpack solving routines More...
class	FEMExceptionItpackSparseMatrixSbagn
	handles errors that occur when unfinalizing the matrix More...
class	FEMExceptionItpackSparseMatrixSbsij
	handles errors that occur when building the matrix More...
class	FEMExceptionLinearSystem
class	FEMExceptionLinearSystemBounds
class	FEMExceptionObjectNotFound
	Object not found exception. More...
class	FEMExceptionSolution
	Base class for all exceptions that can occur when solving FEM problem. More...
class	FEMExceptionWrongClass
	Bad object exception. More...
class	FEMInitialization
	FEM Library initialization and housekeeping. More...
class	FEMLightObject
	Base class for all classes that define the FEM system. More...
class	FEMObjectFactory
	Create objects of derived classes by specifying a class ID. More...
class	FEMP
	Pointer used to store polymorphic elements in STL arrays. More...
class	FEMPArray
	Array for FEMP objects. More...
class	FEMRegistrationFilter
	FEM Image registration filter. The image registration problem is modeled here with the finite element method. Image registration is, in general, an ill-posed problem. Thus, we use an optimization scheme where the optimization criterion is given by a regularized variational energy. The variational energy arises from modeling the image as a physical body on which external forces act. The body is allowed to deform so as to minimize the applied force. The resistance of the physical body to deformation, determined by the physics associated with the body, serves to regularize the solution. The forces applied to the body are, generally, highly non-linear and so the body is allowed to deform slowly and incrementally. The direction it deforms follows the gradient of the potential energy (the force) we define. The potential energies we may choose from are given by the itk image-to-image metrics. The choices and the associated direction of descent are : Mean Squares (minimize), Normalized Cross-Correlation (maximize) Mutual Information (maximize). Note that we have to set the direction (SetDescentDirection) when we choose a metric. The forces driving the problem may also be given by user-supplied landmarks. The corners of the image, in this example, are always pinned. This example is designed for 2D or 3D images. A rectilinear mesh is generated automatically given the correct element type (Quadrilateral or Hexahedral). Our specific Solver for this example uses trapezoidal time stepping. This is a method for solving a second-order PDE in time. The solution is penalized by the zeroth (mass matrix) and first derivatives (stiffness matrix) of the shape functions. There is an option to perform a line search on the energy after each iteration. Optimal parameter settings require experimentation. The following approach tends to work well : Choose the relative size of density to elasticity (e.g. Rho / E ~= 1.) such that the image deforms locally and slowly. This also affects the stability of the solution. Choose the time step to control the size of the deformation at each step. Choose enough iterations to allow the solution to converge (this may be automated). More...
class	FiniteDifferenceFunctionLoad
	General image pair load that uses the itkFiniteDifferenceFunctions. More...
class	GaussIntegrate
	Use the Gauss-Legendre formula to perform integration. More...
class	ImageMetricLoad
	General image pair load that uses the itkImageToImageMetrics. More...
class	ImageMetricLoadImplementation
class	INITClass
	Class that is used in FEM_CLASS_INIT macro. More...
class	ItpackSparseMatrix
	a compressed row sparse matrix representation that makes use of itpack to dynamically assemble the matrix More...
class	LinearSystemWrapper
	Defines all functions required by Solver class to allocate, assemble and solve a linear system of equation. More...
class	LinearSystemWrapperDenseVNL
	LinearSystemWrapper class that uses VNL numeric library functions to define a sparse linear system of equations. More...
class	LinearSystemWrapperItpack
	LinearSystemWrapper class that uses Itpack numeric library functions to define and solve a sparse linear system of equations. More...
class	LinearSystemWrapperVNL
	LinearSystemWrapper class that uses VNL numeric library functions to define a sparse linear system of equations. More...
class	Load
	General abstract load base class. More...
class	LoadBC
	Generic essential (Dirichlet) boundary conditions. More...
class	LoadBCMFC
	Generic linear multi freedom displacement constraint in global coordinate system. More...
class	LoadEdge
	A generic load that can be applied to an edge of the element. More...
class	LoadElement
	Virtual element load base class. More...
class	LoadGrav
	Abstract gravity load class. More...
class	LoadGravConst
	Constant gravity load class. More...
class	LoadImplementationGenericBodyLoad
	Class that holds a templated generic body load implementation. More...
class	LoadImplementationGenericLandmarkLoad
	Class that holds a templated generic landmark load implementation. More...
class	LoadImplementationTest
	Example implementation of templated LoadTest class. More...
class	LoadLandmark
	This load is derived from the motion of a specific landmark. More...
class	LoadNode
	This load is applied on a specific point within the system. More...
class	LoadPoint
	This load is applied on a point in an element. More...
class	LoadTest
	Example to show how to define templated load classes. More...
class	Material
	Base class for storing all the implicit material and other properties required to fully define the element class. More...
class	MaterialLinearElasticity
	Linear elasticity material class. More...
class	ReadInfoType
	Helper class for storing additional information that is required when reading FEM objects from stream. More...
class	Solution
	Provides functions to access the values of the solution vector. More...
class	Solver
	Main FEM solver. More...
class	SolverHyperbolic
	Solver class suitable for hyperbolic problems. More...
class	VisitorDispatcher
	This class provides the functionality needed to apply the correct visitor function to object of some class. The specific visitor function is choosen, based on a given pointer to some object. More...
class	VisitorDispatcherTemplateHelper
typedef void(*	LoadImplementationFunctionPointer )(ConstPointer, Element::LoadPointer, Element::VectorType &)
virtual void	GetLoadVector (Element::LoadPointer l, Element::VectorType &Fe) const
Typedefs
typedef FEMObjectFactory < FEMLightObject >	FEMOF
typedef Element::Node	Node

typedef void(*	c_void_cast )()
Functions
void	Generate2DRectilinearMesh (itk::fem::Element::ConstPointer e0, Solver &S, vnl_vector< double > &orig, vnl_vector< double > &size, vnl_vector< double > &Nel)
void	Generate3DRectilinearMesh (itk::fem::Element::ConstPointer e0, Solver &S, vnl_vector< double > &orig, vnl_vector< double > &size, vnl_vector< double > &Nel)
static INITClass	Initializer_ElementNode (Element::Node::CLID())
Variables
static FEMInitialization	FEMInitialization_var