INTERP_KERNEL.TetraAffineTransform Class Reference

Class representing an affine transformation x -> Ax + b that transforms a given tetrahedron into the unit tetrahedron. More...

#include <TetraAffineTransform.hxx>

Public Member Functions
	TetraAffineTransform (const double **pts)
	PUBLIC INTERFACE METHODS //////////////.
void	apply (double *destPt, const double *srcPt) const
	Calculates the transform of point srcPt and stores the result in destPt.
void	reverseApply (double *destPt, const double *srcPt) const
	Calculates the reverse transform of point srcPt and stores the result in destPt.
double	determinant () const
	Returns the determinant of the linear part A of the transform.
void	dump () const
	Outputs to std.cout the matrix A and the vector b of the transform Ax + b.
Private Member Functions
void	invertLinearTransform ()
	PRIVATE METHODS //////////////.
void	calculateDeterminant ()
	Updates the member _determinant of the matrix A of the transformation.
void	factorizeLU (double *lu, int *idx) const
	Auxiliary methods for inverse calculation ///.
void	forwardSubstitution (double *x, const double *lu, const double *b, const int *idx) const
	Solves the system Lx = b, where L is lower unit-triangular (ones on the diagonal).
void	backwardSubstitution (double *x, const double *lu, const double *b, const int *idx) const
	Solves the system Ux = b, where U is upper-triangular.
Private Attributes
double	_linear_transform [9]
	3x3 matrix A in affine transform x -> Ax + b
double	_translation [3]
	3x1 vector b in affine transform x -> Ax + b
double	_determinant
	The determinant of the matrix A is calculated at the construction of the object and cached.
double	_back_linear_transform [9]
	3x3 matrix AT is transposed A matrix used for y -> ATy - c transformation
double	_back_translation [3]
	3x1 vector c in affine transform y -> ATy - c

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Detailed Description

Class representing an affine transformation x -> Ax + b that transforms a given tetrahedron into the unit tetrahedron.

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Constructor & Destructor Documentation

INTERP_KERNEL.TetraAffineTransform::TetraAffineTransform

(

const double **

pts

)

PUBLIC INTERFACE METHODS //////////////.

Constructor Create the TetraAffineTransform object from the tetrahedron with corners specified in pts. If the tetrahedron is degenerate or almost degenerate, construction succeeds, but the determinant of the transform is set to 0.

Parameters:

pts

a 4x3 matrix containing 4 points (pts[0], ..., pts[3]) of 3 coordinates each

References INTERP_KERNEL.TetraAffineTransform._back_linear_transform, INTERP_KERNEL.TetraAffineTransform._back_translation, INTERP_KERNEL.TetraAffineTransform._determinant, INTERP_KERNEL.TetraAffineTransform._linear_transform, INTERP_KERNEL.TetraAffineTransform._translation, INTERP_KERNEL.TetraAffineTransform.apply(), INTERP_KERNEL.TetraAffineTransform.calculateDeterminant(), INTERP_KERNEL.epsilonEqual(), INTERP_KERNEL.TetraAffineTransform.invertLinearTransform(), LOG, and INTERP_KERNEL.vToStr().

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Member Function Documentation

void INTERP_KERNEL.TetraAffineTransform::apply	(	double *	destPt,
		const double *	srcPt
	)			const

Calculates the transform of point srcPt and stores the result in destPt.

If destPt == srcPt, then srcPt is overwritten safely.

Parameters:

	destPt	double[3] in which to store the transformed point
	srcPt	double[3] containing coordinates of points to be transformed

References INTERP_KERNEL.TetraAffineTransform._linear_transform, INTERP_KERNEL.TetraAffineTransform._translation, and LOG.

void INTERP_KERNEL.TetraAffineTransform::reverseApply	(	double *	destPt,
		const double *	srcPt
	)			const

Calculates the reverse transform of point srcPt and stores the result in destPt.

If destPt == srcPt, then srcPt is overwritten safely.

Parameters:

	destPt	double[3] in which to store the transformed point
	srcPt	double[3] containing coordinates of points to be transformed

References INTERP_KERNEL.TetraAffineTransform._back_linear_transform, INTERP_KERNEL.TetraAffineTransform._back_translation, and LOG.

double INTERP_KERNEL.TetraAffineTransform::determinant

(

)

const

Returns the determinant of the linear part A of the transform.

Returns:

determinant of the transform

References INTERP_KERNEL.TetraAffineTransform._determinant.

void INTERP_KERNEL.TetraAffineTransform::dump

(

)

const

Outputs to std.cout the matrix A and the vector b of the transform Ax + b.

References INTERP_KERNEL.TetraAffineTransform._linear_transform, and INTERP_KERNEL.TetraAffineTransform._translation.

void INTERP_KERNEL.TetraAffineTransform::invertLinearTransform

(

)

[private]

PRIVATE METHODS //////////////.

Calculates the inverse of the matrix A, stored in _linear_transform by LU-factorization and substitution

References INTERP_KERNEL.TetraAffineTransform._linear_transform, testGaussLocalization.b, INTERP_KERNEL.TetraAffineTransform.backwardSubstitution(), INTERP_KERNEL.TetraAffineTransform.factorizeLU(), INTERP_KERNEL.TetraAffineTransform.forwardSubstitution(), and LOG.

void INTERP_KERNEL.TetraAffineTransform::calculateDeterminant

(

)

[private]

Updates the member _determinant of the matrix A of the transformation.

References INTERP_KERNEL.TetraAffineTransform._determinant, and INTERP_KERNEL.TetraAffineTransform._linear_transform.

void INTERP_KERNEL.TetraAffineTransform::factorizeLU	(	double *	lu,
		int *	idx
	)			const [private]

Auxiliary methods for inverse calculation ///.

Calculates the LU-factorization of the matrix A (_linear_transform) and stores it in lu. Since partial pivoting is used, there are row swaps. This is represented by the index permutation vector idx : to access element (i,j) of lu, use lu[3*idx[i] + j]

Parameters:

	lu	double[9] in which to store LU-factorization
	idx	int[3] in which to store row permutation vector

References TestMedCorba7.s.

void INTERP_KERNEL.TetraAffineTransform::forwardSubstitution	(	double *	x,
		const double *	lu,
		const double *	b,
		const int *	idx
	)			const [private]

Solves the system Lx = b, where L is lower unit-triangular (ones on the diagonal).

Parameters:

	x	double[3] in which the solution is stored
	lu	double[9] containing the LU-factorization
	b	double[3] containing the right-hand side
	idx	int[3] containing the permutation vector associated with lu

void INTERP_KERNEL.TetraAffineTransform::backwardSubstitution	(	double *	x,
		const double *	lu,
		const double *	b,
		const int *	idx
	)			const [private]

Solves the system Ux = b, where U is upper-triangular.

Parameters:

	x	double[3] in which the solution is stored
	lu	double[9] containing the LU-factorization
	b	double[3] containing the right-hand side
	idx	int[3] containing the permutation vector associated with lu

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Field Documentation

double INTERP_KERNEL.TetraAffineTransform._linear_transform[9] [private]

3x3 matrix A in affine transform x -> Ax + b

double INTERP_KERNEL.TetraAffineTransform._translation[3] [private]

3x1 vector b in affine transform x -> Ax + b

double INTERP_KERNEL.TetraAffineTransform._determinant [private]

The determinant of the matrix A is calculated at the construction of the object and cached.

double INTERP_KERNEL.TetraAffineTransform._back_linear_transform[9] [private]

3x3 matrix AT is transposed A matrix used for y -> ATy - c transformation

double INTERP_KERNEL.TetraAffineTransform._back_translation[3] [private]

3x1 vector c in affine transform y -> ATy - c