#include <BSplineFreeFormTransformation3D.h>

Inheritance diagram for mirtk::BSplineFreeFormTransformation3D:

Collaboration diagram for mirtk::BSplineFreeFormTransformation3D:

Public Types
enum	ParametricGradientType { PG_Default, PG_Analytic, PG_Convolution, PG_Approximation }
	Options for parametric gradient calculation. More...

Public Types inherited from mirtk::FreeFormTransformation
typedef GenericExtrapolateImageFunction< CPImage >	CPExtrapolator
	Base type used for extrapolation of control point data.

typedef GenericImage< CPValue >	CPImage
	Type of image representation of free-form transformation.

typedef GenericInterpolateImageFunction< CPImage >	CPInterpolator

typedef Vector3D< DOFStatus >	CPStatus
	Type of vector storing status of control point coefficients.

typedef Vector3D< DOFValue >	CPValue
	Type of vector storing the coefficients at a control point.

typedef CPValue	Vector

Public Types inherited from mirtk::Transformation
typedef Status	DOFStatus
	Type of transforamtion parameter status.

typedef double	DOFValue
	Type of transformation parameter value.

Public Member Functions
void	AddApproximateSplineCoefficients (const double , const double , const double , const double , const double , const double , int, double *, double=1., bool=false) const

virtual void	ApproximateDOFs (const double , const double , const double , const double , const double , const double , const double *, int)

virtual void	ApproximateDOFsGradient (const double , const double , const double , const double , const double , const double , const double , int, double , double=1.0) const

virtual double	BendingEnergy (double, double, double, double=0, double=NaN, bool=true) const
	Calculates the bending energy of the transformation.

virtual double	BendingEnergy (bool=false, bool=true) const
	Approximates the bending energy on the control point lattice.

virtual double	BendingEnergy (const ImageAttributes &, double=NaN, bool=true) const
	Approximates the bending energy on the specified discrete domain.

virtual void	BendingEnergyGradient (double *, double=1, bool=false, bool=true, bool=true) const

virtual void	BoundingBox (int, double &, double &, double &, double &, double &, double &, double=1) const

	BSplineFreeFormTransformation3D ()
	Default constructor.

	BSplineFreeFormTransformation3D (double, double, double, double, double, double, double, double, double, double , double , double *)
	Construct free-form transformation for given image domain and lattice spacing.

	BSplineFreeFormTransformation3D (const ImageAttributes &, double=-1, double=-1, double=-1)
	Construct free-form transformation for given image domain and lattice spacing.

	BSplineFreeFormTransformation3D (const BaseImage &, double, double, double)
	Construct free-form transformation for given target image and lattice spacing.

	BSplineFreeFormTransformation3D (const GenericImage< double > &, bool=false)
	Construct free-form transformation from existing 3D+t deformation field.

	BSplineFreeFormTransformation3D (const BSplineFreeFormTransformation3D &)
	Copy Constructor.

virtual bool	CanModifyDisplacement (int=-1) const

virtual bool	CanRead (TransformationType) const
	Whether this transformation can read a file of specified type (i.e. format)

virtual void	DeriveJacobianWrtDOF (Matrix &, int, double, double, double, double=0, double=NaN) const
	Calculates the derivative of the Jacobian of the transformation (w.r.t. world coordinates) w.r.t. a transformation parameter.

virtual void	DisplacementAfterDOFChange (int dof, double dv, GenericImage< double > &dx, double t, double t0=-1, const WorldCoordsImage *i2w=NULL) const

void	Evaluate (double &, double &, double &, int, int) const
	Evaluates the FFD at a lattice point.

void	Evaluate (double &, double &, double &, int, int, int) const
	Evaluates the FFD at a lattice point.

void	Evaluate (double &, double &, double &) const
	Evaluates the FFD at a point in lattice coordinates.

void	EvaluateDerivativeOfJacobianWrtDOF (Matrix &, int, double, double) const

void	EvaluateDerivativeOfJacobianWrtDOF (Matrix &, int, double, double, double) const

void	EvaluateHessian (Matrix [3], int, int) const
	Calculates the Hessian of the 2D FFD at a point in lattice coordinates.

void	EvaluateHessian (Matrix [3], double, double) const
	Calculates the Hessian of the 2D FFD at a point in lattice coordinates.

void	EvaluateHessian (Matrix [3], int, int, int) const
	Calculates the Hessian of the FFD at a point in lattice coordinates.

void	EvaluateHessian (Matrix [3], double, double, double) const
	Calculates the Hessian of the FFD at a point in lattice coordinates.

void	EvaluateInside (double &, double &, double &) const
	Evaluates the FFD at a point in lattice coordinates inside the FFD domain.

void	EvaluateJacobian (Matrix &, int, int) const
	Calculates the Jacobian of the FFD at a point in lattice coordinates.

void	EvaluateJacobian (Matrix &, int, int, int) const
	Calculates the Jacobian of the FFD at a point in lattice coordinates.

void	EvaluateJacobian (Matrix &, double, double) const
	Calculates the Jacobian of the FFD at a point in lattice coordinates.

void	EvaluateJacobian (Matrix &, double, double, double) const
	Calculates the Jacobian of the FFD at a point in lattice coordinates.

void	EvaluateJacobianDetDerivative (double dJ[3], const Matrix &adj, double a, double b, double c, bool wrt_world=true, bool use_spacing=true) const

void	EvaluateJacobianDetDerivative (double dJ[3], const Matrix &adj, int a, int b, int c, bool wrt_world=true, bool use_spacing=true) const

void	EvaluateJacobianDetDerivative (double dJ[3], const Matrix &adj, int i, int j, int k, double x, double y, double z, bool wrt_world=true, bool use_spacing=true) const

void	EvaluateJacobianDetDerivative (double dJ[3], const Matrix &adj, int cp, double x, double y, double z, bool wrt_world=true, bool use_spacing=true) const

void	EvaluateJacobianDOFs (double [3], int, int, double, double) const

void	EvaluateJacobianDOFs (double [3], int, int, int, double, double, double) const

void	EvaluateJacobianDOFs (double [3], int, int, int, int, double, double, double, double) const

void	EvaluateJacobianWorld (Matrix &, double, double) const

void	EvaluateJacobianWorld (Matrix &, double, double, double) const

void	EvaluateLaplacian (double [3], int, int, int) const
	Calculates the Laplacian of the FFD at a point in lattice coordinates.

void	EvaluateLaplacian (double [3], double, double, double) const
	Calculates the Laplacian of the FFD at a point in lattice coordinates.

void	EvaluateLaplacian (double &, double &, double &) const
	Calculates the Laplacian of the FFD at a point in lattice coordinates.

virtual void	FFDJacobianDetDerivative (double dJ[3], const Matrix &adj, int cp, double x, double y, double z, double=0, double=NaN, bool wrt_world=true, bool use_spacing=true) const

virtual void	FFDJacobianWorld (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t either control point displacements or velocities.

virtual int	GetTAfterSubdivision () const
	Number of control points in t after subdivision.

virtual double	GetTSpacingAfterSubdivision () const
	Control point spacing in t after subdivision.

virtual int	GetXAfterSubdivision () const
	Number of control points in x after subdivision.

virtual double	GetXSpacingAfterSubdivision () const
	Control point spacing in x after subdivision.

virtual int	GetYAfterSubdivision () const
	Number of control points in y after subdivision.

virtual double	GetYSpacingAfterSubdivision () const
	Control point spacing in y after subdivision.

virtual int	GetZAfterSubdivision () const
	Number of control points in z after subdivision.

virtual double	GetZSpacingAfterSubdivision () const
	Control point spacing in z after subdivision.

virtual void	Interpolate (const double , const double , const double *=NULL)

virtual void	JacobianDOFs (double [3], int, int, int, double, double, double) const
	Calculates the Jacobian of the transformation w.r.t. the parameters of a control point.

virtual int	KernelSize () const
	Size of support region of the used kernel.

virtual void	LocalHessian (Matrix [3], double, double, double, double=0, double=NaN) const
	Calculates the Hessian for each component of the local transformation w.r.t world coordinates.

virtual void	LocalJacobian (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the local transformation w.r.t world coordinates.

virtual void	LocalTransform (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the local transformation component only.

virtual ParameterList	Parameter () const
	Get (non-DoF) parameters as key/value as string map.

virtual void	ParametricGradient (const GenericImage< double > , double , const WorldCoordsImage , const WorldCoordsImage , double=NaN, double=1) const
	to a gradient w.r.t the parameters of this transformation More...

virtual void	Print (ostream &, Indent=0) const
	Prints the parameters of the transformation.

virtual bool	Set (const char , const char )
	Set named (non-DoF) parameter from value as string.

virtual void	Subdivide (bool=true, bool=true, bool=true, bool=true)
	Subdivide FFD lattice.

virtual	~BSplineFreeFormTransformation3D ()
	Destructor.

Public Member Functions inherited from mirtk::FreeFormTransformation3D
void	BoundingBoxCP (int cp, Point &, Point &, double=1) const

void	BoundingBoxImage (const BaseImage *, int, int &, int &, int &, int &, int &, int &, double=1) const

void	GetStatusCP (int, int, int, DOFStatus &, DOFStatus &, DOFStatus &) const

virtual void	Initialize (const ImageAttributes &)
	Initialize free-form transformation.

virtual void	JacobianDOFs (Matrix &, int, int, int, double, double, double) const
	Calculates the Jacobian of the transformation w.r.t a control point.

virtual void	JacobianDOFs (Matrix &, int, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t a control point.

virtual void	JacobianDOFs (double [3], int, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t a transformation parameter.

void	MultiBoundingBoxImage (const BaseImage *, int, int &, int &, int &, int &, int &, int &, double=1) const

virtual void	ParametricGradient (const PointSet &, const Vector3D< double > , double , double=0, double=NaN, double=1) const

void	PutStatusCP (int, int, int, DOFStatus, DOFStatus, DOFStatus)

virtual	~FreeFormTransformation3D ()
	Destructor.

Public Member Functions inherited from mirtk::FreeFormTransformation
int	ActualNumberOfDOFs () const

virtual double	Approximate (const Transformation *, int=1, double=.0)

virtual double	Approximate (const ImageAttributes &, double , double , double *, int=1, double=.0)

virtual double	Approximate (const double , const double , const double , double , double , double , int, int=1, double=.0)

virtual double	Approximate (const double , const double , const double , const double , double , double , double *, int, int=1, double=.0)

virtual double	ApproximateAsNew (const Transformation *, int=1, double=.0)
	Approximate another transformation and return approximation error.

virtual double	ApproximateAsNew (const ImageAttributes &, double , double , double *, int=1, double=.0)

virtual ImageAttributes	ApproximationDomain (const ImageAttributes &, const Transformation *)

const ImageAttributes &	Attributes () const
	Returns attributes of control point grid.

void	BoundingBox (double &, double &) const
	Gets the temporal bounding box of the free-form deformation (in ms)

void	BoundingBox (double &, double &, double &, double &, double &, double &) const
	Gets the spatial bounding box of the free-form deformation (in mm)

void	BoundingBox (Point &, Point &) const
	Gets the spatial bounding box of the free-form deformation (in mm)

void	BoundingBox (double &, double &, double &, double &, double &, double &, double &, double &) const
	Gets the spatio-temporal bounding box of the free-form deformation (in mm and ms)

void	BoundingBox (Point &, double &, Point &, double &) const
	Gets the spatio-temporal bounding box of the free-form deformation (in mm and ms)

virtual void	BoundingBox (int, double &, double &, double=1) const

virtual void	BoundingBox (int, double &, double &, double &, double &, double &, double &, double &, double &, double=1) const

void	BoundingBox (int, Point &, Point &, double=1) const

bool	BoundingBox (const ImageAttributes &, int, int &, int &, int &, int &, int &, int &, double=1) const

bool	BoundingBox (const ImageAttributes &, int, int &, int &, int &, int &, int &, int &, int &, int &, double=1) const

bool	BoundingBox (const Image *, int, int &, int &, int &, int &, int &, int &, double=1) const

bool	BoundingBox (const Image *, int, int &, int &, int &, int &, int &, int &, int &, int &, double=1) const

void	ControlPointLocation (int, double &, double &) const
	Gets the location of the given control point (in mm)

void	ControlPointLocation (int, double &, double &, double &) const
	Gets the location of the given control point (in mm)

Point	ControlPointLocation (int) const
	Returns the location of the given control point (in mm)

virtual bool	CopyFrom (const Transformation *)

bool	CropPadPassiveCPs (int=0, bool=false)

virtual bool	CropPadPassiveCPs (int, int, int=0, int=0, bool=false)

bool	DOFBoundingBox (const ImageAttributes &, int, int &, int &, int &, int &, int &, int &, double=1) const

bool	DOFBoundingBox (const Image *, int, int &, int &, int &, int &, int &, int &, double=1) const

virtual double	DOFGradientNorm (const double *) const
	Get norm of the gradient vector.

int	DOFToDimension (int) const
	Get index of dimension corresponding to transformation parameter (DoFs)

int	DOFToIndex (int) const
	Get index of control point corresponding to transformation parameter (DoFs)

double	EvaluateRMSError (const Transformation *) const
	Evaluates RMS error of transformation at control points compared to another.

virtual void	ExtrapolationMode (enum ExtrapolationMode)
	Set extrapolation mode.

const CPExtrapolator *	Extrapolator () const

void	Get (int, Vector &) const
	Gets values of the parameters at a control point.

void	Get (int, double &, double &, double &) const
	Gets values of the parameters at a control point.

void	Get (int, int, int, double &, double &, double &) const
	Gets values of the parameters at a control point.

void	Get (int, int, int, int, double &, double &, double &) const
	Gets values of the parameters at a control point.

void	GetOrientation (double , double , double *) const
	Gets the orientation of the free-form deformation lattice.

void	GetSpacing (double &, double &, double &) const
	Gets the control point spacing (in mm)

void	GetSpacing (double &, double &, double &, double &) const
	Gets the control point spacing (in mm)

void	GetStatus (int, CPStatus &) const
	Gets status of the parameters at a control point.

void	GetStatus (int, int, int, DOFStatus &, DOFStatus &, DOFStatus &) const
	Gets status of the parameters at a control point.

void	GetStatus (int, int, int, int, DOFStatus &, DOFStatus &, DOFStatus &) const
	Gets status of the parameters at a control point.

int	GetT () const
	Returns the number of control points in t.

double	GetTSpacing () const
	Returns the of control point spacing in t.

int	GetX () const
	Returns the number of control points in x.

double	GetXSpacing () const
	Returns the of control point spacing in x.

int	GetY () const
	Returns the number of control points in y.

double	GetYSpacing () const
	Returns the of control point spacing in y.

int	GetZ () const
	Returns the number of control points in z.

double	GetZSpacing () const
	Returns the of control point spacing in z.

virtual void	GlobalHessian (Matrix [3], double, double, double, double=0, double=NaN) const
	Calculates the Hessian for each component of the global transformation w.r.t world coordinates.

virtual void	GlobalInverse (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the inverse of the global transformation only.

virtual void	GlobalJacobian (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the global transformation w.r.t world coordinates.

virtual void	GlobalTransform (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the global transformation component only.

virtual void	Hessian (Matrix [3], double, double, double, double=0, double=NaN) const
	Calculates the Hessian for each component of the transformation w.r.t world coordinates.

void	HessianToWorld (double &, double &, double &) const

void	HessianToWorld (double &, double &, double &, double &, double &, double &) const

void	HessianToWorld (Matrix &) const

void	HessianToWorld (Matrix [3]) const

void	IndexToDOFs (int, int &, int &) const
	Get indices of transformation parameters (DoFs)

void	IndexToDOFs (int, int &, int &, int &) const
	Get indices of transformation parameters (DoFs)

void	IndexToLattice (int, int &, int &) const
	Get control point lattice coordinates from index.

void	IndexToLattice (int, int &, int &, int &) const
	Get control point lattice coordinates from index.

void	IndexToLattice (int, int &, int &, int &, int &) const
	Get control point lattice coordinates from index.

void	IndexToWorld (int, double &, double &) const
	Get world coordinates (in mm) of control point.

void	IndexToWorld (int, double &, double &, double &) const
	Get world coordinates (in mm) of control point.

void	IndexToWorld (int, Point &) const
	Get world coordinates (in mm) of control point.

Point	IndexToWorld (int) const
	Get world coordinates (in mm) of control point.

void	Initialize (const ImageAttributes &, double, double, double=-1.0, double=-1.0)
	Initialize free-form transformation.

void	Initialize (const CPImage &, bool=false)
	Initialize transformation from existing vector field.

void	Initialize (const GenericImage< double > &, bool=false)
	Initialize transformation from existing 3D+t vector field.

virtual bool	Inverse (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the inverse of the transformation.

virtual bool	IsActive (int) const
	Whether the control point at given lattice index is active.

virtual bool	IsActive (int, int, int=0, int=0) const
	Whether the control point at given lattice coordinates is active.

virtual void	Jacobian (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t world coordinates.

virtual void	JacobianDetDerivative (double dJ[3], const Matrix &adj, int cp, double x, double y, double z, double t=0, double t0=NaN, bool wrt_world=true, bool use_spacing=true) const

virtual void	JacobianDOFs (TransformationJacobian &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t the transformation parameters.

void	JacobianToWorld (double &, double &) const

void	JacobianToWorld (double &, double &, double &) const

void	JacobianToWorld (Matrix &) const

void	JacobianToWorldOrientation (double &, double &) const
	Reorient 1st order derivatives computed w.r.t 2D lattice coordinates.

void	JacobianToWorldOrientation (double &, double &, double &) const
	Reorient 1st order derivatives computed w.r.t 2D lattice coordinates.

int	KernelRadius () const
	Radius of support region of the used kernel.

int	LatticeToIndex (int, int, int=0, int=0) const
	Get control point index from lattice coordinates.

virtual double	LatticeToTime (double) const
	Transforms temporal lattice coordinate to time (in ms)

virtual void	LatticeToWorld (double &, double &) const
	Transforms lattice coordinates to world coordinates (in mm)

virtual void	LatticeToWorld (double &, double &, double &) const
	Transforms lattice coordinates to world coordinates (in mm)

virtual void	LatticeToWorld (Point &) const
	Transforms lattice coordinates to world coordinates (in mm)

	mirtkPublicAttributeMacro (double, SpeedupFactor)
	Speedup factor for gradient computation.

	mirtkReadOnlyAttributeMacro (enum ExtrapolationMode, ExtrapolationMode)
	Mode used for extrapolation of control point image.

int	NumberOfActiveCPs () const
	Number of active control points.

int	NumberOfCPs () const
	Number of control points.

int	NumberOfPassiveCPs () const
	Number of non-active control points.

void	Put (int, const Vector &)
	Puts values of the parameters at a control point.

void	Put (int, double, double, double)
	Puts values of the parameters at a control point.

void	Put (int, int, int, double, double, double)
	Puts values of the parameters at a control point.

void	Put (int, int, int, int, double, double, double)
	Puts values of the parameters at a control point.

void	PutBoundingBox (double, double, double, double, double, double)
	Puts the spatial bounding box for the free-form deformation (in mm)

void	PutBoundingBox (const Point &, const Point &)
	Puts the temporal bounding box for the free-form deformation (in mm)

void	PutBoundingBox (double, double)
	Puts the temporal bounding box of the free-form deformation (in ms)

void	PutBoundingBox (double, double, double, double, double, double, double, double)
	Puts the spatio-temporal bounding box for the free-form deformation (in mm)

void	PutOrientation (double , double , double *)
	Puts the orientation of the free-form deformation lattice.

void	PutStatus (int, const CPStatus &)
	Puts status of the parameters at a control point.

void	PutStatus (int, int, int, DOFStatus, DOFStatus, DOFStatus)
	Puts status of the parameters at a control point.

void	PutStatus (int, int, int, int, DOFStatus, DOFStatus, DOFStatus)
	Puts status of the parameters at a control point.

void	Subdivide2D ()
	Subdivide lattice in first two dimensions.

void	Subdivide3D ()
	Subdivide lattice in first three dimensions.

void	Subdivide4D ()
	Subdivide lattice in all four dimensions.

int	T () const
	Returns the number of control points in t.

virtual double	TimeToLattice (double) const
	Transforms time (in ms) to temporal lattice coordinate.

virtual void	Transform (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point.

virtual void	WorldToLattice (double &, double &) const
	Transforms world coordinates (in mm) to lattice coordinates.

virtual void	WorldToLattice (double &, double &, double &) const
	Transforms world coordinates (in mm) to lattice coordinates.

virtual void	WorldToLattice (Point &) const
	Transforms world coordinates (in mm) to lattice coordinates.

int	X () const
	Returns the number of control points in x.

int	Y () const
	Returns the number of control points in y.

int	Z () const
	Returns the number of control points in z.

virtual	~FreeFormTransformation ()
	Destructor.

Public Member Functions inherited from mirtk::Transformation
virtual void	Add (const DOFValue *)
	Add change to transformation parameters.

virtual double	Approximate (const ImageAttributes &, const Transformation *, int=1, double=.0)
	Approximate another transformation and return approximation error.

virtual double	Approximate (GenericImage< double > &, int=1, double=.0)

virtual double	ApproximateAsNew (const ImageAttributes &, const Transformation *, int=1, double=.0)
	Approximate another transformation and return approximation error.

virtual double	ApproximateAsNew (GenericImage< double > &, int=1, double=.0)

virtual double	ApproximateAsNew (const double , const double , const double , double , double , double , int, int=1, double=.0)

virtual double	ApproximateAsNew (const double , const double , const double , const double , double , double , double *, int, int=1, double=.0)

virtual void	ApproximateGradient (const ImageAttributes &, const double , const double , const double , double , double=1.0) const

virtual void	ApproximateGradient (const double , const double , const double , const double , const double , const double , int, double *, double=1.0) const

virtual void	ApproximateGradient (const double , const double , const double , const double , const double , const double , const double , int, double , double=1.0) const

virtual void	Displacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point.

virtual void	Displacement (const ImageAttributes &, double , double , double *) const

virtual void	Displacement (GenericImage< double > &, double=NaN, const WorldCoordsImage *=NULL) const
	Calculates the displacement vectors for a whole image domain.

virtual void	Displacement (GenericImage< float > &, double=NaN, const WorldCoordsImage *=NULL) const
	Calculates the displacement vectors for a whole image domain.

virtual void	Displacement (GenericImage< double > &, double, double, const WorldCoordsImage *=NULL) const

virtual void	Displacement (GenericImage< float > &, double, double, const WorldCoordsImage *=NULL) const

double	EvaluateRMSError (const ImageAttributes &, const Transformation *) const
	Evaluates RMS error of transformation compared to another.

double	EvaluateRMSError (const ImageAttributes &, double , double ) const

double	EvaluateRMSError (const ImageAttributes &, double , double , double *) const

double	EvaluateRMSError (const double , const double , const double , double, double , double , double , int no) const
	Evaluates RMS error of transformation compared to displacement field.

double	EvaluateRMSError (const double , const double , const double , const double , double , double , double *, int no) const
	Evaluates RMS error of transformation compared to given displacement field.

virtual double	Get (int) const
	Get value of transformation parameter.

virtual void	Get (DOFValue *) const
	Get values of transformation parameters.

virtual DOFStatus	GetStatus (int) const
	Get status of transformation parameter.

virtual void	GlobalDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the global transformation component only.

virtual void	GlobalInverseDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the inverse of the global transformation only.

virtual double	GlobalJacobian (double, double, double, double=0, double=NaN) const
	Calculates the determinant of the Jacobian of the global transformation w.r.t world coordinates.

virtual bool	HasSameDOFsAs (const Transformation *) const
	Checks whether transformation depends on the same vector of parameters.

virtual bool	Inverse (Point &, double=0, double=NaN) const
	Transforms a single point using the inverse of the transformation.

virtual int	Inverse (PointSet &, double=0, double=NaN) const

virtual bool	InverseDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the inverse of the transformation.

virtual int	InverseDisplacement (const ImageAttributes &, double , double , double *) const

virtual int	InverseDisplacement (GenericImage< double > &, double=NaN, const WorldCoordsImage *=NULL) const

virtual int	InverseDisplacement (GenericImage< float > &, double=NaN, const WorldCoordsImage *=NULL) const

virtual int	InverseDisplacement (GenericImage< double > &, double, double, const WorldCoordsImage *=NULL) const

virtual int	InverseDisplacement (GenericImage< float > &, double, double, const WorldCoordsImage *=NULL) const

virtual bool	IsIdentity () const
	Checks whether the transformation is an identity mapping.

virtual double	Jacobian (double, double, double, double=0, double=NaN) const
	Calculates the determinant of the Jacobian of the transformation w.r.t world coordinates.

virtual void	LocalDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the local transformation component only.

virtual bool	LocalInverse (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the inverse of the local transformation only.

virtual bool	LocalInverseDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the inverse of the local transformation only.

virtual double	LocalJacobian (double, double, double, double=0, double=NaN) const
	Calculates the determinant of the Jacobian of the local transformation w.r.t world coordinates.

int	NumberOfActiveDOFs () const
	Get number of active transformation parameters.

virtual int	NumberOfDOFs () const
	Get number of transformation parameters.

int	NumberOfPassiveDOFs () const
	Get number of passive transformation parameters.

void	ParametricGradient (const GenericImage< double > , double , const WorldCoordsImage *, double=NaN, double=1) const

void	ParametricGradient (const GenericImage< double > , double , double=NaN, double=1) const

virtual void	ParametricGradient (const GenericImage< double > *, int, double , const WorldCoordsImage , const WorldCoordsImage , const double *=NULL, double=1) const

void	ParametricGradient (const GenericImage< double > *, int, double , const WorldCoordsImage , const double =NULL, double=1) const

void	ParametricGradient (const GenericImage< double > *, int, double , const double *=NULL, double=1) const

void	Print (Indent=0) const
	Prints information about the transformation.

virtual void	Put (int, double)
	Put value of transformation parameter.

virtual void	Put (const DOFValue *)
	Put values of transformation parameters.

virtual void	PutStatus (int, DOFStatus)
	Put status of transformation parameter.

virtual void	Read (const char *)
	Reads a transformation from a file.

virtual Cifstream &	Read (Cifstream &)
	Reads a transformation from a file stream.

virtual bool	RequiresCachingOfDisplacements () const

virtual void	Reset ()
	Reset transformation.

virtual void	Transform (Point &, double=0, double=NaN) const
	Transforms a single point.

virtual void	Transform (PointSet &, double=0, double=NaN) const
	Transforms a set of points.

virtual void	Transform (int, double , double , double *, double=0, double=NaN) const
	Transforms a set of points.

virtual void	Transform (int, double , double , double , const double , double=NaN) const
	Transforms a set of points.

virtual void	Transform (WorldCoordsImage &, double=NaN) const
	Transforms world coordinates of image voxels.

virtual TransformationType	TypeOfClass () const
	Returns type ID of the instantiated transformation class.

virtual double	Update (const DOFValue *)
	Update transformation parameters given parametric gradient.

virtual void	Verify ()

virtual void	Write (const char *) const
	Writes a transformation to a file.

virtual Cofstream &	Write (Cofstream &) const
	Writes a transformation to a file stream.

virtual	~Transformation ()
	Default destructor.

Public Member Functions inherited from mirtk::Observable
void	AddObserver (Observer &)
	Add observer.

void	Broadcast (Event, const void *=NULL)
	Broadcast event to observers.

void	ClearObservers ()
	Delete all observers.

void	DeleteObserver (Observer &)
	Delete observer.

void	NotifyObservers (Event, const void *=NULL)
	Notify all observers about given event if this object has changed.

int	NumberOfObservers () const
	Number of current observers.

virtual	~Observable ()
	Destructor.

Public Member Functions inherited from mirtk::Object
virtual const char *	NameOfClass () const =0
	Get name of class, which this object is an instance of.

bool	Parameter (const ParameterList &)
	Set parameters from name/value pairs.

virtual	~Object ()
	Destructor.

Protected Member Functions
	mirtkPublicAttributeMacro (ParametricGradientType, ParametricGradientCalculation)
	Whether to compute parametric gradient using cubic B-spline convolution.

Protected Member Functions inherited from mirtk::FreeFormTransformation3D
	FreeFormTransformation3D (CPInterpolator &, CPInterpolator *=NULL)
	Default constructor.

	FreeFormTransformation3D (const FreeFormTransformation3D &, CPInterpolator &, CPInterpolator *=NULL)
	Copy Constructor.

virtual Cifstream &	ReadDOFs (Cifstream &, TransformationType)
	Reads transformation parameters from a file stream.

virtual Cofstream &	WriteDOFs (Cofstream &) const
	Writes transformation parameters to a file stream.

Protected Member Functions inherited from mirtk::FreeFormTransformation
	FreeFormTransformation (CPInterpolator &, CPInterpolator *=NULL)
	Default constructor.

	FreeFormTransformation (const FreeFormTransformation &, CPInterpolator &, CPInterpolator *=NULL)
	Copy constructor.

void	InitializeCPs (const ImageAttributes &, bool=true)
	Initialize control points.

void	InitializeCPs (const FreeFormTransformation &, bool=true)
	Copy control points from other transformation.

void	InitializeInterpolator ()
	Initialize interpolator of control points.

void	InitializeStatus ()
	Initialize status of control points.

Cofstream &	WriteCPs (Cofstream &) const
	Writes the control point and status information to a file stream.

Protected Member Functions inherited from mirtk::Transformation
void	InitializeDOFs (int)
	Initialize transformation parameters.

void	InitializeDOFs (const Transformation &, int=-1)
	Copy transformation parameters (DoFs) and their status.

	Transformation (int=0)
	Default constructor.

	Transformation (const Transformation &)
	Copy constructor.

	Transformation (const Transformation &, int)
	Copy constructor.

Protected Member Functions inherited from mirtk::Observable
	Observable ()
	Default constructor.

	Observable (const Observable &)
	Copy constructor.

Observable &	operator= (const Observable &)
	Assignment operator.

Protected Member Functions inherited from mirtk::Object
template<typename... Args>
void	Throw (ErrorType err, const char *func, Args... args) const

Protected Attributes
Interpolator	_FFD
	Interpolates control point values at arbitrary lattice locations.

Interpolator2D	_FFD2D

Protected Attributes inherited from mirtk::FreeFormTransformation
const ImageAttributes &	_attr
	Control point lattice attributes.

CPInterpolator *	_CPFunc

CPImage	_CPImage

CPStatus ****	_CPStatus

CPExtrapolator *	_CPValue
	Infinite discrete representation of free-form transformation coefficients.

const double &	_dt
	Read-only reference to _dt attribute of _CPImage.

const double &	_dx
	Read-only reference to _dx attribute of _CPImage.

const double &	_dy
	Read-only reference to _dy attribute of _CPImage.

const double &	_dz
	Read-only reference to _dz attribute of _CPImage.

const Matrix &	_matL2W
	Read-only reference to _matI2W of _CPImage.

const Matrix &	_matW2L
	Read-only reference to _matW2I of _CPImage.

const int &	_t
	Read-only reference to _t attribute of _CPImage.

const int &	_x
	Read-only reference to _x attribute of _CPImage.

const int &	_y
	Read-only reference to _y attribute of _CPImage.

const int &	_z
	Read-only reference to _z attribute of _CPImage.

Protected Attributes inherited from mirtk::Transformation
int	_NumberOfDOFs
	Number of transformation parameters.

DOFValue *	_Param
	Value of each transformation parameter.

DOFStatus *	_Status
	Status of each transformation parameter (Active or Passive)

Additional Inherited Members
Static Public Member Functions inherited from mirtk::FreeFormTransformation3D
static ImageAttributes	DefaultAttributes (double, double, double, double, double, double, double, double, double, const double , const double , const double *)
	Default attributes of free-form transformation lattice.

Static Public Member Functions inherited from mirtk::FreeFormTransformation
static double	Bending3D (const Matrix [3])
	Calculates the bending of the transformation given the 2nd order derivatives.

static ImageAttributes	DefaultAttributes (const ImageAttributes &attr, double dx=-1.0, double dy=-1.0, double dz=-1.0, double dt=-1.0)

static ImageAttributes	DefaultAttributes (double, double, double, double, double, double, double, double, double, double, double, double, const double , const double , const double *)
	Default attributes of free-form transformation lattice.

Static Public Member Functions inherited from mirtk::Transformation
static bool	CheckHeader (const char *)
	Whether magic number in header of given file.

static Transformation *	New (TransformationType)

static Transformation *	New (const Transformation *)

static Transformation *	New (const char *)

static TransformationType	TypeOfClass (const char *)
	Returns type ID corresponding to transformations of the named class.

Static Public Member Functions inherited from mirtk::Object
static const char *	NameOfType ()
	Get name of this class type.

Static Protected Member Functions inherited from mirtk::Object
template<typename... Args>
static void	ThrowStatic (ErrorType err, const char cls, const char func, Args... args)

Detailed Description

Class for free-form transformations based on tensor product B-splines.

This class implements 3D free-form transformation using B-splines.

For more details about the implementation see Lee, Wolberg and Shin, IEEE Transactions on Visualization and Computer Graphics, Vol. 3, No. 3, 1997.

Definition at line 41 of file BSplineFreeFormTransformation3D.h.

Member Enumeration Documentation

§ ParametricGradientType

enum mirtk::BSplineFreeFormTransformation3D::ParametricGradientType

Options for parametric gradient calculation.

Enumerator
PG_Default	Default gradient computation.
PG_Analytic	Analytic derivation w.r.t. DoFs.
PG_Convolution	Convolution with cubic B-spline filter.
PG_Approximation	Approximate voxel-wise non-parametric gradient field with cubic B-spline function, also known as "directly manipulated FFD (DMFFD)".

Definition at line 57 of file BSplineFreeFormTransformation3D.h.

Member Function Documentation

§ AddApproximateSplineCoefficients()

void mirtk::BSplineFreeFormTransformation3D::AddApproximateSplineCoefficients	(	const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		int	,
		double *	,
		double	= `1.`,
		bool	= `false`
	)		const

Approximate displacements: This function takes a set of points and a set of displacements and finds !new! parameters such that the resulting transformation approximates the displacements as good as possible. These parameters are added to the given coefficients using specified weight.

§ ApproximateDOFs()

virtual void mirtk::BSplineFreeFormTransformation3D::ApproximateDOFs	(	const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		int
	)

virtual

Approximate displacements: This function takes a set of points and a set of displacements and finds !new! parameters such that the resulting transformation approximates the displacements as good as possible.

Reimplemented from mirtk::Transformation.

Reimplemented in mirtk::BSplineFreeFormTransformationSV, and mirtk::BSplineFreeFormTransformationStatistical.

§ ApproximateDOFsGradient()

virtual void mirtk::BSplineFreeFormTransformation3D::ApproximateDOFsGradient	(	const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		const double *	,
		int	,
		double *	,
		double	= `1.0`
	)		const

virtual

Finds gradient of approximation error: This function takes a set of points and a set of errors. It finds a gradient w.r.t. the transformation parameters which minimizes the L2 norm of the approximation error and adds it to the input gradient with the given weight.

Reimplemented from mirtk::Transformation.

Reimplemented in mirtk::BSplineFreeFormTransformationSV, and mirtk::BSplineFreeFormTransformationStatistical.

§ BendingEnergyGradient()

virtual void mirtk::BSplineFreeFormTransformation3D::BendingEnergyGradient	(	double *	,
		double	= `1`,
		bool	= `false`,
		bool	= `true`,
		bool	= `true`
	)		const

virtual

Approximates and adds the gradient of the bending energy on the control point lattice w.r.t the transformation parameters using the given weight

Reimplemented from mirtk::FreeFormTransformation.

Reimplemented in mirtk::BSplineFreeFormTransformationStatistical.

§ BoundingBox()

virtual void mirtk::BSplineFreeFormTransformation3D::BoundingBox	(	int	,
		double &	,
		double &	,
		double &	,
		double &	,
		double &	,
		double &	,
		double	= `1`
	)		const

virtual

Returns the bounding box for a control point (in mm). The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Implements mirtk::FreeFormTransformation.

§ CanModifyDisplacement()

virtual bool mirtk::BSplineFreeFormTransformation3D::CanModifyDisplacement ( int = -1 ) const

virtual

Whether this transformation implements a more efficient update of a given displacement field given the desired change of a transformation parameter

Reimplemented from mirtk::Transformation.

§ DisplacementAfterDOFChange()

virtual void mirtk::BSplineFreeFormTransformation3D::DisplacementAfterDOFChange	(	int	dof,
		double	dv,
		GenericImage< double > &	dx,
		double	t,
		double	t0 = `-1`,
		const WorldCoordsImage *	i2w = `NULL`
	)		const

virtual

Updates the displacement vectors for a whole image domain

Parameters

[in]	dof	Transformation parameter.
[in]	dv	Change of transformation parameter value.
[in,out]	dx	Displacement field to be updated.
[in]	t	Time point of start point.
[in]	t0	Time point of end point.
[in]	i2w	Pre-computed world coordinates.

Reimplemented from mirtk::Transformation.

§ EvaluateDerivativeOfJacobianWrtDOF() [1/2]

void mirtk::BSplineFreeFormTransformation3D::EvaluateDerivativeOfJacobianWrtDOF	(	Matrix &	dJdp,
		int	dof,
		double	x,
		double	y
	)		const

inline

Calculates the derivative of the Jacobian of the FFD at a point in lattice coordinates w.r.t a transformation parameter

Definition at line 541 of file BSplineFreeFormTransformation3D.h.

§ EvaluateDerivativeOfJacobianWrtDOF() [2/2]

void mirtk::BSplineFreeFormTransformation3D::EvaluateDerivativeOfJacobianWrtDOF	(	Matrix &	dJdp,
		int	dof,
		double	x,
		double	y,
		double	z
	)		const

inline

Calculates the derivative of the Jacobian of the FFD at a point in lattice coordinates w.r.t a transformation parameter

Definition at line 558 of file BSplineFreeFormTransformation3D.h.

§ EvaluateJacobianDetDerivative() [1/4]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianDetDerivative	(	double	dJ[3],
		const Matrix &	adj,
		double	a,
		double	b,
		double	c,
		bool	wrt_world = `true`,
		bool	use_spacing = `true`
	)		const

Calculate derivatives of Jacobian determinant w.r.t. DoFs of control point

Parameters

[out]	dJ	Partial derivatives of Jacobian determinant w.r.t. DoFs of control point.
[in]	adj	Adjugate of Jacobian matrix evaluated at (x, y, z).
[in]	a	Distance from control point along x axis of lattice in lattice units.
[in]	b	Distance from control point along y axis of lattice in lattice units.
[in]	c	Distance from control point along z axis of lattice in lattice units.
[in]	wrt_world	Whether derivatives are computed w.r.t. world coordinate system.
[in]	use_spacing	Whether to use grid spacing when `wrt_world` is `true`.

§ EvaluateJacobianDetDerivative() [2/4]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianDetDerivative	(	double	dJ[3],
		const Matrix &	adj,
		int	a,
		int	b,
		int	c,
		bool	wrt_world = `true`,
		bool	use_spacing = `true`
	)		const

Calculate derivatives of Jacobian determinant w.r.t. DoFs of control point

Parameters

[out]	dJ	Partial derivatives of Jacobian determinant w.r.t. DoFs of control point.
[in]	adj	Adjugate of Jacobian matrix evaluated at (x, y, z).
[in]	a	Distance from control point along x axis of lattice in lattice units.
[in]	b	Distance from control point along y axis of lattice in lattice units.
[in]	c	Distance from control point along z axis of lattice in lattice units.
[in]	wrt_world	Whether derivatives are computed w.r.t. world coordinate system.
[in]	use_spacing	Whether to use grid spacing when `wrt_world` is `true`.

§ EvaluateJacobianDetDerivative() [3/4]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianDetDerivative	(	double	dJ[3],
		const Matrix &	adj,
		int	i,
		int	j,
		int	k,
		double	x,
		double	y,
		double	z,
		bool	wrt_world = `true`,
		bool	use_spacing = `true`
	)		const

inline

Calculate derivatives of Jacobian determinant w.r.t. DoFs of control point

Parameters

[out]	dJ	Partial derivatives of Jacobian determinant w.r.t. DoFs of control point.
[in]	adj	Adjugate of Jacobian matrix evaluated at (x, y, z).
[in]	i	Index of control point along x axis of lattice.
[in]	j	Index of control point along y axis of lattice.
[in]	k	Index of control point along z axis of lattice.
[in]	x	Point coordinate along x axis of lattice in lattice units.
[in]	y	Point coordinate along y axis of lattice in lattice units.
[in]	z	Point coordinate along z axis of lattice in lattice units.
[in]	wrt_world	Whether derivatives are computed w.r.t. world coordinate system.
[in]	use_spacing	Whether to use grid spacing when `wrt_world` is `true`.

Definition at line 653 of file BSplineFreeFormTransformation3D.h.

§ EvaluateJacobianDetDerivative() [4/4]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianDetDerivative	(	double	dJ[3],
		const Matrix &	adj,
		int	cp,
		double	x,
		double	y,
		double	z,
		bool	wrt_world = `true`,
		bool	use_spacing = `true`
	)		const

inline

Calculate derivatives of Jacobian determinant w.r.t. DoFs of control point

Parameters

[out]	dJ	Partial derivatives of Jacobian determinant w.r.t. DoFs of control point.
[in]	adj	Adjugate of Jacobian matrix evaluated at (x, y, z).
[in]	cp	Linear index of control point.
[in]	x	Point coordinate along x axis of lattice in lattice units.
[in]	y	Point coordinate along y axis of lattice in lattice units.
[in]	z	Point coordinate along z axis of lattice in lattice units.
[in]	wrt_world	Whether derivatives are computed w.r.t. world coordinate system.
[in]	use_spacing	Whether to use grid spacing when `wrt_world` is `true`.

Definition at line 662 of file BSplineFreeFormTransformation3D.h.

§ EvaluateJacobianDOFs() [1/3]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianDOFs	(	double	jac[3],
		int	i,
		int	j,
		double	x,
		double	y
	)		const

inline

Calculates the Jacobian of the FFD at a point in lattice coordinates w.r.t the control point with lattice coordinates (i, j)

Definition at line 516 of file BSplineFreeFormTransformation3D.h.

§ EvaluateJacobianDOFs() [2/3]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianDOFs	(	double	jac[3],
		int	i,
		int	j,
		int	k,
		double	x,
		double	y,
		double	z
	)		const

inline

Calculates the Jacobian of the FFD at a point in lattice coordinates w.r.t the control point with lattice coordinates (i, j, k)

Definition at line 523 of file BSplineFreeFormTransformation3D.h.

§ EvaluateJacobianDOFs() [3/3]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianDOFs	(	double	jac[3],
		int	i,
		int	j,
		int	k,
		int	,
		double	x,
		double	y,
		double	z,
		double
	)		const

inline

Calculates the Jacobian of the FFD at a point in lattice coordinates w.r.t the control point with lattice coordinates (i, j, k)

Note: The temporal coordinates are required by the templated integration methods. These arguments are ignored by this function.

Definition at line 533 of file BSplineFreeFormTransformation3D.h.

§ EvaluateJacobianWorld() [1/2]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianWorld	(	Matrix &	jac,
		double	x,
		double	y
	)		const

inline

Calculates the Jacobian of the FFD at a point in lattice coordinates and converts the resulting Jacobian to derivatives w.r.t world coordinates

Definition at line 496 of file BSplineFreeFormTransformation3D.h.

§ EvaluateJacobianWorld() [2/2]

void mirtk::BSplineFreeFormTransformation3D::EvaluateJacobianWorld	(	Matrix &	jac,
		double	x,
		double	y,
		double	z
	)		const

inline

Calculates the Jacobian of the FFD at a point in lattice coordinates and converts the resulting Jacobian to derivatives w.r.t world coordinates

Definition at line 506 of file BSplineFreeFormTransformation3D.h.

§ FFDJacobianDetDerivative()

void mirtk::BSplineFreeFormTransformation3D::FFDJacobianDetDerivative	(	double	dJ[3],
		const Matrix &	adj,
		int	cp,
		double	x,
		double	y,
		double	z,
		double	= `0`,
		double	= `NaN`,
		bool	wrt_world = `true`,
		bool	use_spacing = `true`
	)		const

inlinevirtual

Calculates derivatives of the Jacobian determinant of spline function w.r.t. DoFs of a control point

This function is identical to JacobianDetDerivative when the DoFs of the control points are displacements. When the DoFs are velocities, however, this function computes the derivatives of the Jacobian determinant of the velocity field instead.

Parameters

[out]	dJ	Partial derivatives of Jacobian determinant at (x, y, z) w.r.t. DoFs of control point.
[in]	cp	Index of control point w.r.t. whose DoFs the derivatives are computed.
[in]	x	World coordinate along x axis at which to evaluate derivatives.
[in]	y	World coordinate along y axis at which to evaluate derivatives.
[in]	z	World coordinate along z axis at which to evaluate derivatives.
[in]	adj	Adjugate of Jacobian matrix evaluated at (x, y, z).
[in]	wrt_world	Whether derivatives are computed w.r.t. world coordinate system.
[in]	use_spacing	Whether to use grid spacing when `wrt_world` is `true`.

Reimplemented from mirtk::FreeFormTransformation.

Definition at line 673 of file BSplineFreeFormTransformation3D.h.

§ Interpolate()

virtual void mirtk::BSplineFreeFormTransformation3D::Interpolate	(	const double *	,
		const double *	,
		const double *	= `NULL`
	)

virtual

Interpolates displacements: This function takes a set of displacements defined at the control points and finds a FFD which interpolates these displacements.

Implements mirtk::FreeFormTransformation.

Reimplemented in mirtk::BSplineFreeFormTransformationSV, and mirtk::BSplineFreeFormTransformationStatistical.

§ ParametricGradient()

virtual void mirtk::BSplineFreeFormTransformation3D::ParametricGradient	(	const GenericImage< double > *	,
		double *	,
		const WorldCoordsImage *	,
		const WorldCoordsImage *	,
		double	= `NaN`,
		double	= `1`
	)		const

virtual

to a gradient w.r.t the parameters of this transformation

Applies the chain rule to convert spatial non-parametric gradient

Reimplemented from mirtk::FreeFormTransformation3D.

Reimplemented in mirtk::BSplineFreeFormTransformationSV, and mirtk::BSplineFreeFormTransformationStatistical.

Member Data Documentation

§ _FFD2D

Interpolator2D mirtk::BSplineFreeFormTransformation3D::_FFD2D

protected

Interpolates control point values at arbitrary 2D lattice locations

Todo:: Remove once BSplineFreeFormTransformation2D is implemented.

Definition at line 80 of file BSplineFreeFormTransformation3D.h.

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

BSplineFreeFormTransformation3D.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

§ ParametricGradientType

Member Function Documentation

§ AddApproximateSplineCoefficients()

§ ApproximateDOFs()

§ ApproximateDOFsGradient()

§ BendingEnergyGradient()

§ BoundingBox()

§ CanModifyDisplacement()

§ DisplacementAfterDOFChange()

§ EvaluateDerivativeOfJacobianWrtDOF() [1/2]

§ EvaluateDerivativeOfJacobianWrtDOF() [2/2]

§ EvaluateJacobianDetDerivative() [1/4]

§ EvaluateJacobianDetDerivative() [2/4]

§ EvaluateJacobianDetDerivative() [3/4]

§ EvaluateJacobianDetDerivative() [4/4]

§ EvaluateJacobianDOFs() [1/3]

§ EvaluateJacobianDOFs() [2/3]

§ EvaluateJacobianDOFs() [3/3]

§ EvaluateJacobianWorld() [1/2]

§ EvaluateJacobianWorld() [2/2]

§ FFDJacobianDetDerivative()

§ Interpolate()

§ ParametricGradient()

Member Data Documentation

§ _FFD2D