#include <Affine.h>

Collaboration diagram for Isis::Affine:

Public Types
typedef TNT::Array2D< double >	AMatrix

Public Member Functions
	Affine ()
	Constructs an Affine transform.

	Affine (const AMatrix &a)
	Create Affine transform from matrix.

	~Affine ()
	Destroys the Affine object.

void	Solve (const double x[], const double y[], const double xp[], const double yp[], int n)
	Given a set of coordinate pairs (n >= 3), compute the affine transform that best fits the points.

void	Identity ()
	Set the forward and inverse affine transform to the identity.

void	Translate (double tx, double ty)
	Apply a translation to the current affine transform.

void	Rotate (double rot)
	Apply a translation to the current affine transform.

void	Scale (double scaleFactor)
	Apply a scale to the current affine transform.

void	Compute (double x, double y)
	Compute (xp,yp) given (x,y).

double	xp () const
	Returns the computed x'.

double	yp () const
	Returns the computed y'.

void	ComputeInverse (double xp, double yp)
	Compute (x,y) given (xp,yp).

double	x () const
	Returns the computed x.

double	y () const
	Returns the computed y.

std::vector< double >	Coefficients (int var)
	Return the affine coeffients for the entered variable (1 or 2).

std::vector< double >	InverseCoefficients (int var)
	Return the inverse affine coeffients for the entered variable (1 or 2).

AMatrix	Forward () const
	Returns the forward Affine matrix.

AMatrix	Inverse () const
	Returns the inverse Affine matrix.

Static Public Member Functions
static AMatrix	getIdentity ()
	Return an Affine identity matrix.

Private Member Functions
void	checkDims (const AMatrix &am) const
	Checks affine matrix to ensure it is a 3x3 standard form transform.

AMatrix	invert (const AMatrix &a) const
	Compute the inverse of a matrix.

Private Attributes
AMatrix	p_matrix
	Affine forward matrix.

AMatrix	p_invmat
	Affine inverse matrix.

double	p_x
	x value of the (x,y) coordinate

double	p_y
	y value of the (x,y) coordinate

double	p_xp
	x' value of the (x',y') coordinate

double	p_yp
	y' value of the (x',y') coordinate

Detailed Description

Affine basis function.

An affine transform in two-dimensional space is defined as

x' = Ax + By + C

y' = Dx + Ey + F

This routine allows the programmer to define three or more mappings from (x,y) to (x',y') and will solve for A,B,C,D,E,F.

If the above coefficients can be computed then the inverse of the affine transform exists and will be computed such that

x = A'x' + B'y' + C'

y = D'x' + E'y' + F'

Alternatively (or in combination), translations and rotations can be applied to create a transform.

See Also: http://www.gnome.org/~mathieu/libart/libart-affine-transformation-matrices.html

Author: 2005-03-24 Jeff Anderson

Todo:

Allow the programmer to apply scale and shear.

Write multiplaction method (operator*) for Affine * Affine.

History:

2006-08-03 Tracie Sucharski, Added Scale method

2007-07-12 Debbie A. Cook, Added methods Coefficients and InverseCoefficients

2008-06-18 Christopher Austin - Added documentation

2008-10-29 Steven Lambright - Corrected usage of std::vector, problem pointed out by "novas0x2a" (Support Forum Member)

2009-07-24 Kris Becker Introduced the AMatrix typedef; added new constructor that accepts an AMatrix; added static method to return an Affine identity matrix; added methods to retrieve forward and inverse AMatrixs; added new method that inverts the matrix.

2010-11-18 Kris Becker Fixed bug in inverse representation when scaling is applied to the current transform.

Definition at line 79 of file Affine.h.

Constructor & Destructor Documentation

Isis::Affine::Affine ( )

Constructs an Affine transform.

The default transform is the identity.

Definition at line 43 of file Affine.cpp.

Isis::Affine::Affine ( const AMatrix & a )

Create Affine transform from matrix.

This constructor creates the affine transform from a forward matrix. The input matrix is checked for the proper dimensions (3x3) and is then inverted to complete the inverse functionality.

The input matrix must be invertable or an exception will be thrown!

Parameters

a	Forward affine matrix

Definition at line 59 of file Affine.cpp.

Isis::Affine::~Affine ( )

Destroys the Affine object.

Definition at line 67 of file Affine.cpp.

Member Function Documentation

void Isis::Affine::checkDims ( const AMatrix & am ) const

private

Checks affine matrix to ensure it is a 3x3 standard form transform.

Parameters

am	Affine matrix to validate

Definition at line 260 of file Affine.cpp.

References _FILEINFO_.

vector< double > Isis::Affine::Coefficients ( int var )

Return the affine coeffients for the entered variable (1 or 2).

The coefficients are returned in a 3-dimensional vector

Parameters

var	The coefficient vector index (1 or 2)

Definition at line 231 of file Affine.cpp.

Referenced by Isis::CameraFocalPlaneMap::CameraFocalPlaneMap(), and Isis::LoCameraFiducialMap::CreateTrans().

void Isis::Affine::Compute	(	double	x,
		double	y
	)

Compute (xp,yp) given (x,y).

Use the methods xp() and yp() to obtain the results.

Parameters

x	The transformation x factor
y	The transformation y factor

Definition at line 204 of file Affine.cpp.

Referenced by Isis::Chip::Extract().

void Isis::Affine::ComputeInverse	(	double	xp,
		double	yp
	)

Compute (x,y) given (xp,yp).

Use the methods x() and y() to obtain the results.

Parameters

xp	The inverse transformation xp factor
yp	The inverse transformation yp factor

Definition at line 218 of file Affine.cpp.

AMatrix Isis::Affine::Forward ( ) const

inline

Returns the forward Affine matrix.

Definition at line 120 of file Affine.h.

References p_matrix.

Referenced by Isis::Chip::Extract().

Affine::AMatrix Isis::Affine::getIdentity ( )

static

Return an Affine identity matrix.

Returns: Affine::AMatrix The identity matrix

Definition at line 74 of file Affine.cpp.

Referenced by Isis::AffineRadio::clone(), Isis::Threshold::hasConverged(), Isis::AffineRadio::operator+=(), and Isis::AffineRadio::Translate().

void Isis::Affine::Identity ( )

Set the forward and inverse affine transform to the identity.

That is, xp = x and yp = y for all (x,y).

Definition at line 86 of file Affine.cpp.

AMatrix Isis::Affine::Inverse ( ) const

inline

Returns the inverse Affine matrix.

Definition at line 124 of file Affine.h.

References p_invmat.

vector< double > Isis::Affine::InverseCoefficients ( int var )

Return the inverse affine coeffients for the entered variable (1 or 2).

The coefficients are returned in a 3-dimensional vector

Parameters

var	The inverse coefficient vector index

Definition at line 246 of file Affine.cpp.

Referenced by Isis::CameraFocalPlaneMap::CameraFocalPlaneMap(), and Isis::LoCameraFiducialMap::CreateTrans().

Affine::AMatrix Isis::Affine::invert ( const AMatrix & a ) const

private

Compute the inverse of a matrix.

This method will compute the inverse of an affine matrix for purposes of forward and inverse Affine computations.

Parameters

a	Matrix to invert

Returns: Affine::AMatrix The inverted matrix

Definition at line 280 of file Affine.cpp.

References _FILEINFO_.

void Isis::Affine::Rotate ( double angle )

Apply a translation to the current affine transform.

Parameters

angle degrees of counterclockwise rotation

Definition at line 164 of file Affine.cpp.

References Isis::PI().

void Isis::Affine::Scale ( double scaleFactor )

Apply a scale to the current affine transform.

Parameters

scaleFactor The scale factor

Definition at line 187 of file Affine.cpp.

void Isis::Affine::Solve	(	const double	x[],
		const double	y[],
		const double	xp[],
		const double	yp[],
		int	n
	)

Given a set of coordinate pairs (n >= 3), compute the affine transform that best fits the points.

If given exactly three coordinates that are not colinear, the fit will be guarenteed to be exact through the points.

Parameters

x	The transformation x coordinates
y	The transformation y coordinates
xp	The transformation xp coordinates
yp	The transformation yp coordinates
n	The number of coordiante pairs

Exceptions

Isis::iException::Math - Affine transform not invertible

Definition at line 105 of file Affine.cpp.

References Isis::LeastSquares::AddKnown(), Isis::BasisFunction::Coefficient(), and Isis::LeastSquares::Solve().

Referenced by Isis::LoCameraFiducialMap::CreateTrans().

void Isis::Affine::Translate	(	double	tx,
		double	ty
	)

Apply a translation to the current affine transform.

Parameters

tx	translatation to add to x'
ty	translation to add to y'

Definition at line 147 of file Affine.cpp.

double Isis::Affine::x ( ) const

inline

Returns the computed x.

Definition at line 108 of file Affine.h.

References p_x.

double Isis::Affine::xp ( ) const

inline

Returns the computed x'.

Definition at line 96 of file Affine.h.

References p_xp.

Referenced by Isis::Chip::Extract().

double Isis::Affine::y ( ) const

inline

Returns the computed y.

Definition at line 113 of file Affine.h.

References p_y.

double Isis::Affine::yp ( ) const

inline

Returns the computed y'.

Definition at line 101 of file Affine.h.

References p_yp.

Referenced by Isis::Chip::Extract().

Member Data Documentation

AMatrix Isis::Affine::p_invmat

private

Affine inverse matrix.

Definition at line 130 of file Affine.h.

Referenced by Inverse().

AMatrix Isis::Affine::p_matrix

private

Affine forward matrix.

Definition at line 129 of file Affine.h.

Referenced by Forward().

double Isis::Affine::p_x

private

x value of the (x,y) coordinate

Definition at line 132 of file Affine.h.

Referenced by x().

double Isis::Affine::p_xp

private

x' value of the (x',y') coordinate

Definition at line 134 of file Affine.h.

Referenced by xp().

double Isis::Affine::p_y

private

y value of the (x,y) coordinate

Definition at line 133 of file Affine.h.

Referenced by y().

double Isis::Affine::p_yp

private

y' value of the (x',y') coordinate

Definition at line 135 of file Affine.h.

Referenced by yp().

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

src/base/objs/Affine/Affine.h
src/base/objs/Affine/Affine.cpp

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation